Evolving Asynchronous Adaptive Systems for an ... - CiteSeerX

Evolving Asynchronous Adaptive Systems for an Exploration of Aesthetic Pattern Formation Katie Bentley EASy MSc Thesis COGs GRC, University of Sussex August 29, 2002 Abstract This paper is an exploration of an interdisciplinary nature. Through studies in fine art, pattern formation in nature, on cellular, organism and ethological levels, and artificial life; a mechanism for a generic process of design is presented within the context of aesthetic pattern formation. Evolved random asynchronous updating schemes implemented in cellular automata and agent swarm systems with pheromonal signalling were compared favourably to deterministic and hand designed alternatives and the curious adaptive properties of the resulting evolved patterns were investigated. Aesthetic production should not be considered in isolation from aesthetic sense and thus reactions and opinions when the work was exhibited at the ICA London and Blip sci-art discussion group are included. Copious future extensions are outlined for this exciting new facet of artificial life.

Acknowledgements Thanks to Ezequiel Di Paolo for constant, wise support and inspiration.

Contents 1 Introduction

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2 Background 2.1 Pattern and Structure Formation in Nature . . . . . . . . . 2.1.1 Biochemical models . . . . . . . . . . . . . . . . . . 2.1.2 Agent based models of structural pattern formation 2.1.3 Reticulation . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Artistic Process . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Painting Updating schemes . . . . . . . . . . . . . . 2.2.2 Artistic Rule Sets . . . . . . . . . . . . . . . . . . . . 2.2.3 Evolution of Style . . . . . . . . . . . . . . . . . . . 2.3 Artificial Art . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 The Models Explained 3.1 Cellular Automata . . . . . 3.2 Agent Design . . . . . . . . 3.2.1 Basic . . . . . . . . . 3.2.2 Pheromonal Agents

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4 Preliminary Experiments 4.1 Synchronous Cellular Automata . . . . . . 4.1.1 Game of Life . . . . . . . . . . . . 4.1.2 Blanket . . . . . . . . . . . . . . . 4.2 Asynchronous Set Cellular Automata . . . 4.2.1 Game of Life . . . . . . . . . . . . 4.2.2 Cow Print . . . . . . . . . . . . . . 4.3 Asynchronous Random Cellular Automata 4.3.1 Game of Life . . . . . . . . . . . . 4.4 Basic Agent Design . . . . . . . . . . . . . 4.4.1 Diagonal reticulation . . . . . . . . 4.5 Pheromonal Agent Design . . . . . . . . . 4.5.1 Neurons . . . . . . . . . . . . . . .

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5 Genetic Algorithm 5.1 CA Genotypes . 5.2 Agent Genotypes 5.3 Evolution . . . . 5.4 Fitness Function

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6 Evolutionary Experiments 6.1 Synchronous Cellular Automata . . . . . . 6.1.1 Islands . . . . . . . . . . . . . . . . 6.1.2 Mosaic . . . . . . . . . . . . . . . . 6.2 Asynchronous Set Cellular Automata . . . 6.2.1 Double Mosaic . . . . . . . . . . . 6.2.2 Spots . . . . . . . . . . . . . . . . 6.2.3 Red Tiles . . . . . . . . . . . . . . 6.3 Asynchronous Random Cellular Automata 6.3.1 Yellow Tiles . . . . . . . . . . . . . 6.3.2 Camouflage . . . . . . . . . . . . . 6.4 Pheromonal Agent Design . . . . . . . . 6.4.1 Spirals . . . . . . . . . . . . . . . . 6.4.2 Coloured Spirals . . . . . . . . . .

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CONTENTS

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7 The Sense of Beauty: Reactions, Opinions and Aesthetics

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8 Conclusions and Future Work

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References

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A Appendix: Reaction Diffusion 49 A.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 A.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 B Colour Plates

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Chapter 1

Introduction “When we stand before great churches, temples, pyramids, and other works of architecture built hundreds, if not thousands of years ago, our minds are filled with awe and admiration. Yet there have been architects millions of years before that. Their work, it is true, owes its existence not to the inspired genius of great artists, but to the unconscious, unremitting activity of the force of life itself.” (Frisch, 1975) Pp.2. There remains a great deal of mystery surrounding the ‘design’ processes involved in the generation of aesthetic and functional forms, as they occur in nature and as generated by humans. Many would still like to believe that both human and natural designs require, at some level at least, a conscious creative plan, some central idea, meaning or goal. Artificial life offers an alternative paradigm of thought, and it is the point of this paper to explore how it can link together the seemingly disparate domains of pattern formation, social insect communication and artistic processes. The preliminary argument of this paper is that the processes involved in formation and generation of shapes and patterns, aesthetic or functional, are best viewed as adaptive systems employing distributed local rules and relying heavily on sensorimotor interactions rather than any global ideals or representations. Having benefited from a formal artistic training, an introspective and experimental analysis of the processes involved in the production of artistic works was undertaken, as well as the computer simulation of cellular automata (CA) and agent based swarm systems to provide preliminary studies on which the final evolutionary CA and agent experiments parameters and hypotheses were based. Intuitively in nature and in the artist, adaptive systems employed for design would have been developed and refined through an evolutionary process (see section 2.2). There is reasonable evidence to suggest that asynchronous updating is more biologically plausible (Di Paolo, 2001) (Harvey, I. and Bossomaier, T., AL97), and it will be shown in section 2.2 that this can also be considered the case for human artistic ‘updating’ of paintings. This led to the final aim of the paper: to show that asynchronous updating, in particular random asynchronous updating, of evolved adaptive systems, is a viable, and also robust, updating environment for producing adaptive, aesthetic patterns within artificial computer simulations. In the next chapter, along with a consideration of pattern formation models to date, the artistic process of design and current work in the field of artificial art will be discussed. Chapter 3 will deal with the detailing of the particular models and parameters that were utilized to perform the investigation: cellular automata with synchronous and asynchronous updating and agent swarm models, basic and with pheromone communication. Chapter 4 is dedicated to the discussion of a selection of the preliminary results obtained and their implications for future work, then chapter 5 contains a detailing of the particulars of the genetic algorithm that was used to evolve the final results, based on the findings in the preliminary experiments. Chapter 6 contains a detailed discussion of a selection of the evolved results and comparisons of their respective adaptability to perturbations, namely random mutation in cell colour. This is analogous to mutation in biochemical cells or unintentional brush strokes in painting. Adaptability to a change in the updating system was also analysed with the aim of highlighting the robustness of random asynchronous updating as a default method to invoke during

CHAPTER 1. INTRODUCTION

evolution. That is, to show that asynchronous random updating is a better generic system to employ in the production of aesthetic patterns, as it would seem to be in the artistic exploits of humans (see section 2.2). A colour plates section containing an assortment of images from the plethora of results obtained can be found in Appendix B. This work necessarily incurs a discussion of the nature of aesthetics and the sense of beauty, as it is paramount, when attempting to generate aesthetics or patterns, that the observer is capable of pattern recognition and in possession of aesthetic sense. Thus section 7 is a discussion of aesthetic sense and public reactions, in particular when exhibited at the ICA in London as part of an interactive workshop on Emergence 1 and the Blip sci-art forum in Brighton as a ‘work in progress’ installation 2 . Finally Conclusions and ideas for future investigations and extensions in this exciting new area and application of adaptive systems theory are outlined.

1 Currently 2 Currently

ICA workshop details can be found at: http://www.ica.org.uk/index.cfm?articleid=4365 Blip details can be found at: http://www.blip.alturl.com/

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Chapter 2

Background There are many areas of nature where ordered patterns occur, it is interesting to note that the overall idea of formation as a result of local interactive signalling to produce adaptations in movement can be used as a model of growth of patterns in both animate and inanimate forms, those of snowflakes, animalcules, nests and mammalian coat patterns to name but a few (Frisch, 1975). Models from biochemistry and social insect ethology will be outlined, then it will be discussed in the latter half of this section how this generic idea can also be attributed to the design process and image formation executed in artistic endeavors.

2.1

Pattern and Structure Formation in Nature “I thought it appropriate briefly to draw the readers attention to the beautiful and well-adapted forms of animal life and present also in the most highly developed organisms - structures that needed no conscious effort from their makers and that existed long before the first master builders and artists consciously set about to create useful and beautiful things.” (Frisch, 1975)

2.1.1

Biochemical models

The first thing that must be said on the subject of pattern formation is that there is as yet no experimental evidence to support any of the proposed theories offered by theoretical biology. These models, however unsupported, are nevertheless useful as tools for understanding and can be demonstrated as possible generators of pattern through the use of computer simulations which also means that they can be used as models for artificial pattern formation. Pattern formation as a topic for study should first be distinguished from the related subjects of cell differentiation and changes in form. Pattern formation is concerned with how the spatial arrangement of cells occurs. It would appear that pattern is generally laid down early on providing good evidence for the autonomy of development as a separate process (Wolpert, L. and Stein, W, D., 1984). Pattern formation was originally dominated by theories in terms of prepatterns, the idea that developmental fields have a non-uniform spatial arrangement of substances in a tissue whose local peaks induce the formation of pattern elements, i.e, pattern is preprogrammed, laid out as a whole, globally - a plan (Kauffman, 1984). The concept of positional information as an alternative approach paved the way for a number of interesting theories that will briefly be discussed here, all incorporating local cell to cell interactions as a method for pattern formation rather than a predefined arrangement of pattern elements. Positional information is a much debated concept within pattern formation. Formulated by Driesch, the theory was derived from the observation that all cells in the early sea urchin embryo appear to have the same capacity for development and that the differences that arise in their development must be due to their position, that is the cells must ‘know’ whereabouts they are relative to the other cells as if they were in some sort of a coordinate system (Driesch, 1901)(Wolpert, L. and Stein, W, D., 1984). In the case of the sea urchin, evidence contrary to this theory has since been discovered. Not only are there differences among the cells (Wolpert, L. and Stein, W, D., 1984), but there are systems which can model the development without the need for the cells to know their position. One such model is the Turing system (Turing, 1952) of reaction-diffusion of chemicals.

CHAPTER 2. BACKGROUND

The reaction diffusion mechanism is one of inhibition. The existing structures diffuse ‘inhibitor’ chemicals which suppress the formation of similar cells within a certain radius, determined by the threshold of ‘reaction’. That is a cell will react by developing into a cell such as the existing ones, only when the amount of inhibitor detected is below a certain threshold, i.e. the cell is far enough away to grow. In Appendix A can be found a description of the particular, simple implementation of this model that was used to generate striping patterns. Cellular Automata have been used to model pattern formation as it occurs in many domains, mammalian coat patterns, sea shell patterns and embryological pattern formation (Bonabeau, E. et al., 1992) mainly because of the general property of local interactions to produce global phenomenon, meaning that they provide a good generic model of other models of pattern formation, for example the Turing system (Bonabeau, E. et al., 1992).

2.1.2

Agent based models of structural pattern formation

The self organization of living structures is beautifully exhibited by the development of aggregate streams in populations of the social amoebae, cellular slime molds. These streams of amoebae as in fig 2.1 1 are starkly aesthetic. They produce a substance called acrasin which diffuses away from them. When acrasin appears at the boundary of one of these creatures it causes it to move towards the source. This simple but remarkable signalling system causes aggregates which are the basis of swirling or branching patterns. Eventually the culture converges forming an organized whole with definite modularity, where different areas take on different roles. The diffusion signalling system performs a valuable function, helping the amoeba to find each other and come together in order to converge and create the modularized whole which, of course, contains the reproductive system (Pask, 1962).

Figure 2.1: Slime mold aggregation: spiral waves of Dictyostelium amoebae

“When Human beings start to build, they first make a plan and try to find the best solution for each individual case. Animals do not need all that. They follow innate drives. Even the greatest architects among them work correctly by instinct.”(Frisch, 1975) There are many species that construct complex architectures, social insects can be seen to generate hugely intricate patterns and structures when nest building, see fig 2.2(d). The possible organizational mechanism put forward by Grassé to explain how this can occur is stigmergy(Grassé, 1959). The basic idea is that the coordination of individuals tasks depends not on any communication between them but on the nest structure itself (Bonabeau, E. et al., 1992). The idea is that a termite picks up a soil pellet, impregnates it with a cement pheromone which then diffuses away. As with the slime mold amoebae above, the termites are attracted by this pheromone, meaning that they tend to drop their soil pellets in the same area. Swarm intelligence is an anti-classical-AI idea where a group of agents may be able to perform tasks, without the use of explicit representations, of their environment or fellow agents, 1 Fig

2.1 taken from http://beelab.cas.psu.edu/publications/USSI/slimemoldaggregation.jpg visited: 28/08/02

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Figure 2.2: 2.2(a) A grain of Pollen extracted from Bat Guano from roosts of the short-tailed bat Mystacina tuberculate, 2.2(b) a section of a mushroom showing the radial pores, 2.2(c) reticulation pattern on the back of a mule,2.2(d) architecture of termite fungus gardens, 2.2(e) reticulation on Gold in jewellery

i.e the swarm is a self organizing system (Bentley, 2002a). Craig Reynolds Boids (Levy, 1992) are the classic example of this, where the interaction of the agents together with their simple, ’innate’ rules produce flocking behaviour. The entire process is based on a succession of sensorimotor loops, where the agents adapt their current trajectory based only on the information they receive about the environment, which includes their fellow Boids. Stigmergic swarm intelligence occurs when the innate rules require that the agents give off a pheromone and are also attracted to areas marked with pheromones (Bonabeau, E. et al., 2000). The process of self organization is distributed, meaning that there is no centralized controller ordering the insects, amoebae or agents to behave in a certain way, only the structure/environment combined with some rules of reaction. For a fuller insight into these and similar processes and the field of artificial art see (Bentley, 2002a).

2.1.3

Reticulation

One particularly interesting and aesthetically pleasing pattern that occurs in abundance in natural, living forms as well as in chemical processes and artworks is that of reticulation, see figure 2.22 3 4 5 6 . Reticulation is characterized by its maze-like inter-twining of two very distinct colours. There are many areas of the artistic world that have incorporated such patterns into their work, custom jewelry and photography are the most notable, where the effects of extreme temperatures incur the shrinking and expanding of substances, resulting in reticulation, see 2.2(e). Following this pattern of proliferation, reticulation also transpires profusely in artificial forms, see chapter 4 and the colour plates section for examples of this.

2.2

The Artistic Process

Generally, in work done using distributed models of pattern and structure formation in nature the method is contrasted with the centralised, plan based methods assumed to be invoked by humans, particularly artists and architects. This can be seen in most of the quotes thus far. This assumption is just as short sighted as the prepattern approach was to pattern formation and it is hoped that the highlighting of this in this project could spark further, more realistic models of design that are all encompassing, as positional information did for pattern formation. 2 2.2(a)

taken from http://www.massey.ac.nz/ aroberts/mystery.html (visited: 16/08/02) from http://www.bluewillowpages.com/mushroomexpert (visited: 16/08/02) 4 2.2(c) taken from http://members.aol.com/stripedhos (visited: 16/08/02) 5 2.2(e) taken from http://www.hgtv.com/HGTV/project (visited: 16/08/02) 6 2.2(d) taken from http://beelab.cas.psu.edu/publications/USSI (visited: 16/08/02) 3 2.2(b)taken


There are certain principles, techniques and medium specific methodologies that contribute to the attractiveness and quality of a piece of painting. It is my opinion that artistic ‘talent’ is far from a magical, undefinable essence, possessed by the few and jinxed by deconstruction. Rather it can be thought of as the conscious or unwitting implementation of an adaptive system, consisting of a particular updating scheme and low level local rules or techniques, which have been arrived at through an evolutionary process. It is this theory that will be explored in this section.

2.2.1

Painting Updating schemes

“I first thought that making a portrait consisted of looking at the model and drawing the portrait, and that this entailed artistic creativity and was quite a mysterious process.”(Tchalenko, 2002) Pp 24 Using eye tracker tests, which record precisely where the eye is looking and motion trackers which track the movements of the hands in space, Tchalenko et al set up to find out what the ‘magical’ process involved in the drawing of a portrait is. Their results back up my own experience and method of portrait painting. To begin with the painter makes very quick precise eye movements on the paper and the sitter followed by very small markings on the paper, but as the picture progresses longer and longer periods are spent looking at larger and larger sections of the paper, and not the sitter, and producing bigger bolder sweeping movements. Tchalenko concluded from these observations that “portrait painting, at least for this painter, was a complex combination of a fading memory image and an increasing presence of the emerging picture” (Tchalenko, 2002) Pp 24. Further to this, and based on the idea that the global image is not assessed at each paint stroke and that the small area viewed is important to the type of stroke made, it is crucial to the development of the picture how each local area to be assessed and altered is selected. It is clear, from the fact that there is generally only one hand making any movements on the canvas at any one time, that the updating of each section of the painting cannot happen at once, the areas of the painting are updated asynchronously. There are many different methodologies employed by artists as to how a picture should develop. For example it is not generally advised to sit and make one tiny area of the painting perfect and polished before painting any other areas. Interestingly enough this discouraged method of ‘knitting’ is the most prolific among untrained artists and school age children. A more practised approach, which is medium specific, is to move about the painting in a systematic or random way (but generally hitting every area of the canvas) and, for example with oils and acrylics only put down dark paint where it is needed and then move on. Only once an area is encountered that needs no more dark are the next lightest shades applied, this process continues until the white highlights are added, then, in theory, the painting is finished, this was the updating scheme used in fig 2.3 . For watercolours the opposite is true, though the updating system is the same, that only light colours should be applied in the first instance graduating through the shades until the darkest colours are placed.

Figure 2.3: random asynchronous updating of contrast in shade and lines rules in acrylic painting. Katie Bentley, 2002

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2.2.2

Artistic Rule Sets

“...beauty of figure becomes a kind of substitute for elegance of motion...it is plain that quick turnings in animals indicate a more sudden exertion of the living power than slow ones, it will likewise follow, that wherever the eye overtakes lines running abruptly into contrary directions, such lines will convey an idea of sudden changes of passion.” (Donaldson, 1970) Pp 23. In formal artistic training, one will come across rules of painting, of which there are limitless possibilities. The rule of complementary colours from colour theory for instance, that each one of the three primary colours’ (red, blue or yellow) complementary colour is the mixture of the other two, which, in terms of a colour wheel, like that shown in fig 2.4 means that a colours complement is the one opposite it on the wheel, yellow suits purple, red suits green and blue suits orange. In particular, there are certain ratios that give the ideal amounts of color complements, according to Johannes Itten (Larmann, 2002) which are also shown in fig 2.4. One other fundamental rule, particularly exercised in still life, but crucial to all areas of painting is that of contrast, that shade supports light. A good still life will always have light next to dark. For example see fig 2.57 whose dramatic lighting and almost black background meant that Zurbar´ an was thought to be one of Dali’s inspirations, particularly when considering his piece seen in fig 2.6 8 where the intricate, incessant use of contrast, also of notable use in Dali’s general style, means that a “faint luminosity seems to be shed by the objects themselves” (Ades, 1995) Pp 32. There are many varieties of rules that can be implemented. In the earlier quote from (Donaldson, 1970), Donaldson is suggesting that a good rule to implement to produce an aesthetic piece is to ensure lines contrast in their direction. He also notes in later chapters, other important rules, including that of contrast in shade as already discussed, these were the primary rules implemented in the painting in fig 2.3.

Figure 2.4: Colour Wheel (Larmann, 2002)

Figure 2.5: Example of contrast in Francisco de Zubar´ an, Still Life with Lemons, Oranges and a Rose, 1633

2.2.3

Evolution of Style

All established artists have a distinct style. They will have experimented with and learnt from other styles and it is through the discovery of new rules and the effect of the interaction of that new rule with others that arts creativity and novelty perpetuates. As with evolutionary models, 7 Taken 8 Taken

from http://www.kfki.hu/ arthp/html/z/zurbaran/1/stillife.html visited: 28/08/02 from http://www.sicilianculture.com/store/bread.htm visited: 28/08/02

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Figure 2.6: example of contrast in Salvador Dali, Basket of Bread, 1926

children’s paintings are in general not aesthetically pleasing, they are the beginning of a very long learning and refining process, picking out the good tricks and the bad ones and repeating pleasing structures but within new environments and with different rules. This process has also been noted in the drawings of apes (Graven, 1968) Pp 143. Recurrent themes and paint application techniques along with updating schemes and implementation of particular aesthetic rule systems like those already described can define an artists unique style.

2.3

Artificial Art

Aesthetic evolution selection by a human observer has been much utilised for the generation of, often stunning, visual images, (Dawkins, 1991), (Sims, 1991), (Sims, 1992), (Dorin, 2001). However, as pointed out by Dorin the images evolved not only reflect the users desires but more importantly the restrictions of the program (Dorin, 2001). Dorin notes that the user selection process is a top down method for generation of form, in a ‘choose your own adventure book’ way. That is, no matter how creative the user tries to be, the image cannot stray out of the ones available in the book. This ‘explorer’ rather than ‘artist’ generative method seems far removed from the true, bottom up procedures invoked by the real ‘artist’. The process of globally assessing the aesthetic merit of an image should not be confused with the local updating of a canvas with aesthetic intention. Art appreciation is not synonymous with art production. What is more important is to get the production method right, not the evolution, and that production method, to be realistic, has to be robust enough to be capable of writing a never ending story traversing all media and styles, rather than a finite collection, that can only exist in software space. The use of computer simulations within this paper are meant as proof of concept, that aesthetic patterns and images can be generated using asynchronously updated distributed adaptive rule based systems, and the experiments with paint such as the picture shown in fig 2.3 were performed in the formation of this hypothesis. However the theory is a general one and reflects the processes observed in design within many fields and also the current trend to explore the computational possibilties for exploiting design theories, such as computer aided design packages for Architecture, robot morphologies, neural topologies, furniture etc... (Hornby, G. and Pollack, J., 2001b), (Hornby, G. and Pollack, J., 2001a), (Bonabeau, E. et al., 1992), (Bonabeau, E. et al., 2000), (Coates, P and Carranza, P, M., 2001), (Broughton, T. et al., 2001), (Bentley, P. J and Corne, D. W.., 2002). Computer simulations have been put forward as works of art themselves. Artist Paul Brown used cellular automata to produce very attractive and distinct images, however, they were aesthetically biased even before the cellular automata rules were initiated. In the image seen in fig 2.7 each of the 16 cells of the CA were in fact tiles with the same pattern on them, the rules of the CA defined the orientation of the tile. As CA’s tend towards small attractor cycles, and the movement of the image was particular pleasing, randomness was often introduced to maintain an unstable state 9 . Because of this, the aesthetic nature of this piece cannot really be attributed to the use of a CA. To avoid this human, artistic influence on any images generated within this project, each cell of the CA or of the agents canvas was 9 Insight

from Paul Brown at Blip discussion group 22/7/02

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Figure 2.7: Desert Storm, Paul Brown, 1999. 4 × 4 CA image

a pixel, and although the development towards a stable state was pleasing to watch, within the scope of this project only a stable state single shot image was assessed for its aesthetic or patterned merit. Only after the stable formation was reached was any graphics rendering performed, and used as a method to highlight the aesthetic qualities of the pattern.

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Chapter 3

The Models Explained 3.1

Cellular Automata

A two dimensional toroidal 1 Cellular Automata was used. This was a 2-D array of M × N cells, where M was the number of rows and N was the number of columns. Each cell represents the pixel in the (m, n) co ordinate position, where m ∈ M, n ∈ N . Each cell was of a possible state s ∈ S where S = {0, 1, ..., C − 1} and C is the specified number of possible colours that the pixel could be. In most types of CA used the radius r of the CA, specifying the range of the update rule, was r = 1. This meant that the updating of a cell relied on the state of that cell and the states of its eight surrounding neighbours only. A radius of 2 was experimented with briefly but different radius values warrant further investigation.

Initial CA cell settings Four different initial settings for the CA cells were experimented with. A blanket setting, where all cells are set to zero; a random setting, where all cells had equal probability of being any of the colours being used in that particular run, a glider setting, named after one of the more interesting recurrent shapes in Conways Game of Life, see section 4.1.1 for details; and finally a random sparse setting on average half the clls were set to zero and the other half had equal chance of being any colour.

Updating Schemes There are many different possibilities for the timing of the updating of each cell. Three types of updating were investigated within this project, synchronous (synch), asynchronous set (asynch set) and asynchronous random (asynch rand). In synchronous updating all cells of the CA were updated at the same time, in parallel. Asynchronous set updating, for this project meant that at each stage only one cell was updated, and that cell was set. So the first cell to be updated was cell (0,0) then cell (0,1), then (0,2) etc... all the way through the rows and columns in order. A time step corresponded to one complete run through all the cells being updated. Although this is asynchronous it is still a deterministic form of updating. In asynchronous random updating one cell was picked at random to be updated at each stage, with replacement - i.e. unlike with asynchronous set updating, after M × N stages not all cells had necessarily been updated, so this was a non-deterministic form of updating. One time step corresponded to M × N number of updating stages. So for all types of updating in a time step on average all cells would have been updated, therefore ‘time step’ was just an arbitrary measure that made comparisons between the patterns formed with each type of updating easier to judge.

Terminology In order to consistently and concisely describe the rule sets and parameters used in each of the experiments an alphabet of symbols must be introduced. Throughout the following sections the cell being updated in the CA will be represented by p for pixel. The amount of neighbours, within the given radius, of a certain colour will be denoted by C0, C1, ... where the different values relate to the different colours of the pixel. So for example equation 3.1 means that if more than seven of the eight neighbours of a given cell are of colour 0 and the cell itself is of colour 1, then change the colour of the cell to 2 (The actual colours that the numbers related to were arbitrary but, for example, 0 generally related to yellow). 1 Toroidal

means that there are no edge effects, that is the array was wrapped around into a torus shape.

CHAPTER 3. THE MODELS EXPLAINED

15

r = 1 : p = 1 & C0 > 7 ⇒ p = 2

3.2 3.2.1

(3.1)

Agent Design Basic

The basic agents model was in essence an asynchronously updated CA, where the cells to update at the next time step were specified by the rule sets. A number N of ‘agents’ were placed in N randomly chosen, with replacement, cells of the CA array. They had an updating radius r = 1 which may or may not be inclusive of the agents cell. The agents all updated the particular cells they ‘inhabited’ synchronously by assessing the states of the cells in the given radius, they then moved to one of their eight neighbouring cells based on rules of movement, again governed by the states of the cells within the updating radius. This movement was either set deterministically, for example: ‘if all eight neighbours are black, change cell colour to yellow and move left’ or it was chosen randomly, for example: ‘if four of the neighbour cells are yellow, change cell colour to green and move off to a randomly picked neighbouring cell ’. Also, combinations of these two forms of movement were utilised in the same rule sets. The conceptual basis of this model was that the agents assessed their local environment and left ‘paint’ trails as they moved around the pixels, reflecting the current state of that area of the image. As all the agents followed the same rules a globally recognisable phenomenon was expected to ‘emerge’. It is intended for future work to analyze the effect of varying r and even introducing other forms of local ‘area for assessment’ selection, possibly closer to the true vision area used by the artist, or the area of cells in pattern formation in nature that affect the pigmentation of a given cell. Also proposed for future work is an investigation into the sorts of patterns and aesthetics that can be produced with asynchronously updated agents, as this is closer to the true nature of painting, as there is in general one part of a painting updated, then a movement is made to another section and that is updated, although, as discussed in section 2.2 there are many different approaches and methods for selecting the area of canvas to update next.

3.2.2

Pheromonal Agents

The pheromonal agents model was an extension to the basic model where each agent was capable of leaving plumes of a ‘pheromone’ that diffused over time and they were also capable of reacting to the given amounts of pheromone detected around it. The pheromone diffusion was based on random walk diffusion (Murray, 1989) after a pheromone plume was dropped at cell (m, n), the amount of pheromone A at any given cell in the array, of Euclidean distance x from (m, n) at time t from when the plume was dropped was given by equation 3.2, where D is the diffusivity constant (how much the chemical diffuses at each time step) and Q is the amount of pheromone dropped. 2

Qe−x /4Dt √ (3.2) 2 πDt Various experiments were done to investigate the effects on pattern/aesthetic formation of the different parameter settings, plume drop times and reaction to pheromone rules. It should be pointed out that one inconsistency that occurred in this project was that the pheromoe was not calculated to diffuse over a toroidal surface, the grid was treated as a 2D plane for the purposes of diffusion. This made the model simpler and seemed to capable enough of generating aesthetic patterns, however it would be wise in a future extension to implement a toroidal diffusion. A=

Chapter 4

Preliminary Experiments A great variety of different rule sets with assorted parameter settings were investigated, far too many to explain every one in this section. What follows is a selected few, detailing the comparisons and contrasts between runs with different parameter settings or updating schemes, and exploring the curious global patterning phenomena particular to each. In the colour plates section are stills taken from some of the other rule sets and runs that have unfortunately had to be omitted from this section. It was important to perform these preliminary experiments to be able to formulate the best structure for rule sets to be evolved, and set parameters so as to minimise evolution time efficiently without the loss of complexity in the patterns. The most notable finding from these initial experiments was that it is almost impossible to hand design rule sets for a specific pattern and that many attempts to design just ‘interesting’ patterns failed.

4.1 4.1.1

Synchronous Cellular Automata Game of Life

Conways’ Game of Life was of course the first stop when trying out rule sets to watch their global behaviour. Conways’ rules, classically simple, notably took years to refine in order to achieve the interesting ‘emergent’ phenomena that can be observed (Levy, 1992). This is undoubtedly due to the peculiar properties of ‘emergence’; that, by definition, the elements that interact to produce the behaviour cannot be defined a posteriori, just as the ‘emergent’ behaviour could not be predicted a priori from the distinct elements (Bentley, 2002b). Each cell could only be either 1 or 0, ‘alive’ or ‘dead’, alive cells were represented by yellow pixels and dead cells were shown as blue pixels. The basic concept is that cells that are alive will die of overcrowding or of isolation, and dead cells will come to life in exactly the right amount of company, three living cells nearby.

Rules: • r=1 • p = 0 & C0 ≤ 1 ⇒ p = 1 • p = 0 & C0 ≥ 4 ⇒ p = 1 • p = 1 & C0 = 3 ⇒ p = 0 A number of different starting states or basins of attraction can lead to the same repeating cycle of states or attractors. The game of life exhibits many different attractors, most distinctive of which are the ‘blinkers’ and ‘gliders’. Gliders are cyclic of order 4, Blinkers are 2-cycles, going from three pixels alive in a horizontal row to three pixels alive in a vertical line. Pictures 4.1(a) to 4.1(e) show the 5 Stages of a glider, pictures 4.1(f) and 4.1(g) show the two stages of a blinker and picture 4.1(h) is an example of a point attractor, which remains unchanged throughout each instantiation of the rules.

CHAPTER 4. PRELIMINARY EXPERIMENTS

(a)

(b)

(f)

(c)

(g)

17

(d)

(e)

(h)

Figure 4.1: Some stable patterns from Conways’ Game of Life

4.1.2

Blanket

It became apparent that many rule sets converge to a blanket grid, where all cells are the same colour (not necassarily 0 as in the initial CA setting: blanket CA). This was a problem, when evolving the rule sets, that had to be overcome, as will be explained in section 6.

4.2

Asynchronous Set Cellular Automata

It became apparent, through numerous tests, that the asynchronous set updating scheme was more robust, in comparison with the synchronous scheme, for producing interesting stable patterns.

4.2.1

Game of Life

When the rules for the game of life, detailed in section 4.1.1 were used with the asynchronous set updating scheme and a blanket ‘alive’ initial CA, a rather interested and unexpected pattern occurred. Best seen in motion, the screen shots shown in 4.2 give a hint at the intricate nature of this reticulation style pattern. A larger version can be found in plate I. The pattern grew outwards starting at the edges and ended in a steady state such as that in fig. 4.2(g), the only movement from this point on was from small, cyclic attractors, that flickered in small areas of the screen. As the initial conditions and the updating scheme were fixed every time, the pattern was completely deterministic. The only variable that could alter the pattern was the size of the CA grid. All patterns, regardless of the size of the grid, followed the same structure of growth and final form, but, on a pixel level, were in no way similar. A pixel that ended up blue in a run with CA size 100 × 100 might well have been yellow in a run with CA size 200 × 200. However the patterns were unmistakeably of the same class on a global level. This pattern is a very good example of the sensitivity a rule set has to the updating system. The difference between the patterns observed with the synchronous and the asynchronous set updating schemes are stark, and again with random updating, as can be seen in section 4.3.1.

4.2.2

Cow Print

Another rule set that was experimented with was the rather curious ‘cow print’ generating system. The blobby patterns that emerged were highly dependent on the initial state of the CA. A blanket screen was observed with any initial setting other than random, and then, though on every run the ‘cow print’ pattern always formed, the positioning of the blobs was totally due to the original arrangement of alive and dead cells. Stills taken at various points from one particular run can be seen in fig 4.3 and an enlarged version can be found in plate II.

Rules • r=1 • p = 0 & C0 > 6 ⇒ p = 0 • p = 1 & C1 > 6 ⇒ p = 1 • p = 0 & C0 < 4 ⇒ p = 1


18

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Figure 4.2: Screen shots from Conways Game of Life when using the asynchronous set updating scheme


(a)

(b)

19

(c)

(d)

(e)

Figure 4.3: Screen shots from one run of Cow Print pattern generated using asynch set updating and a random initial CA

(a)

(b)

(c)

(d)

Figure 4.4: Four separate runs of Conways’ Game of Life when using the random asynchronous updating scheme

• p = 1 & C0 > 4 ⇒ p = 0

4.3 4.3.1

Asynchronous Random Cellular Automata Game of Life

Implementing the game of life rules within a random asynchronous updating scheme produced remarkably similar patterns on each run, in 4.4(a) and 4.4(c) a blanket initial CA was used, whereas 4.4(b) had a random initial CA, these are still very similar, however initialising the CA with only a glider caused the greatest differences between runs, as in 4.4(d). This is understandable as, apart from five cells, all the initial cells were dead, meaning that if the cells in the vicinity of the glider were not the ones to be updated early on then nothing would happen, and then when it did, the pattern was highly dependent on the order of the particular cells near the glider that got updated.

4.4

Basic Agent Design

Many experiments were performed without the use of pheromone, trying out different rule sets, parameters and also different mechanisms for how the actual agents should work, all to try and see what sort of settings would encourage the system to produce aesthetic forms or patterns. Again, not all can be described within the scope of this paper, however some interesting images from other rule sets can be found in the colour plates section. All agent based patterns reached a stable state with point attractors or small cyclic attractor states, this was an unexpected result, as the agents continued to move around the screen but after a while, no changes needed to be made, this can perhaps be compared with the idea of a painting being ‘finished’.

4.4.1

Diagonal reticulation

One of the simplest rule sets implemented generated an extremely evocative moving image, as the pattern developed, stages of which can be seen in fig 4.5, diagonal lines elongated until they filled the screen, then, in the opposing direction reticulation like splinters hatched across the image. Plate VIII shows the stable state that one run of this pattern reached. This rule set served to confirm that random movements and complicated rule sets, and indeed large numbers of agents, such as those instantiated in the generation of plates X, XI, XII and XIII were not necessarily needed to generate aesthetic patterns. This finding wholly contributed to the design of the agents genotypes detailed in section 5.2. When initialised with any other CA type, this pattern resulted in a whole screen of reticulation, it seems the diagonal lines were dependent on the initial blanket colour 0 to occur.


20

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Figure 4.5: Development of the basic agent pattern Diagonal reticulation, 4.5(f) shows the stable state and 4.5(g) is an enhanced section of this stable state


(a)

21

(b)

(d)

(c)

(e)

Figure 4.6: 4.6(a) to 4.6(c) show three stages of the Neuron rule set, 4.6(e) and 4.6(d) show the amounts of pheromone at two time steps

Rules • C0 > 4 ⇒ p = 1, Agent(x, y) = Agent(x + 1, y + 1) • C0 < 4 ⇒ p = 0, Agent(x, y) = Agent(x, y − 1) • C0 == 4 ⇒ p = 0, Agent(x, y) = Agent(x + 1, y − 1)

4.5

Pheromonal Agent Design

Several experiments were done where plume drop rules were incorperated into the existing basic agents rule sets. Examples of these are shown in plates XIV and ??. This changed the spatial arrangement of the pattern quite strikingly.

4.5.1

Neurons

When the agents were set to leave a red trail and a plume of pheromone at each time step wherever they went, and to constantly move to the neighbour cell which had the most pheromone present, shapes reminiscent of neurons developed as the agents converged to be in little groups. This development can be seen in fig 4.6. With this set up the agents were not in any way reacting to the ‘paint’ found around them, simply to signalling cues. This isolated the sort of movement of agents, incurred by the signalling system, from the patterns that the agents made with the adaptive change of pixel colour rules.

Chapter 5

Genetic Algorithm The genetic algorithms (GA) employed for the evolution of the various forms of CA and the agent designs were of the same generic structure, however it became necessary to alter the various parameters given the different situations as it became clear that the updating systems greatly affect the size of the searchspace, given that asynchronous updating means that the same rule-set genotype can map to several, albeit similar, phenotypes. It was not known if there would be patterns that could form independently from this random updating and even if they could cope with the asynchronous nature of updating within the CA or the agent system, although the results obtained in the preliminary experiments suggested that there would be.

5.1

CA Genotypes

The genotypes for the CA GA encoded the particular rules to be implemented, see fig 5.1(a). The genotype was split into eight blocks, one for each rule. The position of a block in the genotype was crucial as the first two were the rules to implement if the pixel was of the first colour, the next two blocks if it was the second colour and so on for each of the four colours. Each block contained four genes. The first gene in a block chose the counter to assess, the second related to the operation to use in the rule, five operations were possible, =, , ≤, ≥. The third gene was the condition, and the fourth was the action. There was a probability of 0.5 that no action would be taken. So if the four genes of the first block were 1, 2, 3, 2 then the rule would expand to be: if p = 0 & C1 > 3 ⇒ p = 2. The rules expanded in a hierarchical format, as rules could well overlap, i.e if C0 was 7 and the first rule was if C0 > 6 ⇒ p = 1 and the second was if C0 < 8 ⇒ p = 2 then the pixel would be changed to colour 1 as this rule came first. This resulted in a lot of the genotype being ’junk DNA’, i.e. reduntant, unused rules, but important in preserving the hierarchical structure and also allowing the genotype to determine how many of the six rules it needed to use.

5.2

Agent Genotypes

The agent genotypes were split into eight blocks with six genes each, see fig 5.1(b). Unlike the CA GA the state of the cell that the agent inhabited was not assessed. However the position of a block was just as important, as a hierarchical rule system was again implemented. The first four of the six genes related to the same rule specifications as in the CA genotypes, the last two were binary encodings, where the fifth related to either move to the neighbour cell with highest pheromone content or move to the neighbour cell with lowest pheromone and the sixth specified whether a plume of pheromone was to be dropped or not. Thus the movement system was simple, move towards or away from other agents but the choice of which was dependent on the surrounding pixels states, this was seen as enough to create complexity in the resulting image, however including rules of movement closer to those used in the basic agents model would, it is hypothesised increase the complexity by an order of magnitude and deserves future investigation. The agent genotypes then had an extra four genes that specified the amount of pheromone to be dropped in a plume, the diffusivity constant to use, the amount of time a plume should take to diffuse and the optimum number of agents. Unfortunately, due to the effect large numbers of agents and plume diffusion time had on evolution run time a limit of 20 for each

CHAPTER 5. GENETIC ALGORITHM

23

(a)

(b)

Figure 5.1: 5.1(a) The general CA genotype, 5.1(b) the general agent Genotype

(a)

(b)

Figure 5.2: 5.2(a): a random initial CA, 5.2(b): the blanket initial CA

had to be enforced, this was found to be small enough to allow a pattern to develop and for run time to be realistic.

5.3

Evolution

In general a population of 100 genotypes was evolved for 100 generations. The system was elitist in that the top scoring genotype would be replaced into the next population. The top 10 fittest genotpyes would beome the parents of the next generation, and from this parent pool random parents, with replacement, were picked to be crossed over at some random starting point of a rule block in their gene string. The resulting 32 genes were then subject to mutation, where each one had the same probability, 0.05 of being mutated, so on average 1.6 genes were mutated. After many preliminary experiments it was found that the parameters defining the size of the CA were of great importance to the type of patterns formed, however the smallest size, that still would retain enough of the complexity of the pattern was found to be 30 × 30, larger than this was generally better, but as the size grew, so did the computation time for an evolutionary run so for the CA GA a grid size of 40 × 40 was used and in the agent GA, which had more computations it had to be 30 × 30, however runs still took around 12 hours. For all the CA evolutionary runs an initial random CA was used where all pixels had equal probability of being set as any of the four colours. Although alterations were occasionally made colour 0 was displayed as yellow, colour 1 as purple, 2 as red and 3 as dark burgundy. See fig 5.2(a) 1 for an example screen shot of an initial CA, as it is worth noting that even when there are less than four colours present in an evolved pattern, the rules had to deal with all four colours to get to that point. In the evolution of agent design rules the initial CA was a blanket CA where all cells were set to 0, as in fig 5.2(b). 1 SOAP

stands for Self Organised Adaptive Patterns, the name of the program.

CHAPTER 5. GENETIC ALGORITHM

5.4

24

Fitness Function

Every member of the population was subjected to 5 trials to eliminate patterns that were dependent on the initial conditions. The fitness was judged on each of these trials and the total score for a genotype was the sum of these. In general the fitness was judged at the 40th time step allowing the pattern to develop into its stable state. Asynch rand updating needed 100 steps to develop. Functions for agents that didn’t reward for colour 0 surrounds, i.e the canvas colour, also needed around 100 time steps for the canvas to be covered in other colours in development. Again, a certain formal system for describing the fitness functions must be introduced. The amount of the sixteen neighbours, outside of r = 1 but within r = 2, of a certain colour will be denoted by R2C0, R2C1, ... where, again the different values relate to the different colours of the pixel. zero, one, two, three refer to the number of cells in the CA that are of the respective colour. The fitness function was of the following general form, where there are n conditions (RC) that must be satisfied to be rewarded and m conditions (PC) that if satisfied, the function is penalised and reset to 0 (see equations 5.1 and 5.2).

       

0 0 .. . f itness(CA) =   0

     PN ×M p=0

if P C1 is true if P C2 is true .. . if P Cm is true f (p)

(5.1)

otherwise

 1 if RC1 is true      1 if RC2 is true f (p) =

.. .. . .      1 if RCn is true 0

(5.2)

otherwise

The constants that determine the rate of diffusion and the number of Agents are to be represented as follows: AGEN T S is the ideal number of agents, T IM E refers to the amount of time a plume takes to diffuse, Q is the amount of plume to be dropped and D is the diffusivity constant. As was mentioned in section 4.1.2, a blanket grid, where all cells are the same colour, became an issue when evolving both the CA rules and the Agent rules. This was due to certain fitness functions, originally designed to reward for clustering, actually being optimised by a blanket grid. This was an uninteresting state for the CA to be in and thus in every experiment a harsh penalty (fitness set to zero) was incurred if, at the time step where fitness was evaluated, a blanket grid was detected, such that those rule sets never got to flood the gene pool. However, one problem with only evaluating the fitness at one time step meant that the rule set may be on course to converge to a blanket, but after the evaluation time step, meaning that it optimised the fitness function, avoided the penalty and remained an uninteresting ‘pattern’. Harsher penalties thus ensued, where fitness would be set to zero if more than half the cells were of the same colour. With this, it was rarely seen, but blankets, with extra long times before convergence, still sneaked in.

Chapter 6

Evolutionary Experiments 6.1 6.1.1

Synchronous Cellular Automata Islands

One of the first fitness functions that was chosen can be seen below and was designed to reward for pixels of one colour to be completely surrounded by eight pixels of one other colour, with some sort of mosaic like pattern in mind for the final outcome. The first evolutionary run with this function instead produced curious results. The image quickly reached a steady state where most of the screen was one colour with small islands of another colour. On the next time step this image would invert so that the islands would be of one colour, with a rim of a different colour and the ‘background’ was another colour, and again on the next time step the background was the colour of the original islands and the islands were all of the original background colour. This flicking then continued in this 3-cycle ad infinum with no change in the shapes of the islands. The first and third stages of the stable pattern can be seen in fig 6.1 The image had scored a very high fitness however, as the fitness was only measured at one time step this seemed to be inconsistent. What this test revealed was that evolution had found a very good solution to the unintended function that was caused by a certain oversight in the design of the scoring system. The CA worked by calculating the various counters, counting how many of a pixels eight neighbours were of which colour, then following the appropriate

(a)

(b)

(c)

(d)

Figure 6.1: 6.1(a) and 6.1(b) show two stages of the evolved synchronous CA with fitness function islands 6.1(c) is a section taken from 6.1(a) and 6.1(d) is an enhanced, rendered version of this section

CHAPTER 6. EVOLUTIONARY EXPERIMENTS

rule to change that pixels colour based on the rule system. Once this was done the fitness, at the appropriate time step, was evaluated. But the counters had not been updated to represent that pixels current neighbours states. Essentially the conditions that the state of the pixel needed to satisfy in the fitness function were being judged at the correct time step, whereas the conditions that the counters needed to satisfy were being scored from the previous time step. The flicking image with the islands was the optimal solution to this, as a pixel that was yellow would have all red neighbours in the time step before. Of course the absolute optimum image would be a blanket screen that flicked from one colour to another, but the blanket pattern held a penalty so could not occur.

Fitness function: RC1 : if C0 = 8&p = 1 RC2 : if C1 = 8&p = 2 RC3 : if C2 = 8&p = 3 RC4 : if C3 = 8&p = 0

P C1 : if zero or one or two or three ≥ (N × M ) − 30

One particularly interesting shape that emerged from the interactions of these rules is shown enlarged in fig 6.1(c) the same section of the image with rendered graphic effects added to enhance some of the qualities of the pattern and to add in greater contrast, colour effects and shade, to increase the aesthetic nature of this image can be seen in fig 6.1(d). This section was chosen by a human observer and the aesthetic ‘extras’ were also determined by the human and it could be said that this is detrimental to the artificial art plight. These issues will be discussed in sections 7 and 8.

Rules: r=1 p = 0 & C1 = 4 ⇒ p = 3 p = 0 & C1 < 6 ⇒ p = 2 p = 1 & C0 > 6 ⇒ p = p p = 1 & C1 ≤ 7 ⇒ p = 3 p = 2 & C3 ≥ 0 ⇒ p = 3 p = 2 & C1 = 5 ⇒ p = 3 p = 3 & C3 < 6 ⇒ p = p p = 3 & C0 < 6 ⇒ p = 0

The interaction of the rules within this rule set is hard to define, it is clear that the last rule is being implemented as it is likely that counter 0 is less than 6 around any colour 3 pixels as colour 3 pixels tend to be clustered by the effect, most probably of the fourth and fifth rules, that will invariably send all pixels of colour 1 and 2 to be colour 3. Again the rule that sends colour 0 pixels to colour 2 is likely to be implemented and this backs up the observation that there is a 3-cycle happening once stability has been reached, where 0 goes to 2, 2 goes to 3 then 3 goes to 0. It is quite evident from the complexity that ensues from the use of these rules that it would have been near impossible to engineer a set of rules like these by hand to produce the pattern observed.

26


27

1400

1200

1000

Fitness

800

600

400

200

0

0

20

40

60

80

100 Generation

120

140

160

180

200

Figure 6.2: Graph showing the growth of fitness of rules sets with the mosaic function

Figure 6.3: Pattern evolved with the synchronous CA and the mosaic function

6.1.2

Mosaic

Adjusting the design of the CA from this point on, so that the counters were calculated before and after the rules had been implemented, meant that the fitness function described for the previous pattern, but with a slight change as can be seen below, produced a very different result, which had the qualities of a mosaic. The highest score in this instance was much lower than before as the fitness function is by its very nature a competitive one. That is if one pixel is completely surrounded by pixels of another colour and receives a point, all its eight neighbours will necessarily not be able to receive points, as one of their neighbours is definitely a different colour to the others, namely the previous pixel assessed. The growth of fitness for this function can be seen in fig 6.2 which shows that the top score was around 1400, whereas the highest score possible, if every pixel satisfied the function, would be 8000 (1600 pixels every 5 runs). It was found that for this particular function 200 generations were needed to secure a robust solution, as obviously the randomness of the initial CA could produce, but then wipe out rule sets that were dependent on certain initial conditions.

Fitness function: RC1 : if C0 = 8 & p = 2 RC2 : if C1 = 8 & p = 3 RC3 : if C2 = 8 & p = 0 RC4 : if C3 = 8 & p = 1

The pattern can be seen in fig 6.3. Though this pattern too reached a stable state in that shapes that formed remained static, the colours cycled as those in the previous pattern did, however each colour cycle still maintained the fitness of this pattern.

Rules r=1 p = 0 & C3 = 4 ⇒ p = 3


28

p = 0 & C0 > 7 ⇒ p = 3 p = 1 & C1 < 3 ⇒ p = 3 p = 1 & C2 > 4 ⇒ p = p p = 2 & C0 > 7 ⇒ p = p p = 2 & C3 ≤ 0 ⇒ p = 0 p = 3 & C0 < 7 ⇒ p = 0 p = 3 & C1 < 6 ⇒ p = 2

Adaptation to Perturbations This pattern could cope with the mutation of various numbers of its cells, the development of the pattern, as well as its reaction to perturbations can be seen in fig 6.4, a graph showing how the fitness of the pattern resumed even in the face of extreme perturbations can be seen in fig 6.5 which also shows the stability of the pattern once a high fitness is reached. When the patterns updating scheme was changed however an interesting phenomenon occurred. The pattern would take less time to develop into its steady state and would also, generally be of higher fitness when using the asynch set scheme. The graph in fig 6.6 shows this unexpected result, however fig 6.3 shows that although the asynch set updating still produced a stable fit pattern it lacked the characteristic red chunks that the pattern had when updated synchronously, it retained the isolated spots but there are more purple islands than there were when using synch updating. This was also the case for asynch rand updating, however, the developmental period was almost 200 times the length of that with synch updating and the resulting stable pattern was generally of lower fitness. It would seem that although the pattern was evolved using synchronous updating, the generation of a fitter version of the pattern was possible using the asynchronous updating schemes. Either the particular rules set here was robust, or the asynch schemes allow for more pixels to succeed to higher fitness. This deserves further investigation.

6.2 6.2.1

Asynchronous Set Cellular Automata Double Mosaic

Carrying on the mosaic theme, the previous fitness function was extended to include an assessment of the cells within a radius of 2. It was found that to specify a condition of the form: if p = x, C0 = y and R2C1 = z was too hard for the initial random population to satisfy, first the population size was increased, but this had a detrimental effect on the time evolution took to run, so the fitness function was altered to allow for the population size to stay at 100 whilst still rewarding patterns where more of the R2 neighbours were of some specified colour, see equation 6.1 for the modified fitness function.

 1 + R2Cx      1 + R2Cy f (p) =

.

..      1 + R2Cz 0

if RC1 is true if RC2 is true .. . if RCn is true otherwise

(6.1)

Fitness function: RC1 : if C0 = 8 & p = 1 ⇒ f (p) = 1 + R2C2 RC2 : if C1 = 8 & p = 2 ⇒ f (p) = 1 + R2C3 RC3 : if C2 = 8 & p = 3 ⇒ f (p) = 1 + R2C0 RC4 : if C3 = 8 & p = 0 ⇒ f (p) = 1 + R2C1

P C1 : if zero or one or two or three ≥ (N × M ) − 30 Fig 6.8 shows a section of the double mosaic pattern, white represents the colour 0, blue the colour 1 and black the colour 2. It is clear how this pattern coped with the competitive fitness function, all blue pixels are completely surrounded by white, as specified in the fitness function, and then surrounding that white are some number of colour 2 pixels, this pattern


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Figure 6.7: mosaic evolved synch rule set when updated with asynch rand updating

Figure 6.8: Enhanced section of the evolved asynch set CA Double mosaic


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coped with the laying of white pixels around blue ones by putting white around most other colours too, this lowered the amount of black pixels in the R2 region but increased the number of blue pixels surrounded by white, which took precedence in the fitness function. It is worth pointing out that this pattern also reached a stable state reasonably quickly where the shapes remained and only the colours of the single pixel islands cycled between colour 1 and 2, the cycling of the colours still satisfied the fitness function, but the fitness oscillated depending on the number of pixels isolated on their own, as only blue pixels were satisfying the fitness function, if too many of these turned black then the fitness decreased for that timestep, but was then reinstated as they turned blue again on the next time step, this oscillation is apparent in fig 6.10 .

Adaptation to Perturbations The double mosaic pattern was subjected to mutations of a random number of its cells at three intervals over the course of a run, the changes in fitness as this occurred can be seen in fig 6.10 and the re-organisation of the pattern after one of these perturbations can be seen in fig 6.9. It should be pointed out that the fact that the oscillations in fitness, once the pattern had re-reached stability, decrease as the pattern is perturbed more; is purely coincidental. The pattern generally had the top peak of its oscillation around 2700 whatever the starting CA arrangement was, whereas the trough could have any low or high fitness related only to the initial conditions. When the Rule set was updated using the other two schemes, it was found that a good fitness and very similar pattern was achievable with the asynch rand updating, although the fitness never reached a stable oscillation. This is to be expected, as the steady oscillation before was due to all the blue single pixels changing to black and vice versa for the black single pixels, however with the rand asynch updating not every single pixel will necessarily have been updated, so even though the pattern stayed stable, the fitness roamed through various oscillations. Also, the developmental stage, as the pattern approached its stable state was longer with this updating scheme, as with asynch set updating it had been evolved to be steady by the 50th time step. The fitness was higher during the developmental stage for all


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updating schemes, but the pattern was not robust enough in these periods to maintain this high score and settled for a lower but steady fitness. Using the synchronous updating however caused a massive change in the global pattern, a blanket blue image was the best this scheme could produce, which scores a fitness of zero. This difference in pattern formation that occurs between asynch and synch updating of the same rules reflects those seen in the preliminary results, particularly with the game of life rules.

6.2.2

Spots

Using the following fitness function, which is of the same form as the one that generated the mosaic pattern in the synch updating section, asynch set updating was able to find a much fitter solution, titled spots for the obvious reason (see fig 6.12).

Fitness function: RC1 : if C0 = 8 & p = 1 RC2 : if C1 = 8 & p = 2 RC3 : if C2 = 8 & p = 3 RC4 : if C3 = 8 & p = 0



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Adaptation to perturbations The graph in fig 6.14 shows very similar results to those found with the double mosaic pattern. In comparison with the results seen with the mosaic rules, with the asynch rand updating the developmental period was more than halved and the resulting stable solution was undifferentiable from the original pattern, whereas the mosaic pattern had almost totally been distorted. Again, when the pattern was updated with the synch scheme, it almost totally failed to form, highlighting the crucial differences that the updating scheme causes.

6.2.3

Red Tiles

The pattern evolved with the following fitness function is shown in fig 6.16 and tentatively titled ‘red tiles’. The fitness function again was a competitive one, similar to that used to produce double mosaic, however the global image is very different, there are less occurrence of fit pixels, but those that are have more of their R2 neighbours of one colour than those in double mosaic. The top fitness reached by the 100th generation was also notably higher than that with double mosaic, see fig 6.15. Whether this means that each evolutionary run can give very different top scores and patterns, or whether this particular arrangement of conditions to satisfy is easier to solve deserves further investigation, but was not within the scope of this project, it is hypothesised that the former is the case based on other runs that were performed but not detailed here.

Fitness function: RC1 : if C0 = 8 & p = 2 ⇒ f (p) = 1 + R2C1


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Figure 6.16: Red tiles pattern evolved with asynch set updating

RC2 : if C1 = 8 & p = 3 ⇒ f (p) = 1 + R2C2 RC3 : if C2 = 8 & p = 0 ⇒ f (p) = 1 + R2C3 RC4 : if C3 = 8 & p = 1 ⇒ f (p) = 1 + R2C0


Rules p = 0 & C0 ≥ 1 ⇒ p = 2 p = 0 & C3 > 2 ⇒ p = 1 p = 1 & C3 < 7 ⇒ p = 2 p = 1 & C2 < 4 ⇒ p = 1 p = 2 & C0 < 1 ⇒ p = 3 p = 2 & C3 ≤ 5 ⇒ p = p p = 3 & C3 < 3 ⇒ p = 2 p = 3 & C0 = 2 ⇒ p = 0

Adaptation to perturbations Red tiles was able to adapt to the perturbations it faced with notably similar successes to spots and double mosaic, see fig 6.17 , especially because most of the pixels in the synchronously updated version didn’t satisfy the conditions of the fitness function, which was the case for both the afore mentioned patterns, see fig 6.18.


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Figure 6.19: Yellow tiles evolved asynch rand rules

6.3 6.3.1

Asynchronous Random Cellular Automata Yellow Tiles

This is the sister pattern to red tiles, where the fitness function was designed to be very similar. Interestingly the global patterns are both also very similar, suggesting that evolution just fell into a local optima trap with the double mosaic pattern.



Rules p = 0 & C2 ≤ 0 ⇒ p = 3 p = 0 & C1 = 4 ⇒ p = 3 p = 1 & C1 ≥ 4 ⇒ p = 3 p = 1 & C0 ≤ 6 ⇒ p = 2 p = 2 & C1 = 6 ⇒ p = 2 p = 2 & C0 < 7 ⇒ p = 3 p = 3 & C2 ≥ 1 ⇒ p = 0 p = 3 & C3 = 0 ⇒ p = p

Adaptation to perturbations The yellow tiles pattern was again able to re-organise itself after being faced with perturbations, as can be seen in fig 6.20. Due to the nature of the random asynch updating scheme patterns took longer to form but were then of very high fitness. They also coped with much more consistency, with the other updating schemes, than patterns evolved with the other two schemes. This can be seen in fig 6.21. The asynch set and synch updating of yellow tiles both very quickly stabilized into a recognisable version of this pattern, as can be seen in fig 6.22, however they then both stayed exactly as this, where all cells are point attractors. When this pattern was updated with the rand asynch scheme it kept moving, albeit slowly, to a more intricate, fitter image. This can be thought of in terms of gradient descent, the deterministic updating systems very quickly get stuck in the local minima, whereas the rand asynch scheme keeps ‘trying to improve’ the image by continuing to randomly pick sections to assess and try to form more yellow tiles. This at least was how the final state was observed to be developing. This is very close to the reality observed in the artistic updating of images.

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6.3.2

Camouflage

In order to evolve a pattern that didn’t cheat the fitness functions restrictions on blanket formation, by only developing into a blanket once the time step where fitness was judged, a tougher penalty was enforced, such that a colour could not take over more than half the screen at judgement time. This did not completely rule out blanket formation, but it did mean it was considerably less likely. The resulting pattern from the following fitness function exhibited pseudo periodic behaviour such as those described by Di Paolo (Di Paolo, 2001). Camouflage like shapes formed with flickering boundary cells.


P C1 : if zero or one or two or three ≥ (N × M ) × 0.5

Adaptation to Perturbations The graphs in fig 6.24 and fig 6.25 show that this pattern was highly successful at retaining its fitness in the face of perturbations in cell state and in updating scheme.

6.4

Pheromonal Agent Design

6.4.1

Spirals

Using a fitness function that rewarded for a pixel to be partially surrounded by a specific colour other than its own, led to an interesting spiral pattern. When analysed the rules were particularly curious in their simplicity. The agents were only actually ever implementing one rule. The second rule, that if C0 is less than or equal to eight, which of course it always


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was, occurred above any other rules meaning that, through the hierarchy system, the others were made obsolete. So essentially the agents were always leaving pheromone and always moving away from it. What emerged from this very simple set up was a spiralling pattern, interestingly similar to that of the social amoebae pictured in fig 2.1, especially as it seems to be the opposite signalling system to that currently proposed.

Fitness function: RC1 : if C1 ≥ 5 & p 6= 1 RC2 : if C2 ≥ 5 & p 6= 2 RC3 : if C3 ≥ 5 & p 6= 3

P C1 : if zero or one or two or three ≥ (N × M ) − 30 P C2 : if TIME = 0

Rules: • C1 ≥ 2 ⇒ p = p, move away from pheromone, leave plume • C0 ≤ 8 ⇒ p = 3, move away from pheromone, leave plume • C3 = 0 ⇒ p = 2, move away from pheromone • C0 > 7 ⇒ p = p, move towards pheromone, leave plume • C2 > 0 ⇒ p = p, move away from pheromone • C3 ≤ 4 ⇒ p = p, move towards pheromone • C0 > 4 ⇒ p = p, move away from pheromone, leave plume • AGEN T S = 18 • T IM E = 11 • Q = 7.408590 • D = 3.661763

6.4.2

Coloured Spirals

A fitness function very close to the previous one was explored next, to try to evolve a pattern that used more than two of the available four colours. What occurred, interestingly, was a pattern very similar to the spirals pattern described above, except that the ‘trail’ that the agents were leaving was two tone.


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CHAPTER 6. EVOLUTIONARY EXPERIMENTS Fitness function RC1 : if C1 ≥ 5 & p 6= 1 & p 6= 0 RC2 : if C2 ≥ 5 & p 6= 2 & p 6= 0 RC3 : if C3 ≥ 5 & p 6= 3 & p 6= 0

P C1 : if zero or one or two or three ≥ (N × M ) − 30 P C2 : if TIME = 0

Rules • C1 = 7 ⇒ p = 1, move towards pheromone, leave plume • C2 = 5 ⇒ p = p, move away from pheromone • C1 < 0 ⇒ p = 2, move away from pheromone, leave plume • C3 = 0 ⇒ p = 3, move away from pheromone, leave plume • C1 ≤ 5 ⇒ p = 1, move away from pheromone • C3 = 7 ⇒ p = 3, move away from pheromone, leave plume • C0 ≥ 0 ⇒ p = p, move away from pheromone, leave plume • AGEN T S = 18 • T IM E = 16 • Q = 2.116669 • D = 4.098941 Again, most of the rules correspond to junk DNA, only two of the rules were ever executed. The fourth and fifth were the only necessary rules for this pattern. When there was no colour 3 then the pixel was changed to colour 3 and a plume signal was dropped. If some colour 3 was present then the pixel was changed to colour 1 and no plume was dropped. Only after many time steps and if there were many agents would there be any possibility of the other rules coming into play, but even then, as the agents were constantly trying to avoid each other there was little chance that there would ever be more than five colour 1 pixels surrounding an agent, which would be the necessary condition to break out of the two rule cycle. The spiralling pattern was notably less rigid, agents moved for longer in the direction of another agent before turning, and often lines met, which didn’t occur at all to start with in the previous pattern. This can be attributed to the halved number of plumes being dropped and also to the fact that when a plume was dropped there was more than three times less pheromone than was dropped by agents in the first spiralling pattern. Neither Agent patterns discussed here could cope with the sort of perturbations that the CA patterns could, this is most probably due to the initial blanket CA they were evolved with causing them to only develop rules to cope with this situation. It would be a next step to evolve agent systems with paint spots already on the blank canvas, as it were, so that they would be able to cope when mutations occurred at later stages.

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Chapter 7

The Sense of Beauty: Reactions, Opinions and Aesthetics “...the questions that most press upon us; namely, how an ideal is formed in the mind, how a given object is compared with it, what is the common element in all beautiful things ... and finally, how we come to be sensitive to beauty at all, or to value it. These questions must be capable of answers, if any science of human nature is really possible. ” (Santayana, 1955) Pp 10. There is a whole wealth of knowledge concerning aesthetic sense, and it is unfortunately beyond the scope of this paper to give it the attention it deserves here, for it is foolish to study aesthetic production separately from aesthetic sense. One particular insight that is reassuring to the plight of artificial art is that objects are beautified by the accrued meanings of observers and not by some intrinsic meaning or intention in the form itself. This point, in (Santayana, 1955) is illustrated by the example of a sunset. “The colours of the sunset have a brilliancy that attracts the eye; while the many associations of the evening and of heaven gather about this kindred charm and deepen it.” Pp 48. This means that although there must be some inherent perceptual pleasure to be taken in the object or form, it needn’t have been generated in a vitalistic vein, by a creative artist with a conscious impenetrable plan, to be beautiful. One fascinating theory on the origin of aesthetic sense, not least because its formation predates any artificial life theories on evolution such as (Harvey, I., 1997)1 , is that aesthetic sense is a bi-product of evolution, due to it not being optimisation. After describing an optimised system for reproduction and mate selection, Santayana in (Santayana, 1955) makes the point that “If this ideal had been reached, the instinct, like all those perfectly adjusted, would tend to become unconscious; and we should miss those secondary effects with which we are exclusively concerned in aesthetics. For it is precisely from the waste, from the radiation of the sexual passion, that beauty borrows warmth.” Pp 38. This rather suggests that using a sexual selection mechanism in evolution as opposed to the natural selection method used in this project and letting aesthetic sense evolve with the aesthetic production method, might eradicate the difficulties in fitness function definition. Overall the general reception of the images generated through this project was positive, smudged ink and the asynch set updating of Conways game of life being the general favourites from the hand designed systems, and spirals from the evolved designs, see plates I, X and VII. In an exhibition sense, the developmental period of patterns tended to attract more attention than the stable states, which relates to Paul Brown’s observations of his own work detailed in section 2.3. This was unintended but a factor that was unavoidable when using a projector, which was the case at the Blip installation and at the ICA. Had the patterns been mounted as prints, movement would not have been expected. “Overall I thought the designs played a key role in understanding the principles we were trying to apply to live dance and music. It allowed the audience to see a quick, more schematic version of the emergence principles that would then be enacted in different ways by the dancers/singers. Because of the fact that human beings are harder to control (sadly...), the emergent properties of the ’games’ set 1 Santayana

(1955) was originally printed in 1896

CHAPTER 7. THE SENSE OF BEAUTY: REACTIONS, OPINIONS AND AESTHETICS 44

into motion were less obvious and slower to take shape than with a computer model. ” Daniel Biro, Music Coordinator for the ICA Emergence Workshop 2 . The reaction of dancers at the ICA workshop to the explanation of emergence as a scientific concept was initially complete puzzlement and then the realisation came that we were simply saying in a different language concepts that they took for granted, and that were highly established already within their particular field. This highlighted the necessity for a greater communication between the various ‘ivory towers’ that disciplines endeavour to build for themselves, as ideas and concepts that form within one domain can lie dormant for centuries, due to a lack of communication, before their poignancy and relevance for another field is discovered - reinventing the wheel everytime. Sections chosen to increase the aesthetics of balance and arrangement and to highlight interesting emergent patterns, not needed so much in agent designs, tended to be easier for observers to appreciate. “...the photoshop versions are probably a bit nicer. But the kinds of manipulations you’ve made to ‘prettify’ them could probably be automated and even evolved...” Peter Bentley 3 .

2 quoted 3 quoted

from correspondence 28/08/02 from correspondence 13/08/02

Chapter 8

Conclusions and Future Work Although very simple systems, without the use of pheromones, asynchronous updating or evolution could generate aesthetic patterns, the defining of such rules systems from scratch was so close to impossible, by the, albeit unsatisfying, definition of emergence (Bentley, 2002b), and unrelated to the true processes involved in design by the artist or nature, that it should be discarded as a general approach to aesthetic pattern formation modelling. This project has confirmed the suspicion that the evolution of asynchronously updated systems (CA’s or agents), in particular random asynch updating, is a better generic method for the production of adaptive aesthetic patterns and images, in agreement with observations made of the artistic process. There must be a similarity in the genotypes of patterns with similar phenotypes otherwise the evolutionary process invoked in this project would not work. This was something that was not known at the outset of this project. Although cellular automata rules have been evolved to perform computations they have not, it would seem, been evolved to form aesthetic patterns, and the same is true of agent pheromonal signaling rules with adaptive rules for the leaving of ‘paint trails’. It was also unknown whether evolution would be able to find any rule sets robust enough to cope with the asynchronous set and random updating schemes and the asynchronous nature of the agent design system. Through this project it is clear that evolution can find robust solutions to form patterns in the face of random initial conditions, a random updating scheme and random perturbations as long as, throughout the evolutionary process the population is exposed to randomness in the initial conditions and in the updating scheme. The choice of time step for testing the fitness of the patterns played a crucial role in the type of pattern that formed. If the fitness was judged too early then the pattern could still dissolve away into a blanket state and if it was too late then it rewarded for patterns with very long developmental periods. It would be interesting to investigate the developmental stage further to see what other catagories of patterns occur with different fitness evaluation schemes. Perhaps even testing the fitness at several different time steps, for different fitness functions, could reveal patterns that can alter their basic properties over time, metamorphosis patterns, such as the 3-stager agent pattern shown in plates XII and XIII. It would be highly relevant to test other random asynchronous updating schemes as a future extension, especially as the replacement of cells in the asynch rand system used in this project may well have been the cause of the elongated development times of patterns, in comparison with the other two schemes. In agreement with Peter Bentley’s suggestion, evolving the colour choice and rendering effects etc... to be unique to the pattern would be a next natural step. It would be interesting to see if evolution comes up with similar rules to those in colour theory. This, however would require a much deeper analysis of the aesthetic properties of the patterns, and perhaps the implementation of a sexual selection evolution such as described in section 7 as defining a sound aesthetics fitness function is still a very real obstacle. Although reaction diffusion experiments (in Appendix A) stood to defend the principle idea that diffusion of chemicals could be involved in the generation of patterns, the diffusion used in the agents system was not of an inhibitory nature. The agents reacted to the diffusing chemicals, but they did this in a constant way, there was no threshold imposed. It would be interesting to see the difference in pattern formation that the use of a signalling system that mimicked Turings activator-inhibitor mechanisms would cause.

CHAPTER 8. CONCLUSIONS AND FUTURE WORK

In the evolved pheromonal agent design experiments, the only options for movement were move to and move away from pheromone. There is alot of scope to extend this simplified system to incorporate more intricate signaling, and also the possibility of movement based on the state of the pixels around the agent, independent of the pheromone. This was the case in the pheromonal set agent rules experiments, such as the pheromonal implementation of the diagonal reticulation rule set shown in plate XIV. The signalling system that was implemented can be seen as a slight detraction from the initial premise of this paper, based on the artists updating of paintings outlined in section 2.2.1, where it was felt that updating of images should take place asynchronously but where all areas have equal chance of being updated in each cycle of updating the whole canvas. With the pheromonal cues set so that agents were attracted to one another, after a few time steps there were areas that would have no chance of being updated. For this reason, as the agent updating system stands, the random asynchronous updating used in the evolved CA’s can be seen as a closer analogy of the painting process. However the pheromonal cues played a large part in keeping the spatial balance of the image aesthetic. The CA had no positional information being transmitted and so although there could be pleasing sections, chosen by the human eye, generally the overall image was not aesthetically satisfying. The Agent images with pheromonal signalling also had sections that were pleasing, but in general they had a good overall balance displayed in the total image. Inspiring insights can come from interdisciplinary research. There is a great deal of scope to extend this work and investigate the variety of curious properties of aesthetic patterns and their hypothesised evolutionary, asynchronous, distributed formation process. “Maybe this is how science progresses: an initial mystery based on ignorance, then a discovery and a learning stage, and a final mystery based on knowledge. Sounds a bit like art.” Tchalenko (2002)Pp 25.

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Bibliography Ades, D. (1995). Dali. World of Art Series, Thames and Hudson Ltd. Bentley, K. (2002a). Artificial Forms. EASy MSc Simulation of Adaptive Behaviour mid-term paper. COGs University of Sussex. Available at (29/8/02): www.cogs.susx.ac.uk/users/masters/easymcs2001/kate. Bentley, K. (2002b). The Problems Faced When Defining Emergence. EASy MSc History and Philosophy of Adaptive Systems Mid-term Paper. COGS University of Sussex. Available at (29/08/02): www.cogs.susx.ac.uk/users/masters/easymsc2001/kate. Bentley, P. (2002c). Aspects of evolutionary design by computers. Computer Science Department, UCL, London. http://www.cs.ucl.ac.uk/staff/P.Bentley/ (visited: 29/08/02). Bentley, P. and Kumar, S. (1999). Three ways to grow designs: A comparison of embryogenies for an evolutionary design problem. In et al., B., editor, Proceedings of the Genetic and Evolutionary Computation Conference, pages 35–43. Bentley, P. J and Corne, D. W.. (2002). Introduction to creative evolutionary systems. In Bentley, P. J and Corne, D. W., editors, Creative Evolutionary Systems, pages 1–76. Morgan Kaufman. Bonabeau, E. (1997). From classical models of morphogenesis to agent-based models of pattern formation. In Langton, C., editor, Artificial Lfe 3, pages 191–211. Massachusetts Institute of Technology. Bonabeau, E., Dorgio, M., and Theraulaz, G. (2000). Inspiration for optimisation from social insect behaviour. Nature, 406:39–42. Bonabeau, E., Guerin, S., Snyers, D., Kuntz, P., and Theraulaz, G. (1992). Three dimensional architectures grown by simple stigmergic agents. Biosystems, 56:13–32. Broughton, T., Coates, P., and Jackson, H. (2001). Exploring 3d design using lindenmayer systems and genetic programming. CECA University of East London, London. http://ceca.uel.ac.uk/cad/’ visited 2002-03-14. Coates, P and Carranza, P, M. (2001). Swarm modelling: The use of swarm intelligence to generate architectural form. CECA University of East London, London. http://ceca.uel.ac.uk/cad/ : visited 2002-03-14. Dawkins, R. (1991). The Blind Watchmaker. Penguin Books. Di Paolo, E. A. (2001). Rhythmic and non-rhythmic attractors in asynchronous random boolean networks. To appear in BioSystems. Donaldson, J. (1970). The Elements of Beauty. Also, Reflections on the harmony of sensibility and reason. Garland Publishing, New York. Dorin, A. (2001). Aesthetic fitness and artificial evolution for the selection of imagery from the mythical library. To appear in Advances in Artificial Life Proc 6th European Conf on Artificial Life. Driesch, H. (1901). Die Organischen Regulationen. Leipzig. Frisch, K, V. (1975). Animal Architecture. Hutchinson of London, 1st edition. Grassé, P.-P. (1959). La Reconstruction du nid et les coordinations inter-individuelles chez Bellicositermes natalensis et Cubitermes sp. La théorie de la stigmergie:. Elsevier Science. Graven, J. (1968). Non Human Thought. Arlington Books, London. Harvey, I. (1997). Cognition is not computation; evolution is not optimisation. 1997: 685-690. In ICANN, pages 685–690. Harvey, I. and Bossomaier, T. (ECAL97). Time out of joint: Attractors in asynchronous random boolean networks. In Husbands, P. and Harvey, I., editors, Proceedings of the Fourth European Conference on Artificial Life, pages 67–75.

BIBLIOGRAPHY

Hornby, G. and Pollack, J. (2001a). The advantages of generative grammatical encodings for physical design. DEMO Lab, Brandeis University, Waltham, MA. Hornby, G. and Pollack, J. (2001b). Evolving l-systems to generate virtual creatures. Elsevier Science Ireland. Kauffman, S. (1984). Pattern generation and regeneration. In Malacinski, G. M. and Bryant, S. V., editors, Pattern Formation, pages 73–102. Macmillan Publishing Company, New York. Larmann, R. (2002). Art studio chalk boardcolour wheel and colour complements. http://www.saumag.edu/art/studio/chalkboard/c-wheel.html (visited: 20/08/02). Levy, S. (1992). Artificial Life: The Quest for a New Creation. Penguin Books, London. Lindenmayer, A. (1968). Mathematical models for cellular interaction in development, parts i and ii. Theoretical Biology, 18:280–315. Murray, J. D. (1989). Mathematical Biology. Springer-Verlag, Berlin. Pask, G. (1962). Principles of Self-organisation, chapter A Proposed Evolutionary Model, pages 229–253. Symposium Publications Division, Pergamon Press, Oxford Pp. Santayana, G. (1955). The Sense of Beauty: Being the Outline of Aesthetic Theory. Dover Publications, 1st edition. first published by Charles Scribner’s and Sons in 1896. Sims, K. (1991). Artificial evolution for computer graphics. In Computer Graphics (Siggraph ’91 proceedings), pages 319–328. Sims, K. (1992). Interactive evolution of dynamical systems. In Varela and Bourgine, editors, Towards a Practice of Autonomous Systems:Proc of first international conf of Artificial Life, pages 171–178. Sumpar, M. (1984). Pattern formation during embryogenesis of the multicellular organism Volvox. In Malacinski, G. M. and Bryant, S. V., editors, Pattern Formation, pages 197–212. Macmillan Publishing Company, New York. Tchalenko, J. (2002). The painters eye revisited. Science and Art: Seeing Both Sides, Wellcome News Supplement, The Wellcome Trust, 5:24–25. Turing, A, M. (1952). The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. of London, Series B:Biological Sciences, 237:37–72. Whitelaw, M. (2001). Breeding aesthetic objects: Art and artificial evolution. Available at: citeseer.nj.nec.com/399361.html. Wolpert, L. and Stein, W, D. (1984). Positional information and pattern formation. In Malacinski, G. M. and Bryant, S. V, editors, Pattern Formation, pages 3–22. Macmillan Publishing Company, New York.

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Appendix A

Appendix: Reaction Diffusion A.1

Model

The reaction diffusion model used was very simple, employing only integer values for the rate of diffusion and only diffusing in one direction: right. See fig A.1 for an illustration of how reaction diffusion works. The experiments performed with reaction diffusion systems mainly involved only one type of diffusing chemical and two types of cell, however it is very easy to add one more element, another cell type, a diffusing activator etc... and the level of complexity of the patterns can increase by an order of magnitude. The basic system worked by the following rules: if the cell is of type 1 and the left hand cell has only 2 as the amount of chemical being diffused then the cell is not inhibited and becomes cell type 2, if the cell type is 2 then the cell drops a plume of chemical to diffuse of size 10, at all times the chemical diffuses to the right at a rate of 1 for each cell it passes.

Figure A.1: Reaction Diffusion. When the threshold is set to 1.5, all cells receiving less pheromone than that are not inhibited from becoming cell type A

A.2

Results

After implementing the straight forward reaction diffusion system described in section A the pattern shown in fig A.2(a) formed. Then another cell type was added, that diffused its own inhibitor. This new cell type took precedence over the development of a cell into type 2 or 3. The pattern that formed can be seen in fig A.2(b)

(a)

(b)

Figure A.2: Striping patterns generated using Turings reaction diffusion model

Appendix B

Colour Plates

PLATES

51

Plate I: Asynch set CA Game of Life

Plate II: Asynch set CA Cow Print

Plate III: Asynch rand set CA Reticulation, enhanced section

PLATES

52

Plate IV: Evolved asynch set CA Spots, enhanced section

Plate V: Evolved asynch set CA Red Tiles, section

Plate VI: evolved rand asynch CA Camouflage, enhanced

Plate VII: Evolved pheromonal agents pattern Spirals, enhanced section

PLATES

53

Plate VIII: Agent design Diagonal Reticulation

Plate IX: Basic agent Diagonal reticulation, enhanced section

Plate X: Agents design with variable paint trail width Smudged Ink

PLATES

54

Plate XI: Agent Design psychadelic, using 90000 agents

Plate XII: Agent Design 3 stager, stage 1. Converged into a 3-cycle pattern

Plate XIII: Agent Design 3 stager, stage 2. Converged into a 3-cycle pattern

PLATES

55

Plate XIV: Agent design Diagonal Reticulation with pheromonal agents

Plate XV: Variation on agent design Diagonal Reticulation with pheromonal agents

Plate XVI: Evolved asynch set CA Red Tiles filter enhanced section

Plate XVII: Evolved synch CA Islands, filter enhanced

PLATES

56

Plate XVIII: Agent design psychedelic filter enhanced

Plate XIX: Evolved asynch set CA Mosaic, filter enhanced