Mosely snowflake

7/29/2017

Mosely snowflake - Wikipedia

Mosely snowflake From Wikipedia, the free encyclopedia

The Mosely snowflake (after Jeannine Mosely) is a Sierpiński– Menger type of fractal obtained in two variants either by the operation opposite to creating the Sierpiński-Menger snowflake or Cantor dust i.e. not by leaving but by removing eight of the smaller 1/3-scaled corner cubes and the central one from each cube left from the previous recursion (lighter) or by removing only corner cubes (heavier). In one dimension this operation (i.e. the recursive removal of two side line segments) is trivial and converges only to single point. It resembles the original water snowflake of snow. By the construction the Hausdorff dimension of the lighter snowflake is

and the heavier .

Footnotes

Mosley snowflake formation during four recursion steps

References Slocum, Jerry (2011), The Mosely snowflake sponge: construction guide, California : USC Libraries. Retrieved from "https://en.wikipedia.org/w/index.php? title=Mosely_snowflake&oldid=780328207"

This page was last edited on 14 May 2017, at 10:29. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.

https://en.wikipedia.org/wiki/Mosely_snowflake

Mosley snowflake (heavier) formation during four recursion steps

1/1

7/29/2017

Menger sponge - Wikipedia

3. Wolfram Demonstrations Project, Volume and Surface Area of the Menger Sponge (http://demonstrations.wolfram.com/Volume AndSurfaceAreaOfTheMengerSponge/) 4. University of British Columbia Science and Mathematics Education Research Group, Mathematics Geometry: Menger Sponge (http://scienceres-edcp-educ.sites.olt.ubc.ca/files/2012/0 8/sec_math_geometry_menger.ppt) 5. Chang, Kenneth (27 June 2011). "The Mystery of the Menger Sponge" (http://nytimes.com/2011/06/28/science/28math-menge r.html). Retrieved 8 May 2017 – via NYTimes.com. 6. Tim Chartier. "A Million Business Cards Present a Math Challenge" (http://huffingtonpost.com/tim-chartier/a-million-busi ness-cards_b_6128880.html). Retrieved 2015-04-07. 7. "MegaMenger" (http://www.megamenger.com/). Retrieved 2015-02-15. 8. Robert Dickau (2014-08-31). "Cross Menger (Jerusalem) Cube Fractal" (http://www.robertdickau.com/jerusalemcube.html). Robert Dickau. Retrieved 2017-05-08. 9. Wade, Lizzie. "Folding Fractal Art from 49,000 Business Cards" (https://www.wired.com/2012/09/folded-fractal-art-cards). Retrieved 8 May 2017. 10. W., Weisstein, Eric. "Tetrix" (http://mathworld.wolfram.com/Tetr ix.html). mathworld.wolfram.com. Retrieved 8 May 2017.

Sierpinski-Menger snowflake. Eight corner cubes and the one central cube are kept each time at the lower and lower recursion steps. This peculiar three dimensional fractal has the Hausdorff dimension of the natively two dimensional object like the plane i.e. log 9 log 3 =2

Iwaniec, Tadeusz; Martin, Gaven (2001), Geometric function theory and non-linear analysis, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, ISBN 978-0-19-850929-5, MR 1859913 (http s://www.ams.org/mathscinet-getitem?mr=1859913). Zhou, Li (2007), "Problem 11208: Chromatic numbers of the Menger sponges", American Mathematical Monthly, 114 (9): 842

External links Menger sponge at Wolfram MathWorld (http://mathworld.wolfram.com/MengerSponge.html) The 'Business Card Menger Sponge' by Dr. (http://theiff.org/oexhibits/menger01.html) Jeannine Mosely – an online exhibit about this giant origami fractal at the Institute For Figuring An interactive Menger sponge (http://www.mathematik.com/Menger/Menger2.html) Interactive Java models (http://ibiblio.org/e-notes/3Dapp/Sponge.htm) Puzzle Hunt (http://santisan.free.fr/coco/extras2.htm) — Video explaining Zeno's paradoxes using Menger– Sierpinski sponge Menger Sponge Animations (http://www.pure-mirage.com/html/Optimized%20Menger%20Sponges.htm) — Menger sponge animations up to level 9, discussion of optimization for 3d. Menger sphere (https://www.flickr.com/photos/fpsunflower/337024546/), rendered in SunFlow Post-It Menger Sponge (https://www.flickr.com/photos/rougeux/sets/72157621702780335/) – a level-3 Menger sponge being built from Post-its The Mystery of the Menger Sponge. (https://www.nytimes.com/2011/06/28/science/28math-menger.html?_r =1) Sliced diagonally to reveal stars Number of cards required to build a Menger sponge of level n in origami (http://oeis.org/A212596) Woolly Thoughts Level 2 Menger Sponge (http://www.woollythoughts.com/menger.html) by two "Mathekniticians" Retrieved from "https://en.wikipedia.org/w/index.php?title=Menger_sponge&oldid=787925863" https://en.wikipedia.org/wiki/Menger_sponge

4/5

7/29/2017

Tree-looking variation of Sierpinski sponge obtained by recursively removing the 8 corner, 6 face-centered and the central cubes (totally 15 cubes) with the fractal dimension

Sierpinski sponge - Wikipedia

Another tree but Pine-like looking variation obtained by recursively removing 12 edge cubes with the fractal dimension

Retrieved from "https://en.wikipedia.org/w/index.php?title=Sierpinski_sponge&oldid=734635847"

This page was last edited on 15 August 2016, at 17:59. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.

https://en.wikipedia.org/wiki/Sierpinski_sponge

2/2