Logo by tomot - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Follow us on Twitter
 
*
Welcome, Guest. Please login or register. October 20, 2020, 05:22:26 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Anti-fractal?  (Read 3466 times)
0 Members and 1 Guest are viewing this topic.
heneganj
Guest
« on: February 23, 2007, 01:39:27 PM »

I stumbled across this interesting article.  What do you call something that is infinitely complex but not self-similar?  I like the name 'anti-fractal', but would 'chaotic' suffice?  Does chaos imply lack of order?  These patterns are completely mathematically ordered...

http://www.reuters.com/article/scienceNews/idUSN2245118920070222?src=022207_1643_ARTICLE_PROMO_also_on_reuters&pageNumber=1

Medieval Muslims made stunning math breakthrough



WASHINGTON (Reuters) - Magnificently sophisticated geometric patterns in medieval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday.

By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasicrystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science.

Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry.

Logged
gandreas
Explorer
****
Posts: 53



WWW
« Reply #1 on: February 23, 2007, 04:41:49 PM »

I stumbled across this interesting article.  What do you call something that is infinitely complex but not self-similar?  I like the name 'anti-fractal', but would 'chaotic' suffice?  Does chaos imply lack of order?  These patterns are completely mathematically ordered...

In complexity theory, "chaos" is that fine (or sometimes broad) line between "order" and "random".  (For a good introduction, check out Stuart Kauffman's "At Home in the Universe")

And the term "Fractal" derives from fact that it has fractional dimensionality - for example, that jagged line that represents the shoreline isn't straight (1 dimensional), yet it doesn't actually fill 2 dimension, but is like (for example) 1.3245 d.  It does not require self similarity (there are many fractals that are not self similar, but they aren't all that aesthetically interesting for the most part either)

And speaking of Islamic star patterns, Craig Kaplan wrote a Java based applet that lets you experiment with them (and has good paper on his techniques at http://www.mi.sanu.ac.yu/vismath/kaplan/index.html - his web site also has a bunch of other interesting material that isn't directly fractal related, but is definitely useful for those interested in the whole "procedural/generated art".
Logged
heneganj
Guest
« Reply #2 on: February 25, 2007, 10:10:15 AM »

Excellent thanks for the link.  Although it is repeating (tiling) the pattern.  Would be nice to see a non-repeating version of this program.
Logged
bradorpoints
Guest
« Reply #3 on: April 11, 2007, 04:40:58 PM »

Good article; it got me interested.  I've often wodnered about such patterns for the mid and far east.  It didn't have any detail (for good reason).  Here's a link to a paper which goes into some of the how's and why's. 

http://www.physics.harvard.edu/~plu/publications/Science_315_1106_2007.pdf
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
partial anti-buddhabrot Images Showcase (Rate My Fractal) Freakadella 6 1537 Last post December 21, 2012, 06:05:13 PM
by Alef
To anti-alias, or not to anti-alias? Hit the button or leave it alone? Sterlingware « 1 2 » chaos_crystal 18 4058 Last post December 19, 2012, 08:01:11 PM
by chaos_crystal
3D Anti-buddhabrot Programming ker2x 7 1106 Last post July 29, 2014, 06:57:45 PM
by knighty
Anti-Gravity Antennae anti-attract an anti-gravity sphere Mandelbulber Gallery mclarekin 0 829 Last post August 31, 2014, 01:15:13 AM
by mclarekin
An Anti-Planck Field Protects An Orb Mandelbulber Gallery mclarekin 0 310 Last post May 31, 2015, 04:40:56 AM
by mclarekin

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.116 seconds with 28 queries. (Pretty URLs adds 0.006s, 2q)