Title: Snowflakes Post by: Tglad on July 19, 2014, 05:38:51 AM I found a way to make my previous binary rules fractals (https://sites.google.com/site/tomloweprojects/scale-symmetry/automataFinder) have hexagonal symmetry:
(http://4.bp.blogspot.com/-Gz39kKK5msw/U8kHEAvHGUI/AAAAAAAAAcM/172MAAMI0ug/s1600/snow1.png) (http://4.bp.blogspot.com/--biIF6SLa8I/U8kHHuIsymI/AAAAAAAAAck/c0NlNOhnRyM/s1600/snow4.png) (http://3.bp.blogspot.com/-LyED_TRiQ5o/U8kHJB1v6uI/AAAAAAAAAcw/oAztGw5OoYY/s1600/snow5.png) You can apply the system to a random start: (http://2.bp.blogspot.com/-pZ2k6AuqTOc/U8kUlx_w2eI/AAAAAAAAAds/ODjCw14OEOM/s1600/rand1.png) (http://1.bp.blogspot.com/-B33UiTgtdJk/U8kUpoAvj-I/AAAAAAAAAeQ/LwiJN4hptb0/s1600/rand5.png) (http://4.bp.blogspot.com/-H4innv3EUjE/U8kUpf6VaDI/AAAAAAAAAeM/TDW5k6_S_vA/s1600/rand7.png) I also tried using an even simpler formula, which also has some good results: (http://4.bp.blogspot.com/-_EyLhrXmzM8/U8nlYqcF5xI/AAAAAAAAAek/M-Rdz-GJC08/s1600/type2.png) (http://3.bp.blogspot.com/-ZS5wS22zG8g/U8nlZNtL7CI/AAAAAAAAAeo/fDBzmSQyh4U/s1600/type2b.png) (http://4.bp.blogspot.com/-1-APQeAFKDQ/U8nlZERpzPI/AAAAAAAAAew/AXTJoImX49A/s1600/type2c.png) (http://4.bp.blogspot.com/-5wv6LsLEFYQ/U8nlb0Ox07I/AAAAAAAAAe8/nEbt4hYcFhY/s1600/type2d.png) and applying this with a random seed, give a nice web-like effect: (http://4.bp.blogspot.com/-stvvmpC65XU/U8nlcJ1uhvI/AAAAAAAAAfA/0HFcdP9ebkc/s1600/type2rand.png) The trick to getting hexagonal (rather than square) symmetry is to actually make a 3d cubic fractal and the 2d image is a slice perpendicular to the long diagonal of the cube. Title: Re: Snowflakes Post by: matsoljare on July 19, 2014, 09:29:27 PM Fascinating, now can you animate them?
Title: Re: Snowflakes Post by: Tglad on July 20, 2014, 11:45:49 AM Maybe.. but no time to try unfortunately, it wouldn't be straightforward.
Title: Re: Snowflakes Post by: KRAFTWERK on July 20, 2014, 01:04:22 PM Lovely results! That third image with the "simpler" formula has parts which looks like a power 8 mandelbulb :o (with minibulbs)
Is it possible to go 3D? Title: Re: Snowflakes Post by: Tglad on July 21, 2014, 01:22:08 AM Yes, you construct a 4D grid, then run rule sets on the coarse set of 4d voxels to generate progressively half size voxels. Then a cross section of the long diagonal (x + y + z + w = 0) gives a 3d fractal. I'm pretty sure it would give octahedral symmetry... which isn't a lot more than cubic that I have already (8 vs 6 sides), but it is different and might look cool. There is a very interesting 'grid' in 4d called D4 which may give more symmetry in its 3d cross section... but who knows. |