Title: Space filling 2d patterns without mirrors Post by: s31415 on July 11, 2011, 12:06:53 AM Hi there,
Just to mention a recent blog post http://www.algorithmic-worlds.net/blog/blog.php?Post=20110710 explaining how to use the same ideas as in the Ducks algorithm to create radically new space-filling 2d fractal patterns. I say "radically" different, because they do not display the mirror symmetries of Ducks and its cousins. Interestingly, these patterns are very reminiscent of Julia patterns, but they are space filling. You can see pictures here: http://www.algorithmic-worlds.net/expo/expo.php?CollSearch=0&Collection=Inverted+Julia I didn't write explicitly the algorithm in the post... But the information should be sufficient for people here to figure out their own version. :) As it uses the squaring operation, it does not have a 3d equivalent, unfortunately. Best, Sam Title: Re: Space filling 2d patterns without mirrors Post by: Kali on July 11, 2011, 03:21:34 PM Very interesting, Sam. Nice patterns. I've done something like this using 1/(z*z+c), but no sure if it's the same or related.
This is one of my images using that formula and "exponential smoothing" for coloring: (-0.067077429209711, 0.65224480299896) (http://img4.imageshack.us/img4/1747/invjulia.jpg) (http://img4.imageshack.us/i/invjulia.jpg/) And this is the same formula but with a coloring algorithm I made that renders this bright "wires": http://fractkali.deviantart.com/gallery/29839985?offset=0#/d3dyose Still prefer the patterns using mirrors, and I think there must be some nice unexplored possibilities with them ;) Title: Re: Space filling 2d patterns without mirrors Post by: s31415 on July 11, 2011, 04:43:52 PM Yes, it's related, I'm using inversions as well. The iteration count is a bit low, but it does look space filling. Nice! |