All my recent works are obtained by iterating rational maps of the Riemann sphere to itself that have dense chaotic orbits. Each point on the sphere corresponds to an orbit, and is essentially colored according to the mean distance of the orbit to a given point on the sphere. Because of the dense chaotic orbits, dense fractal patterns appear in this way. Related patterns appear when one considers iterations of the original map. One can picture the nth iteration of the map by taking into account only every nth point in the orbit when computing the average distance of the orbit. The resulting patterns are closely related, their structures disintegrating slowly as n is increased.

The above series of works exemplifies this phenomenon. The rational map is a Nova map with exponent 4. The images depict respectively the 1st, 4th, 6th, 8th and 12th iteration of the Nova map.

(Source: algorithmic-worlds.net)

20110425-1. Another old image now available as a very high resolution zoomable picture.

20110425-1. Another old image now available as a very high resolution zoomable picture.

A blog post about Lattès Julia sets, which I have been picturing recently.

20121110-1. Click for a zoomable image.
20121020-1, click for a zoomable image.
20120628-1, click for a zoomable image.

20120628-1, click for a zoomable image.

20120626-1. Click for a zoomable image. 

20120626-1. Click for a zoomable image. 

20120603-1. Click for a zoomable image.

An animation based of periodic dense Julia patterns. Check this blog post for more information:

http://algorithmic-worlds.net/blog/blog.php?Post=20120330

(Source: vimeo.com)

A 3d printed dense Julia set. Information here, more photos here. 

A 3d printed dense Julia set. Information heremore photos here