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2015-06-23 Inceptionism

2015-04-26 Exhibit

2014-12-14 Earth View

2014-10-05 Iterations

2014-08-24 Frank Berg

2014-08-13 Bridges 2014

2014-04-09 High ball stepper

2014-03-30 Appolonian gaskets

2014-03-02 Michael Faber

2014-02-23 New panorama applet

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A blog about algorithmic art and fractal aesthetic. Click here to subscribe to the RSS feed.

October 5th 2014

Iterations

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 following 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. Click on the pictures to get to the page of the work, where you can either zoom into the picture, or see the whole spherical pattern panoramically.

20140905-1. A dense Nova Julia set, first iteration.

20140906-1. A dense Nova Julia set, fourth iteration.

20140907-1. A dense Nova Julia set, sixth iteration.

20140908-1. A dense Nova Julia set, eighth iteration.

20140909-1. A dense Nova Julia set, twelfth iteration.