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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

2013-06-09 Variations on Nova

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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.

Picture of a Nova Julia set, by Samuel Monnier

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



Picture of a Nova Julia set, by Samuel Monnier

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



Picture of a Nova Julia set, by Samuel Monnier

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



Picture of a Nova Julia set, by Samuel Monnier

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



Picture of a Nova Julia set, by Samuel Monnier

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


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