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)

20140912-1. Click for a zoomable image. Nova fractal

20140912-1. Click for a zoomable image.

Nova fractal

20140911-1. Click for a zoomable image. Nova fractal.

20140911-1. Click for a zoomable image.

Nova fractal.

20140910-1. Click for a zoomable image. Nova fractal.

20140910-1. Click for a zoomable image.

Nova fractal.

20140909-1. Click for a zoomable image. Nova fractal.

20140909-1. Click for a zoomable image.

Nova fractal.

20140908-1. Click for a zoomable image. Nova fractal

20140908-1. Click for a zoomable image.

Nova fractal

20140907-1. Click for a zoomable image. Nova fractal

20140907-1. Click for a zoomable image.

Nova fractal

20140906-1. Click for a zoomable image.
20140905-1. Click for a zoomable image. Nova fractal

20140905-1. Click for a zoomable image.

Nova fractal

Anonymous said: Hello. Would it be ok to ask you how do you make your fractals to be able to zoom in? Do you render a very large image, and do something like Google Maps API?

Hello. Yes this is the same idea as google maps. You have to render a large image and then break it into a “pyramid of tiles”, so that only part of the tiles need to be loaded to display the location you’re zooming on, For that I use a little program that, at least at the time, was freely downloadable at Zoomify. To display the zoomable images, I am using the OpenZoom applet, which is no longer supported. Another one is OpenSeaDragon. There are also several websites that allow you to upload a big picture and display it as a zoomable image, see Extrazoom, Gigapan, Closr.