Previously featured artist: Jos Leys. In his own words:

I am a mechanical engineer and have always had an interest in
mathematics. That is why, for over five years now, I enjoy working with Ultra Fractal mostly because one can write one's own algorithms. I am always on the look-out for mathematical theories that can produce images that no one has ever seen before. Translating these into Ultra Fractal code is my main hobby. I am 53 years old and live near Antwerp, Belgium with my wife Gilberte and our two cats.

(Note: Most of the formulas used by Jos Leys are not in the public domain so you should not expect to be able to recreate these images immediately. However, Ultra Fractal users have access to a very large database of public formulas, of which some are capable of producing similar results.)

Hyperbolic animation
A hyperbolic tiling of the Poincaré disc...
Kleinian group
A Kleinian group, a very special kind of fractal...
Spiral surface
Another exercise in viewing 3D objects...
Trefoil knot
This was an exercise in the presentation of 3D objects...

Some of the things I have programmed are 3D, so they beg to be animated for a really good view. It was possible to make animations using older versions of Ultra Fractal, but it was quite cumbersome and required manipulation of parameter files in a word processing program. The built-in animation features of version 4 make this obsolete, and animation is now very easy!

 
Perspective
Raytracing routines involving light shadows.
Alexander's Horn
Alexander's horned sphere: a famous object in topology...
Circle inversions
Circle inversions of a 3D object...
Rolling circle inversions
The basic object here is repeated infinitely using a circle inversion transformation...
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