Over the past few years I have made a hobby of writing graphing software to generate these stills and animations.
I have long been a fan of abstract art, but using mathematics to generate it has been a very rewarding and
surprising process. It has allowed me to transform the creative process from a challenge of dexterity into an
entirely thought based pursuit.
Maths is beautiful to begin with — I'm just trying to find ways to illustrate that.
This fractal is based on the fractal flame algorithm. It is an iterated function system that I wrote that focuses on animating between spatial variations instead of interpolating between sets of equations as in the flam3 project and it's child, The Electric Sheep Screensaver. Motion blur is used to give the visualisation a much richer and more dynamic feel.
These fractals are julia sets. The colouring is done by mapping hue to density and cycling it using modulo arithmetic. The interesting textures are generated by mapping saturation and brightness to various formulas involving the argument of the density.
These visualisations are based on the popcorn algorithm. The animation was generated by using cosines to modulate the fractal parameters, giving the animation a sense that it is flowing, almost like water. Hue cycling is used to add visual appeal. This algorithm has a dark feel which makes it unique amongst most of my visualisation projects.
These are plasma fractals based on the Diamond-square algorithm. The algorithm is well suited to creating cloud-like imagery. The algorithm produces a density map. When mapped to hue and then cycled using modulo arithmetic it creates a lovely flowing visualisation giving the illusion of motion.
This was just a prototype of a recursive algorithm I wrote to generate a tree structure. This is the most neglected of all my fractal projects. It has great potential for creating plant-like structures and perhaps at a later date I will refine it to greatly surpass this basic mock-up.