はじめまして

Here be generative images. Start by looking at the examples below. Then, maybe browse through some of the posts, with more to explore and greater details. Almost all images have links to higher resolution versions and there is source code to try out.

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show."

– Betrand Russel

Mandelbrot Set

The Mandelbrot set is the set of complex numbers for which the function does not diverge when iterated from, i.e., for which the sequence, etc., remains bounded in absolute value. Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot. Wikipedia

Buddhabrot

The Buddhabrot is the probability distribution over the trajectories of points that escape the Mandelbrot fractal. Its name reflects its pareidolic resemblance to classical depictions of Gautama Buddha, seated in a meditation pose with a forehead mark (tikka), a traditional topknot (ushnisha) and ringlet hair. Wikipedia

Julia Set

In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets (Julia “laces” and Fatou “dusts”) defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is “regular”, while on the Julia set its behavior is “chaotic”. Wikipedia

Cellular Automata

A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computer science, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Wikipedia