Wednesday, December 14, 2011

Spherical version of the 2.5 dimensional Julia Set
The basic inverse quaternion julia set.
Ikeda Attractor by Paul Bourke
This image was created by Jonathan McCabe from a cellular automata program he wrote.
"Each pixel represents the state of the 4 cells of 4 cellular automata, which are cross coupled and have their individual state transition tables. There is a "history" or "memory" of the previous states which is used as an offset into the state transition tables, resulting in update rules which depend on what has happened at that pixel in previous generations. Different regions end up in a particular state or cycle of states, and act very much like immiscible liquids with surface tension."
Circles generated by Mobius transform by Ed Pegg Jr.

Tuesday, December 13, 2011

3D totalistic cellular automata
John Conway's Game of Life is a cellular automaton in which randomized cells evolve according to a fixed set of rules. Usually this evolution appears as an animation, here we see the evolution through time in a still image, with height from top to bottom corresponding to subsequent generations of cells.

Monday, December 12, 2011

Quaternion Julia Fractals
"Girih tiles have interior angles that are multiples of π/5. In the examples shown here I’ve applied the girih concept to polygons with angles that are multiples of π/7."

By Joe Bartholomew
A 3-d model of tuna, anchovy and bluefish populations given certain parameters.
The Catalan numbers are a sequence of numbers, much like the Fibonacci numbers, which are given by the equation

Like the Fibonacci numbers, they too pop up all over the place, for example, the Catalan numbers correspond to the number of ways a regular n-gon can be divided into n-2 triangles.
Above is a visualization of the Catalan numbers.

By John C. Hart in 1989
Read more about quaternion fractals (and see more images) here and here.
A map of the internet by Barrett Lyon

Thursday, December 8, 2011

Snowflake hitting the ground
Photos by Andrew Osokin using a macro lens.