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Most visualizations of the Lorenz attractor are of a long history of a single point after convergence to the attractor has occurred. I was interested in what the surrounding space looked like, so I randomly selected 20,000 starting points from a three dimensional Gaussian distribution with a standard deviation of 100. Each point was iterated, [...]

Relax to a slow flythrough of an interesting subset of the quaternion Julia fractals.

Ski lift operators have proved that it’s not only conidae snails who can produce the Sierpinski triangle in their natural environment.

My three dimensional unfolding of the quaternion Julia sets finally finished rendering.

This undulating plane is a visualization of all quaternion Julia sets.

These beautiful shapes are three dimensional slices of four dimensional objects known as quaternion Julia sets.

The patterns on this sea shell appear to be very similar to that of a mathematical structure called a Sierpinski triangle.