A view from the quintic Mandelbrot set.

# Pretty Pictures

# Image of the Week #184

A conjugate quintic Julia set. Reticulation rules!

# Image of the Week #183

A deep zoom into the cubic Mandelbrot with color and more color.

# Image of the Week #182

A Julia set with an added spin component. Whee!

# Image of the Week #181

Lurking deep in the Mandelbrot set…

# Generating Complex Ecologies in a Computer

This post is about some of Occupy Math’s current research. The picture at the left represents a 200×200 cell “ecology”. Each cell in the grid is occupied by one type of simulated critter. The critters compete with one another to take over cells (the rules for this are lower down in the post). The simulation is run for 1,000 seasons and one of the 40,000 creatures is mutated each season to create a new type of critter. We start with ten types of critters, but mutation sometimes drives the number of types of critters into the hundreds by season 1,000. The picture above is the state of the simulation, with different colors representing different critters, in the thousandth season. This project is generating a diverse collection of these small, complex artificial ecologies.

# Image of the Week #180

Golden medusa in the fifth order Mandelbrot set.

# Image of the Week #179

This week we have a combination of Newton’s method and Julia iterators that yield a type of object called a feather snake. The pallet is chosen to yield a number of contrasting regions.

# Image of the Week #178

This week, Occupy Math returns to Newton Space with some fractal microbes.

# Image of the Week #177

A complex view into a Newton’s method fractal.