Image of the Week #185

A view from the quintic Mandelbrot set.


Generating Complex Ecologies in a Computer

topThis 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.

Continue reading

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.