## Sunday, December 25, 2011

## Friday, December 23, 2011

## Monday, December 19, 2011

## Thursday, December 15, 2011

## Wednesday, December 14, 2011

"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."

## Tuesday, December 13, 2011

## Monday, December 12, 2011

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

By Joe Bartholomew

By Joe Bartholomew

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.

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.

## Thursday, December 1, 2011

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