Pattern Study - 1

I recently came across this interesting geometric pattern that involves squares (trapezoids, more precisely). This is an exploration of this pattern.

All illustrations on this page are programatically generated in your browser. View source to see more.

This pattern is made up of several alternating squares, each containing a number of rhombuses.

The different elements become more clear when the squares are randomly coloured.

This is an individual box.

It's constructed as illustrated below, by inscribing successively smaller rhombuses inside the original square. Each of the rhombuses are slightly rotated with respect to the previous one.

Alternate squares are rotated in opposite directions.

It is interesting how a spiral emerges from a figure constructed entirely out of straight lines.

Finally, I used an animation to really bring the figure to life. The outermost square is rotated through 20 degrees in each step. Each inscribed one is rotated by a successively smaller amount, and this leads to some very interesting patterns emerging.

And an individual tile on its own.

View the source of this webpage to see the code used to generate these images.

It's fascinating how sometimes a simple set of rules applied multiple times results in something quite unlike what was started with.