# Realm of Chaos

Caution: this post is for nerds only.

I watched this numberphile video last night and was fascinated by the point pattern that was created in it. I thought I would quickly program my own version to recreate it and then look at patterns made by more points.

I didn’t realise until afterwards that there is actually a web version of the program used in the video here. It is a bit limited though so my code was still worthwhile.

A fractal triangular pattern can be created by:

1. Setting three points
2. Picking a randomly placed seed point
3. Rolling a die and going halfway towards the result
4. Repeat last step

If the first three points are randomly placed the pattern is skewed, so I added the ability to generate an equilateral triangle. Here is the result.

and here are the results of a triangle through to a decagon.

All of these are generated with one million points using alpha=0.25. The triangle, pentagon and hexagon make nice patterns but the square and polygons with more than six points make pretty uninteresting patterns.

Watching the creation of the point pattern from a triangular set is quite fun. This is 30000 points with a frame every 10 points.

Here is the code.

Some other notes: this version runs in IgorPro. In my version, the seed is set at the centre of the image rather than a random location. I used the random allocation of points rather than a six-sided dice.

The post title is taken from the title track from Bolt Thrower’s “Realm of Chaos”.