## Chaos Game and the Hexagon

For a hexagon the chaos game forms the same pattern at 1.5 as it does 0.5. Posted in Uncategorized | 1 Comment

## The Chaos Game and PHI

The outer chaos game shows some interesting patterns with phi as a magnitude.

## 3D Shapes Painted by Sections of the Outer Chaos Game

Square with magnitude range 1.4-1.5: Pentagon with magnitude range 1.3-1.4: ## Personal Website

I have setup a personal website koozdra.ca.

There is a preliminary demo of the Chaos Game Path Plotter.

http://koozdra.ca/chaosgame/main.html

## More Interesting Patterns Hidden in the Chaos Game

UPDATE: Interactive version Chaos Game

I was curious to see what would happen If generated chaos games in ascending magnitudes and drew them together. Typically a pattern emerges from 0.5 to 1.5 magnitudes depending on the number of attractors. I split up the spectrum into two parts 0.5 to 1 and 1 to 1.5. This is done because values above 1 draw into the middle of the attractors. This interferes with the internal pattern.

## 175

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## 1.5 Magnitude Pentagon Chaos Game

If at each iteration in the chaos game the current point is moved 1.5 times the distance to a randomly selected pentagonal vertex attractor, this image is created. This image seemed familiar to me. I had created a magnetic shape that looked very similar. ## Adding a Little More Chaos to the Chaos Game

The Chaos Game defines a set of attractors and an iterative process that moves a point towards a random attractor by a specified magnitude.

This image is generated by having five attactors, the points of a pentagon. At each iteration the current point moves towards a point on the pentagon by PHI (0.618) times the distance to the attractor. I wanted to see what would happen if the magnitude of attraction was also chaotic. At each stage of the algorithm a random attraction magnitude is chosen between [0.5,1.5]. More Resources:
Mathworld Chaos Game Page
Wikipedia Chaos Game Page

[Update] Processing code to generate the shapes above:
``` var attractors = []; var current = [random(800),random(800)]```

``` for(var i = 0; i < 6; i++){ attractors.push([cos(i * 2 * PI/5) * 300, sin(i * 2 * PI/5) * 300]); } var attraction = 0.5; void draw(){ translate(width/2, height/2); rotate(PI/2); stroke(0); for(var i = 0; i < attractors.length; i++){ rect(attractors, attractors, 5,5); } for(var i = 0; i < 100; i++){ point(current,current); var target = attractors[Math.floor(Math.random() * (attractors.length-1))] current = current - (current - target) * attraction; current = current - (current - target) * attraction; } attraction = Math.random()+.5; ```

```} ```

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