The Chaos Game
January 16, 2022
I have been watching Numberphile from the last 3 years and everytime its something new and interesting from the wonderful community, However, except a few I hardly remember the concepts after days. Information overflow is real!
Math is beautiful! It comes with a myriad patterns resembling nature. Some are quite obvious, while most of them are quite fascinating.
“Mathematics is the Science of Patterns and nature exploits just about every pattern that there is.” -Ian Stewert
Hence I decided to write small scripts to validate the concepts taught in the videos and retrieve the information through this blog whenever I feel like. Thus this effort!
The Chaos Game is based on just interatively finding the mid-point concepts. I am following the Numberphile video by Brady word by word. You can watch Brady’s video here. So, Let’s go step by step :
Step 1: Randomly plot three points on a canvas. [Make it truely random - Math doesn’t care]. Say he points are A, B and C.
Step 2: Mark a fourth point. Again let it be another random one. Let’s say this point is “X”.
Step 3: Roll a six-faced-dice. We have to make some rules here.
- If the rolled dice shows 1 or 2. The next X will be the mid point between A and previous X.
- If the rolled dice shows 3 or 4. The next X will be the mid point between B and previous X.
- If the rolled dice shows 5 or 6. The next X will be the mid point between C and previous X.
Step 4: Repeat the steps a lot (?) of times (may be 1000 or more).
Step 5: Voila! You got the nice and preety pattern. Math did it.
I have written the script using p5js. The code can be found here. Try it out yourself!
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