Fourier Series Square Wave by Cats Circling Cats Circling... remix
GREEN FLAG = Begin
RIGHT/LEFT = More/Less Cats (More/Less sine waves)
SPACE = Clear
About: How to approximate a square wave by having cats walk circles around each other.
Notes: A square wave is one example of a shape that can be created by adding together sine waves. A sine wave can be made by graphing the y position of a cat walking in circles. If you then have a second cat walking circles around a first cat walking circles, and you graph the y position of the second cat, then you are graphing the sum of 2 sine waves. If you adjust the speed and size of the circle of the 2nd cat just right, you can make it's y position be similar to a square wave. Then you can add a 3rd cat circling the 2nd cat at just the right speed and size, and it gets to be even more like a square wave. Etc. I used the formula sin(t) + sin(3t)/3 + sin(5t)/5 + etc.
@jay's original project is pretty swaggy but it doesn't support gigantic numbers of sprites. I remixed it into a clone based system so you can really see how accurate the approximation gets as you increase the number of iterations.
(Unfortunately that means that I had to delete almost all of @jay's original scripts --- sorry :package:)