Attractors are basically a set of rules that define how a system can evolve over time. By "system", I mean choosing a random point on the screen and then drawing another point based on its current position. Do this 10 million times and it turns out to be a very pretty image!
There are many (infinite?) sets of rules, or functions, that can generate this behavior. I played around with a few sets to get different results. Here's an example of one of the more complex ones:
You may be familiar with the sine, cosine, and arctangent functions from trigonometry. The other parts of the functions -- the constants a, b, c, and d -- are very important to the final output. Only a small set of all possible values will generate something pretty like the images you see here. For example, setting a = 2.1314 and running the program could generate a blank screen, but change it by just 0.001 and you'll get something amazing. The constants I used were between -4 and 4 but that range really depends on the functions used.
Attractors -- also known as strange attractors, which just sounds cool -- emerge from chaos theory, which sounds even cooler. Small changes in the initial state of something can lead to drastic changes further down the line. That's what the BUTTERFLY EFFECT is.
