My journey into finding beauty in math.

2020

Look, I didn't vibe with math in the past. I recall my SAT score for math was alright but I straight despised it. In adulthood I never worked jobs prior to tech that facilitated much math skills, even as a coffee roaster things didn't get much more complicated than fractions and division.

The Science Behind the Butterfly Effect is a video that Veritasium released in Dec 2019. Mr Veritasium aka Derek Muller goes on to describe the discovery of the first chaotic attractor by Edward Lorenz. A lot of big words are used and I can't even understand the jargon without spamming my tabs with wikipedia pages so here's the key point. Following Chaos theory, something is deemed chaotic if it exhibits **sensitive dependence on initial conditions**.

Chaos theory is a branch of mathematics that studies apparent random states of disorder and irregularities that are actually governed by deterministic laws that are highly sensitive to inital conditions.

I created these in p5.js, the javascript version of the processing library. These are specifically Clifford Pickover's equations for a chaotic attractor.

The exact equation is:

```
xn+1 = sin(a yn) + c cos(a xn)
yn+1 = sin(b xn) + d cos(b yn)
Where a,b,c,d are variables,
that define each attractor.
```

Makes no sense right? Look I got all my math credits early. I dont know either.

Well this is a 4 parameter system, there is a numeric range that suits this equation best as far as beauty goes, being each variable should be in a range between -3 to 3. Within a graph each equation will provide a value to plot, one for the X-cord and one for the Y-cord.

Here's the p5 editor implementation of the Clifford attractor. Just click the play button to render it on your browser.

Be warned it can take about 30 seconds to render because **It's plotting 1 million dots on a graph**, it would take you a while too!