For some reason, I started thinking about math a couple of days ago. I don’t know why exactly; I floundered around in math during my time at school until finally flunking out in grade 10. It wasn’t pretty.

I had no idea what was going on! I couldn’t understand how the other kids could listen to the gobbledegook language the teacher was speaking, (like the muffled wah-wah noises the off-panel teachers in the Peanuts cartoons spoke with), nod with bored expressions, -and write it down and understand it and pass tests and such! It was amazing! I’d just feel stunned and look around sometimes for the hidden camera. No way did any of that make sense..!

But it did, and I failed often and badly.

Still.., there’s always been something about numbers which appeals to me. I find the whole mystery fascinating. And, to be fair, I was very good at geometry. -In a balancing kind of way, I was very good at it when it served to confound the other students. That was my mystery language! -Once I could visualize things, there was no stopping me! However, that’s a rather limited super-power, because once I got beyond 3 dimensions, it became impossible to visualize the results, and I become lost and hopeless once more. I’m evidently a creature meant to function best in 3D.

Anyway…

I decided a couple of days ago to do some thinking about Fractals. -They’re nothing new, and everybody has seen the famous shapes on the covers of science magazines and nerdy posters, but I couldn’t remember how they worked or why, so I decided to figure it all out again. It didn’t take too long, because fractals are really quite simple, so that even a dunderhead like me can work it out.

And the Mandelbrot Set blows my mind!

Check it out:

Z = Z² + C

That’s it!

The idea is that you pick some arbitrary number for Z and for C, run the equation, and when you do, you get a new number out the other end. Then you take that new number and make it equal Z, and then you run the equation again. Rinse and repeat. You get a unique number every single time. Then you use a basic plotting scheme with simple rules. X, Y coordinates. -And you end up putting dots all over the chart. Those dots create fantastically complex shapes that never seem to repeat.

When you run the equation a HALF BILLION times, why, you get a shape which is super complex and deep. The authors of this little math experiment made a video (above) where they zoom into it, and it feels like you’re a parachute jumper falling endlessly into god’s eyeball or something

Anyway, I thought that was cool; how you can find an infinitely deep shape in such a simple equation!