# Fractals to the people!

In 1904 the Swedish mathematician Helge von Koch published a paper about a wonderful fractal curve, which since then has variously been called the Koch Curve, Koch Star or Koch Snowflake. I talked about this curve recently on this blog, because I used it to create a Fractal Holiday Decoration on my 3D printer.

Today I wanted to create a way for you to make your own fractal shapes. In the last few days I’ve done a little research on the web around the idea of “making your own fractal”. What I’ve learned is that there are a lot of sites that want to sell you software to make your own fractals, and I was appalled to discover that they’re all pretty much the same.

What these sites all say, in essence, is: “You, the person reading is, are a complete idiot. But there are other people out there somewhere who are a lot smarter than you. They are called ‘mathematicians’, and they do this really arcane, magical mystical thing called ‘mathematics’ — something that you could never hope to understand. But just because you are a hopeless simpleton, well that doesn’t mean you shouldn’t have any fun, or even be allowed outside on occasion. So I’m going to do you a really big favor and let you send me ten bucks so I can give you a way to play around with the Mandelbrot set. You won’t have the faintest idea what’s going on (being a complete idiot and all), but you’ll still be able to make pretty pictures with nice colors.”

In fact there isn’t anything obscure or mysterious about fractals. Fractals are simply shapes that continue to repeat themselves at progressively smaller scales. If you understand that straightforward concept, then you’re a mathematician. My goal today was to create a sort of fractal playground, so you can make your own fractal shapes — with no mystery at all about what you are doing.

If you’ve read my post about making those holiday decorations, you’ll recall that they were Koch snowflakes, created with a very simple recipe: