Fractals: they’re gorgeous, seemingly simple and yet infinitely complex. But they’re not just pretty to look at --what if we could harness the mathematics of these fascinating patterns...and use them to totally transform our electronics?
But first, we need to cover what fractals are. A fractal is a ‘self-similar’ shape, so if you zoom into it, you will see that same shape again. Take a fern --each little frond is a miniature replica of the larger plant. Or take Romanesco broccoli, a snowflake, or even the blood vessels in your lungs. Each smaller part looks like a miniature version of the whole.
But the thing about fractals in nature is that they are not mathematically perfect. The mini version of the fern leaf may differ slightly from the whole. Plus, if you zoom in enough you’ll hit the cellular, molecular, and atomic levels that don’t adhere to the pattern. There’s only so far you can go before the fractal breaks down.
That’s in contrast to pure fractals that are mathematically infinite. These are the kind used to create those screensavers you’ve probably seen, the most famous being the Mandelbrot set. This visualization is the result of a relatively simple math formula that includes something called recursion, which applies the same mathematical step to each further iteration of the shape.
Short Summary: Fractals aren’t just crazy cool mathematically infinite shapes. They might just have the capacity to revolutionize modern electronics as we know it.