Where Mathematics meets visual art — Fractals

Fractals are some of the most beautiful and most bizarre geometric shapes. In essence, a fractal is a never-ending pattern at different scales and sizes. They are created by repeating a simple process over and over. For example, draw a square, then divide it into 4 equal squares. Then divide those 4 squares too into 4 equal squares each. Keep going infinitely, that is a fractal.

Below is an example of a famous fractal — Sierpinski Gasket [start with a triangle and repeatedly cut out the centre of every segment]

A fascinating thing about fractals is that it is very common in nature, hiding in plain sight all around us. For example a fern. The leaves are shaped like little copies of the branches. If you see more closely, you will realise that the entire fern is mostly built up from the same basic shape repeated over and over again at ever smaller scales.

Another example of fractals include our lungs — their fractal geometry allows them to pack lots of surface area into a small volume. A lightning strike reveals a fractal pattern too — each branch resembles a small copy of the whole shape. But to really appreciate these shapes, you need to see them. Check out here some stunning images of fractals in nature: