More Mathematical Patterns: Fractals

Fractals are complex, often chaotic, geometric shapes which divide into parts which are smaller-sized versions of the whole thing. In maths they are used to describe certain graphs and geometric principles, but they also make beautiful art. You can see them in nature in ferns

electrical discharges

and Romanesco broccoli, to name but a few

(images from http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html )

Examples llike the Koch Snowflake can be used to create beautiful tiled patterns like these from Mathworld