Look around! Nature is full of patterns and shapes like the spiral symmetry of a pinecone. True, there are shapes that also appear fragmented or irregular but often there are smaller, self-similar shapes to the larger shape - for example, a tree branch has a similar shape to the larger tree. Mathematician Benoit Mandelbrot defined these "family of shapes" as "fractals" or the "geometry of nature."
Visit the Fractal Foundation for fun fractivities, make a Koch snowflake (snowflake made up of fractal curves) or create your own fractal art with Frax, a fantastic mobile app. Branch out like the leaf structure to Fibonacci numbers and find the golden ratio in a seashell. Numbers, and the world they describe, are beautiful.