Symmetry: why your left is like your right (and why it's different) -- Fractals: why mountains look like molehills -- Spirals: why there's maths in snails and sunflowers -- Flow: patterns in motion -- Waves and dunes: how to make a chemical clock -- Bubbles and foam: why bees know best and froth inspires architects -- Arrays and tilings: why crystals aren't five-sided -- and how to make impossible ones that are -- Cracks: how things fall apart, and how a giant made his staircase -- Spots and stripes: how the zebra paints its coat.