Nature follows a number of intricate and subtle mathematical rules to produce the patterns, shapes, and colours that we find so mesmerizing.

**Part I**

Wherever we find patterns and symmetry in nature, we also find that nature conforms to certain rules. Rules that combine elegance with efficiency. Rules that shape trees and river estuaries alike, and that continue to baffle scientists by their often unfathomable ubiquity.

**Part II**

Mathematical formulas can be found in the arrangement of seeds on a sunflower, the structure of the spirals in the shells of certain marine animals, and the distribution of leaves around a plant stem. These formulas recur in nature from snowflakes to the stripes on a zebra.