There’s a reason fashion designers look to animal prints for inspiration. Creatures have evolved a dizzying array of patterns: stripes, spots, diamonds, chevrons, hexagons and even mazelike designs.

Nature follows mathematical rules and creates repeating patterns across completely different organisms and environments.

Some patterns arise simply or randomly, but others develop via complex, precise interactions of pattern-generating systems. Their beauty aside, the intricacies of these systems are inspiring the ...