Summary
Highlights
The living world displays a vast array of beautiful and complex shapes and patterns. The fundamental question is how such diversity arises from simple components like cells and chemical instructions. This variety is often described by an elegant mathematical idea, a 'code' not of DNA, but of math.
Zebras are black with white stripes, a fact determined by observing zebras born without stripes. The purpose of these stripes isn't camouflage, but rather to confuse bloodthirsty biting flies. This explanation tells what stripes do, but not their origin or how such patterns are possible, leading us to mathematics.
In 1952, mathematician Alan Turing published simple mathematical rules explaining many natural patterns, including stripes, spots, and labyrinths, now known as 'Turing patterns'. While known for codebreaking and computing, Turing was deeply fascinated by biological problems, particularly 'morphogenesis' – the generation of form.
Turing's 'Chemical Basis of Morphogenesis' proposed that complex shapes arise spontaneously from simple initial conditions using two chemicals, 'morphogens', that spread and react at different rates. These 'reaction-diffusion equations' combine diffusion (spreading) and reaction (interaction) to create patterns. Historically, diffusion was thought to stabilize systems, but Turing showed it could destabilize and form patterns.
A reaction-diffusion system involves an activator chemical that creates more of itself and an inhibitor chemical that turns off the activator. Using the analogy of a cheetah's spots as fires (activator) and firefighters (inhibitor), the key to spotted patterns is the inhibitor spreading faster than the activator. Adjusting variables in Turing's rules generates diverse patterns, with the surface shape also influencing the outcome.
Turing's 1952 paper was initially overlooked, overshadowed by other biological discoveries. However, after its rediscovery in the 1970s by Gierer and Meinhardt, biologists began searching for actual morphogens in nature. Decades later, molecules matching Turing's predictions have been found, forming patterns like mouth ridges, bird feathers, and shark scales, validating his mathematical model. Even complex systems like mammal limb development show elaborate interactions of activator/inhibitor signals.
Alan Turing never witnessed the full recognition of his theories. In 1952, he faced criminal charges for his homosexual relationship, leading to chemical castration. He died two years later from cyanide poisoning, likely suicide. Pardoned retrospectively in 2013, Turing's contributions extended beyond patterns; his codebreaking shortened WWII, and his work on programming logic underpins modern computing. His lifelong fascination with mathematical patterns continues to inspire biological research.
Turing's mathematical equations for patterns are often too complex for manual calculation, requiring computers – a technology he pioneered. His personal notes, written in a unique binary code, attest to his advanced vision. The world lost an unparalleled intellect with Turing's premature death, someone whose thoughts were often far ahead of his contemporaries. His work highlights the profound beauty of mathematics, not just in describing reality, but in deepening our understanding of it.