Turing patterns arise from two virtual chemicals — an activator and an inhibitor — that react with each other while diffusing across a surface at different rates. When the inhibitor spreads faster than the activator, small random fluctuations get amplified into stable, repeating structures instead of smoothing out. This is the mechanism Alan Turing proposed in his 1952 paper "The Chemical Basis of Morphogenesis" to explain how uniform biological tissue can spontaneously organize into complex shapes. The same activator-inhibitor dynamics are believed to underlie many natural pigmentation patterns, from zebra stripes and leopard spots to the markings on tropical fish and seashells.

• Governed by two parameters: feed rate F (how fast chemical A is replenished) and kill rate k (how fast chemical B is removed).
• Different F/k combinations produce distinct regimes: spots, stripes, mazes, worms, or traveling waves.
• The two chemicals typically diffuse at a roughly 2:1 rate ratio (here D_A = 1.0, D_B = 0.5) — the inhibitor diffuses slower/faster relative to the activator to enable pattern formation.
• In biology, analogous roles are played by real diffusible signaling proteins ("morphogens") such as Wnt, BMP, and Nodal during embryonic development.
• Reaction-diffusion systems are widely used in computer graphics for procedural texture synthesis (animal coats, rock, coral).
• The system is computed on a GPU via a ping-pong shader: each frame reads the previous state texture and writes a new one, several steps per rendered frame.