DIRECTORY / SANDBOXES / REACTION-DIFFUSION.TURING

GRAY-SCOTT MORPHOGENESIS

Alan Turing's 1952 morphogenesis equations driving chemical reaction-diffusion spot and stripe patterns.

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GRAY-SCOTT TURING HUD

// MORPHOGENESIS PRESETS

FEED RATE (F) 0.0545

KILL RATE (k) 0.0620

[Click & drag to paint chemical catalyst seeds]

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RESEARCH & LEARNING VAULT // Gray-Scott Chemical Morphogenesis

Turing pattern formation, autocatalysis, and biological spot/stripe emergence.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Alan Turing published 'The Chemical Basis of Morphogenesis' in 1952, proposing that reaction and diffusion of two chemical morphogens explains animal coat patterns and organism development.

// GOVERNING EQUATIONS

\frac{\partial u}{\partial t} = D_u \nabla^2 u - u v^2 + F(1 - u), \quad \frac{\partial v}{\partial t} = D_v \nabla^2 v + u v^2 - (F + k) v

// BROWSER IMPLEMENTATION

Computes discrete 2D 5-point Laplacian spatial convolutions and nonlinear cubic reaction kinetics ($u v^2$) across contiguous typed arrays.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

1Mitosis Cell Division

🎯 Action:Select 'Mitosis Division' preset and drag across the canvas.

✨ Observe:Watch individual chemical spots grow, elongate, pinch in the middle, and divide into daughter cells.

// CURATED PAPERS, RFCS & RESOURCES

The Chemical Basis of Morphogenesispaper

By Alan M. Turing (Philosophical Transactions of the Royal Society, 1952)

Alan Turing's seminal paper introducing reaction-diffusion systems in biology.

Complex Patterns in a Simple System (Gray-Scott)paper

By John E. Pearson (Science, 1993)

Comprehensive classification of spot, stripe, and spiral chaos phase spaces.