The Chemical Basis of Morphogenesis.¶
Turing, A. M. (1952). The Chemical Basis of Morphogenesis. Philosophical Transactions of the Royal Society of London, Series B, 237(641), 37-72.
Cited by¶
6 citations across 6 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Diffusion
- Turing's
This sourceShows that coupled chemical reactions with diffusion can destabilize a homogeneous equilibrium and spontaneously break spatial symmetry, generating patterns (Turing patterns).
- Turing's
- Gradient
- In biology and chemistry, electrochemical gradients across membranes power ATP synthesis and neural firing; morphogen gradients shape embryonic patterning
This sourceLandmark analysis of reaction-diffusion instability: shows that coupled chemical reactions with diffusion can spontaneously break spatial symmetry and create patterns (Turing patterns); cross-links diffusion with chaos (DP-04) and demonstrates that deterministic nonlinear coupling produces complex organized structure from diffusion. Turing patterns, reaction-diffusion instability, symmetry-breaking, morphogenesis, spatial structure formation, deterministic pattern.
- In biology and chemistry, electrochemical gradients across membranes power ATP synthesis and neural firing; morphogen gradients shape embryonic patterning
- Nonlinearity
- … relativity. Biology and ecology uses nonlinearity for logistic population growth (Verhulst), predator-prey dynamics (Lotka-Volterra), enzyme kinetics (Michaelis-Menten), Holling's saturating functional responses, gene regulatory networks with switches, and Turing's reaction-diffusion pattern-formation framework
This sourceLandmark analysis of reaction-diffusion instability: shows that coupled chemical reactions with diffusion can spontaneously break spatial symmetry and create patterns (Turing patterns); cross-links diffusion with chaos (DP-04) and demonstrates that deterministic nonlinear coupling produces complex organized structure from diffusion. Turing patterns, reaction-diffusion instability, symmetry-breaking, morphogenesis, spatial structure formation, deterministic pattern.
- … relativity. Biology and ecology uses nonlinearity for logistic population growth (Verhulst), predator-prey dynamics (Lotka-Volterra), enzyme kinetics (Michaelis-Menten), Holling's saturating functional responses, gene regulatory networks with switches, and Turing's reaction-diffusion pattern-formation framework
- Spinodal Decomposition
- In reaction–diffusion chemistry, Turing instabilities produce preferred-wavelength patterns from a homogeneous chemical state through the same wavenumber-selective amplification.
This sourceReaction-diffusion instability that amplifies a preferred wavenumber from a homogeneous chemical state — the same wavenumber-selective amplification underlying spinodal patterns.
- In reaction–diffusion chemistry, Turing instabilities produce preferred-wavelength patterns from a homogeneous chemical state through the same wavenumber-selective amplification.
- Universality
- Developmental biology and economics: Turing patterns, allometric scaling laws, and branching morphologies recur across very different machinery; power-law distributions of firm and city sizes recur across very different market microstructures.
This sourceDerives reaction–diffusion (Turing) patterns recurring across very different developmental machinery, a universality of morphological form.
- Developmental biology and economics: Turing patterns, allometric scaling laws, and branching morphologies recur across very different machinery; power-law distributions of firm and city sizes recur across very different market microstructures.
Domain-specific¶
Verification¶
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