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
- 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.
- 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.
Supported in partVerified against the publisher's abstract
Turing's own abstract supplies the reaction-diffusion half — instability of a homogeneous chemical state yielding stationary-wave patterns — and nothing about a Jeans length or spinodal collapse of matter.
“Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances.”
- 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.
Supported in partVerified against the publisher's abstract
The abstract grounds reaction-diffusion (Turing) patterns as a mechanism of morphogenesis, but says nothing about allometric scaling, branching morphologies, or firm and city power laws.
“It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves.”
- 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¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 2 of 6 citations: 2 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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