"THE CHEMICAL BASIS OF MORPHOGENESIS." by TURING, Alan - August 1952

TURING, Alan. "THE CHEMICAL BASIS OF MORPHOGENESIS." A fine

first-edition offprint from the Philosophical Transactions of the

Royal Society of London, Series B. Biological Sciences, No. 641,

Vol. 137, pp. 37-72, 14 August 1952. Published for the Royal

Society by the Cambridge University Press, London. Publisher's 1952

offprint, with "Price Eight Shillings" on cover. Many mathematical

equations and two figures in text. Quarto, 30 x 23.5 cm,

publisher's brick wrappers, title information to upper wrap and

spine. Fine.

In this, Alan Turing's most heavily-cited work, the pre-

eminent mathematician, computer scientist, and hero of WW II turned

his brilliant mind towards the biological sciences, proposing a

model of pattern-formation that proved seminal in not only biology

but also across many scientific fields. In what would be his only

published work in the field, Turing addressed a fundamental

problem: morphogenesis, the process by which a single cell develops

into the complex, asymmetrical organisms found in nature.

Turing designed a simple family of models in which stable

initial distributions of change-creating chemicals called

morphogens (this work introduced the term to the scientific

lexicon) become unstable in the presence of any diffusion process,

such as the mixing of fluids found in living tissue. Using this

elegant diffusion-reaction system, understandable with college-

level mathematics, Turing explains the asymmetric pattern-formation

of living organisms starting from a simple early state, providing

a mathematical justification for everything from the dappling of

fur and seashells, the tentacle-like appendages of Hydra organisms,

to the separation of the nervous system during embryonic

development (gastrulation).

This ground-breaking work has formed the basis for a broad

array of advances in biology, from models of tumor growth, epidemic

spread, and evolutionary biology, to the shapes of neuronal

dendrites and neuronal polarization. Outside of the biological

sciences, this paper has inspired advances in areas as diverse as

the behavior of sensor networks, image processing, economic

geography, spatial ecology, and machine learning models for

computer vision. The universality of this pattern formation model

is perhaps unsurprising given Turing's polymathy, and no less

magnificent.

While this article is not uncommon appearing in the bound

volumes held by numerous institutions, the 1952 offprint, which

appears in two states, the commercially distributed--with printed

price, and the author's copy--lacking the price, are both rare.