
Alan Turing and the mathematics of pattern formation in nature - YeGoblynQueenne
https://www.nytimes.com/2018/05/08/science/alan-turing-desalination.html
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DonHopkins
I typed in the preface to Morphogenesis, and scanned the drawing inside the
front cover by Alan Turing's mother of her son watching the daisies grow.

[https://donhopkins.com/home/archive/Turing/Morphogenesis.txt](https://donhopkins.com/home/archive/Turing/Morphogenesis.txt)

Hockey or Watching the Daisies Grow:
[https://i.imgur.com/AX6Bg9q.jpg](https://i.imgur.com/AX6Bg9q.jpg)

Turing, Alan Mathison, 1912-1954. Morphogenesis / edited by P. T. Saunders. p.
cm. -- (Collected works of A. M. Turing, Volume 3). Includes bibliographical
references and index. ISBN 0 444 88486 6. 1. Plant morphogenesis. 2. Plant
morphogenesis -- Mathematical models. 3. Phyllotaxis. 4. Phyllotaxis --
Mathematical models. (C) 1992 Elsevier Science Publishers B. V. All Rights
Reserved.

[https://books.google.nl/books?id=GX7NCgAAQBAJ&pg=PR8&lpg=PR8](https://books.google.nl/books?id=GX7NCgAAQBAJ&pg=PR8&lpg=PR8)

Watching the daisies grow: Turing and Biology

[http://tokillamachine.co.uk/alan-turing/watching-the-
daisies...](http://tokillamachine.co.uk/alan-turing/watching-the-daisies-grow-
turing-and-biology/)

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dmos62
Thank You for typing this up.

> Not all biologists, however, have accepted this view. One of the strongest
> dissenters was D'Arcy Thompson (1917), who insisted that biological form is
> to be explained chiefly in the same way as inorganic form, i.e., as the
> result of physical and chemical processes. The primary task of the biologist
> is to discover the set of forms that are likely to appear. Only then is it
> worth asking which of them will be selected. Turing, who had been very much
> influenced by D'Arcy Thompson, set out to put the program into practice.
> Instead of asking why a certain arrangement of leaves is especially
> advantageous to a plant, he tried to show that it was a natural consequence
> of the process by which the leaves are produced. He did not in fact achieve
> his immediate aim, and indeed more than thirty-five years later the problem
> of phyllotaxis has still not been solved. On the other hand, the reaction-
> diffusion model has been applied to many other problems of pattern and form
> and Turing structures (as they are now called) have been observed
> experimentally (Castets at al. 1990), so Turing's idea had been vindicated.

Reading most of this introduction, especially this last paragraph, I couldn't
but help think about Stephen Wolfram's A New Kind of Science. Wolfram's book
is very empirically philosophical, or maybe I should say just purely
explorational, and he goes into the problems described above almost word for
word. He uses programs to demonstrate that, for example, the variation in
patterns on shellfish is due to minimal changes in genetic programs.

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twic
D'Arcy Thompson's 'On Growth and Form' is worth a read.

As a lapsed biologist, I would say he's right that in biology, shape results
from the interaction of physical forces and the properties of materials. But
he misses the point that the properties of materials are governed by genes.
There's no gene that makes a sea urchin spherical, but there are genes such
make its skin flexible but inelastic (or whatever), and it's spherical because
of that. Evolution is perfectly happy to form the shape indirectly by
selecting alleles of those genes. But a notional anti-Thompson who thinks
genes are everything would be missing the point that lots of shapes are
impossible, because there's no plausible combination of force and material
which would produce them.

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mjfl
Your fingers are patterned by a system just as proposed by Turing:

[http://science.sciencemag.org/content/345/6196/566](http://science.sciencemag.org/content/345/6196/566)

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amai
Link to Turing's original paper:
[http://www.dna.caltech.edu/courses/cs191/paperscs191/turing....](http://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf)

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n-exploit
Anyone have a mirror?

~~~
BlackMonday
It seems the article was saved to archive.is a few months ago [0] but you can
also read it by using NoScript or uBlock.

[0] [http://archive.is/VuXE7](http://archive.is/VuXE7)

