The Mathematical Intelligencer

, Volume 40, Issue 4, pp 39–61 | Cite as

Are All Fish the Same Shape If You Stretch Them? The Victorian Tale of On Growth and Form

  • Stephen Wolfram

Is there a global theory for the shapes of fishes? It’s the kind of thing I might feel encouraged to ask as a result of my explorations of simple programs and the forms they produce. But for most of the history of biology, it’s not the kind of thing anyone would ever have asked. With one notable exception: D’Arcy Wentworth Thompson.

And it’s now 100 years since D’Arcy Thompson published the first edition of his magnum opus On Growth and Form—and tried to use ideas from mathematics and physics to discuss global questions of biological growth and form. Probably the most famous pages of his book are the ones about fish shapes:



For help with facts and materials, I thank Matthew Jarron, Maia Sheridan, Isabella Scott, Special Collections at the University of St. Andrews Library and the “On Growth and Form 100” Conference in Dundee/St. Andrews.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Wolfram ResearchChampaignUSA

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