Thompsonian Transformations

Abstract

Thompsonian transformations are a graphical method for studying the relations of the morphologies of organisms in terms of overall patterns of modifications to their shared geometries.

Keywords: morphometrics; biomathematics; homology; allometry; biomechanics

Figure 1.

Transformation diagram showing how one fish species (the sunfish Orthagoriscus, on the right) can be derived by geometric deformation of the morphology of another (the porcupine fish Diodon, on the left). From Thompson .

Figure 2.

A Thompsonian transform relating the skull of a chimpanzee (left) to the skull of a baboon (right). From Thompson .

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References

Bonner JT (1996) Sixty Years of Biology: Essays on Evolution and Development. Princeton: Princeton University Press.

Bookstein FL (1977) The study of shape transformation after D'Arcy Thompson. Mathematical Biosciences 34: 177–219.

Bookstein FL (1991) Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge: Cambridge University Press.

Bookstein FL (1996) Biometrics, biomathematics and the morphometric synthesis. Bulletin of Mathematical Biology 58: 313–365.

Calder WA (1996) Size, Function, and Life History. Mineola: Dover.

Clark WELG and Medawar PB (eds) (1945) Essays on Growth and Form Presented to D'Arcy Wentworth Thompson (includes papers by Huxley, Medawar and Woodger). Oxford: Clarendon Press.

Dawes B (1952) A Hundred Years of Biology. London: Duckworth.

Dawkins R (1996) Climbing Mount Improbable. London: Viking.

Ghyka M (1946) The Geometry of Art and Life. New York: Sheed and Ward.

Gould SJ (1971) D'Arcy Thompson and the science of form. New Literary History II(2): 229–258.

Kauffman SA (1993) The Origins of Order. Self‐Organization and Selection in Evolution. New York: Oxford University Press.

Kemp M (1995) Spirals of life: D'Arcy Thompson and Theodore Cook, with Leonardo and Durer in retrospect. Physics 32: 37–54.

Lawlor R (1982) Sacred Geometry. Philosophy and Practice. London: Thames & Hudson.

Mayer E (1943) Book review. Anatomical Record 85: 111–116.

Medawar P and Medawar J (1984) Aristotle to Zoos. A Philosophical Dictionary of Biology. Oxford: Oxford University Press.

Murray J (1989) Mathematical Biology, 1st edn. Berlin: Springer.

Oxnard CE (1984) The Order of Man. A Biomathematical Anatomy of the Primates. New Haven, CT: Yale University Press.

Raup DM (1961) The geometry of coiling in gastropods. Proceedings of the National Academy of Sciences of the USA 47: 602–609.

Raup DM and Michelson A (1965) Theoretical morphology of the coiled shell. Science 147: 1294–1295.

Stewart I (1998) Life's Other Secret. The New Mathematics of the Living World. London: Allen Lane.

Thompson D'Arcy W (1917) On Growth and Form. Cambridge: Cambridge University Press.

Thompson D'Arcy W (1942) On Growth and Form, 2nd edn. Cambridge: Cambridge University Press.

Thompson D'Arcy W (1992) On Growth and Form, abridged edition. Cambridge: Cambridge University Press. (With foreword by Gould.).

Thompson Ruth D'Arcy (1958) D'Arcy Wentworth Thompson. The Scholar Naturalist 1860–1948 (with a Postscript by PB Medawar). London: Oxford University Press.

Webster G and Goodwin B (1996) Form and Transformation. Generative and Relational Principles in Biology. Cambridge: Cambridge University Press.

Further Reading

Brown JH and West GB (2000) Scaling in Biology. New York: Oxford University Press.

Gould SJ (2002) The Structure of Evolutionary Theory. Cambridge, MA: Belknap Press.

Horder TJ (2005) D'Arcy Wentworth Thompson, on growth and form. In: Gratton–Guiness I (ed.) Landmarks Writings in Western Mathematics, 1640–1940, pp. 823–832. Amsterdam: Elsevier

Keller EF (2002) Making Sense of Life. Explaining Biological Developments with Models, Metaphors, and Machines. Cambridge, MA: Harvard University Press.

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How to Cite close
Horder, Tim(Jan 2006) Thompsonian Transformations. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1038/npg.els.0004179]