D'ARCY W. THOMPSON'S MATHEMATICAL TRANSFORMATION AND THE ANALYSIS OF GROWTH

@article{Richards1955DARCYWT,
  title={D'ARCY W. THOMPSON'S MATHEMATICAL TRANSFORMATION AND THE ANALYSIS OF GROWTH},
  author={Oscar W. Richards},
  journal={Annals of the New York Academy of Sciences},
  year={1955},
  volume={63}
}
  • O. W. Richards
  • Published 1 November 1955
  • Philosophy
  • Annals of the New York Academy of Sciences
In 1915 D’Arcy Wentworth Thompson (FIGURE 1) compared the shapes of related adult organisnis by means of transformed coordinates and, in 1917, he elaborated the method in the final ~hapter~~-3? of his masterful work, Grozilh and Form. The resulting spectacular diagrams created interest and soon appeared in other books. It is my pleasant task in this paper to review Thompson’s work with respect to current problems and developments. 
11 Citations
The Study of Shape Transformation after D'Arcy Thompson
The boundary represents the shape, but it is not the boundary which grows. A rubber band released from tension happens to return to its elongate resting shape. In the course of release, the band isExpand
One Biologist's View of Morphometrics
TLDR
The forms to be characterized may be the external dimensions of some simple biological object, the complex internal patterns revealed by such methods as dissection and radiography, or the complicated and multidimensional "structure" of data relevant to a biological problem. Expand
The specific growth rates of tissues: a review and a re-evaluation.
  • S. Cowin
  • Engineering, Medicine
  • Journal of biomechanical engineering
  • 2011
TLDR
This review and re-evaluation is to present a brief history of efforts to mathematically model the growth of tissues and to place this historical material in a current perspective where it may be of help in future research. Expand
Planar morphometry, shear and optimal quasi-conformal mappings
  • G. Jones, L. Mahadevan
  • Mathematics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
To characterize the diversity of planar shapes in such instances as insect wings and plant leaves, we present a method for the generation of a smooth morphometric mapping between two planar domainsExpand
On the nature of catastrophic forms
Abstract The impact of humans on the Earth’s ecosystem has led to the declaration of a new geological era, the Anthropocene. Earth systems stable for millennia are now threatened by anthropogenicExpand
Mahadevan quasiconformal mappings Planar morphometry , shear and optimal
References 3.full.html#ref-list-1 http://rspa.royalsocietypublishing.org/content/469/2153/2012065 This article cites 31 articles, 2 of which can be accessed free Subject collections (77 articles)Expand
Greek classicism in living structure? Some deductive pathways in animal morphology.
  • G. Zweers
  • Mathematics, Medicine
  • Acta biotheoretica
  • 1985
TLDR
Three deductedive methods for explanation of living structure in animal morphology are proposed: the parts, the compromise, and the transformation deduction, which show clearly the high explanatory power of deductive methods in morphology. Expand
Scale effects in animal joints. I. Articular cartilage thickness and compressive stress.
  • W. Simon
  • Materials Science, Medicine
  • Arthritis and rheumatism
  • 1970
TLDR
Among the species, the low ratio of highest/lowest stress on the femoro-tibial joint suggests that limb structures are optimally designed to maintain low static pressures on the joint surface, and the possibility that other stresses, noncompressive or dynamic, may be related to cartilage thickness is excluded. Expand
ALLOMETRY AND SIZE IN ONTOGENY AND PHYLOGENY
  • S. Gould
  • Biology, Medicine
  • Biological reviews of the Cambridge Philosophical Society
  • 1966
...
1
2
...

References

SHOWING 1-10 OF 49 REFERENCES
Essays on Growth and Form presented to D'Arcy Wentworth Thompson
THE production of a Festschrift is not a usual practice in Britain ; but there are some men whose influence has been so decisive in stimulating the widespread exploration of a scientific problemExpand
The pattern of change in size and shape
  • S. Zuckerman
  • Proceedings of the Royal Society of London. Series B - Biological Sciences
  • 1950
In introducing a discussion on the subject of growth, it is unnecessary to add to the many definitions of the word which previous writers have provided. It is, however, useful to try to define theExpand
XXVII.—Morphology and Mathematics.
The study of Organic Form, which we call by Goethe's name of Morphology, is but a portion of that wider Science of Form which deals with the forms assumed by matter under all aspects and conditions,Expand
Problems of Relative Growth
DURING the greater part of his life, man changes but little in form. In this important character he differs greatly from the majority of living organisms. By reference to ourselves, the concept ofExpand
On Growth and Form
THIS book, at once substantial and stately, is to the credit of British science and an achievement for its distinguished author to be proud of. It is like one of Darwin's books, well-considered,Expand
Growth in Relation to Differentiation and Morphogenesis
TLDR
Of the diverse approaches to the theory of heredity made in the nineteenth century, Mendel’s seemed the most unpromising, yet it alone disclosed foundations that could be soundly built upon. Expand
The shape of the human being as a function of time
  • P. Medawar
  • Engineering
  • Proceedings of the Royal Society of London. Series B - Biological Sciences
  • 1944
It is shown that the change of shape of the male human being from the 5th month of foetal life to maturity may be represented by a continuous one-parameter set of transformations. The method ofExpand
The Analysis of the Relative Growth Gradients and Changing Form of Growing Organisms: Illustrated by the Tobacco Leaf
TLDR
A method is presented which relates the transformed coordinate method with the allometric expression of growth gradients for the analysis of the form changes of organisms. Expand
On the form of plants and animals
TLDR
The relation between the amount of nervous tissue and the form of an animal is discussed in more detail and expressions for different shapes of plants are derived. Expand
The fels composite sheet
TLDR
The growth curves of height and weight and rate of appearance of ossification centers of a number of children, as plotted in terms of standard scores on the Fels Composite Sheet, reveal more dramatically the growth progress of a child, his growth response to good or bad environment or nutrition, and his body type and its changes. Expand
...
1
2
3
4
5
...