D'Arcy Thompson's Affine Fish Transformations
D'Arcy Thompson's Affine Fish Transformations
D'Arcy Wentworth Thompson (1860–1948) was a pioneer in mathematical biology, best known for his classic On Growth and Form (1917). He showed that in several classes of organisms, notably fish, the morphology of related species could be generated by simple geometric transformations. This Demonstration considers a subset of these, namely affine transformations—rotations, scaling, and shearing—that are readily carried out by Mathematica. These can be represented by a matrix equation , in which you control the rows and by dragging two locators.
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c | d |
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a | b |
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c | d |