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nydus/On Growth and FormPublic
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CHAPTER XVII ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON OF RELATED FORMS

manner, the still more bizarre outlines of other fishes of the same family of Chaetodonts will be found to correspond to very slight modifications of similar co-ordinates; in other words, to small variations in the values of the constants of the coaxial curves.

In Figs. 377〓380 I have repôÙreôÙsentôÙed another series of AcanôÙthopôÙterôÙygian fishes, not very disôÙtantly related to the foregoing. If we start this series with the figure of Polyprion, in Fig. 377, we see that the outlines of PseudoôÙpriaôÙcanôÙthus (Fig. 378) and of Sebastes or Scorpaena (Fig. 379) are easily derived by substituting a system of triangular, or radial, co-ordinates for the rectangular ones in {750} which we had inscribed PolyôÙprion. The very curious fish Antigonia capros, an oceanic relative of our own 〜boar-fish,〝 conforms closely to the peculiar deforôÙmaôÙtion represented in Fig. 380.

A transformation grid from D'Arcy Thompson's "On Growth and Form" showing how a rectangular grid deforms a fish.

Fig. 377. Polyprion. Fig. 378. Pseudopriacanthus altus.

D'Arcy Thompson's comparison of two fish species using a Cartesian grid to demonstrate geometric morphological transformation.

Fig. 379. Scorpaena sp. Fig. 380. Antigonia capros.

Fig. 381 is a common, typical Diodon or porcupine-fish,

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