This text was written by D’Arcy Thompson, this was his master work.
His main thesis is that biological form can reflect physical and mathematical principles. For instance, the spicules of sponges adopt a number of characteristic shapes. D’Arcy argued that these were the consequence of slight differences in the “starting conditions” witch might well reflect some aspect of natural selection, but the resulting morphology of the spicules did not.
One clear demonstration of his notions of the dynamic influence of starting conditions lies in the morphology of shells and horns. D’Arcy Thompson showed that all horn and shell morphologies could be described in simple mathematical terms readily derived from the incremental nature of growth.
Even if a morphology was plainly functional, this did not imply for D’Arcy that it was incorporated into the genome by natural selection. For instance, geometrical rules of packing determine cell arrangements. These need not be specified, but can arise spontaneously. Yet the packing arrangement may be “useful” in minimising the space occupied by the cells, by maximizing cell-cell contacts, by establishing different categories of cells, “inside” versus “outside”, and so on.
Perhaps the most famous images from ‘On Growth and Form’ are the transformations. D’Arcy showed that gross variation in form between related species could be modeled by the consistent deformation of a sheet.
The consistency of the deformation is the crucial point here: it is obvious that any fish form could be made to look like any other fish form, if it were sketched on a perfectly deformable elastic sheet, and stretched in many directions at once. But D’Arcy Thompson showed that if the sheet were stretched in one particular pattern, then a new species form would be generated. This remarkable and curious observation has not been fully explained even today.