On Growth and FormD’Arcy Thompson’s master work was “On Growth and Form”. In this elegantly written book, he advanced his main thesis: 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” such as ionic concentrations and other physical parameters. Thus, the initial conditions might well reflect some aspect of natural selection, but the resulting morphology of the spicules did not.

figures from 'On Growth and Form'One clear demonstration of his notions of the dynamic influence of starting conditions lies in the morphology of shells and horns. These are the permanent, non-living, three-dimensional record of a temporary, two-dimensional living state – the base of the horn,  or the mantle of the shellfish. 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.

figures from 'On Growth and Form'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.

About D'Arcy

D’Arcy Wentworth Thompson (1860-1948) was one of the most famous scientific personalities of his time – and that time was extensive, for he occupied important University chairs for a total of 64 years. He was greatly admired by many scientists, but his direct influence is hard to trace. In part, this is because some of his ideas have been accepted so entirely that they seem self-evident. Equally, it is because some of his ideas are not yet fully accepted.

D'Arcy took up the first Chair of Biology at what was then University College Dundee in 1885. He quickly acquired a reputation as an inspirational (and increasingly eccentric) teacher, while also playing an active role in local organisations such as the Dundee Social Union, the Dundee Naturalists Society and the Dundee Working Men's Field Club. During his 32 years in Dundee he founded and developed a large and impressive Zoology Museum, collecting specimens from all over the world. Although the building was demolished in the 1950s, a new version of the museum was opened in 2008, featuring many of his original specimens.

D'Arcy's collection provided the bedrock for his ongoing research into the mathematical principles of nature, work which would culminate in 1917 in the publication of his landmark book "On Growth and Form". It pioneered the science of bio-mathematics and has been hailed as "the greatest work of prose in 20th-century science." As well as continuing to inspire biologists and mathematicians today, it also proved hugely influential to such celebrated artists as Richard Hamilton, Eduardo Paolozzi and Ben Nicholson. The book was, however, just one of around 300 works published during his career.

In 1917 D'Arcy also moved to St Andrews to take up the Chair of Natural History at the University. While at St. Andrews, D’Arcy built up the Bell Pettigrew Museum of Natural History and added considerably to its displays. One correspondent reports that he met D’Arcy when he was 8, in 1932. On visiting the Museum he was hailed by the Professor, who showed the young man round its exhibits, and afterwards gave him a glass jar of stick insects, pointing out that these should be fed on fresh privet leaves.

Knighted in 1937, D’Arcy was a polymath, equally well qualified to occupy chairs of Zoology, Mathematics and Physics. His mathematical abilities are well to the fore in 'On Growth and Form', while his fluency in Greek and Latin are to be seen in his translations of Aristotle and his 'Glossary of Greek Birds' and 'Glossary of Greek Fishes'. He worked in other languages too. In the last year of his life he was teaching a group of St. Andrews students the history of Natural History. One day he was reading from a book rather hesitantly, and a student asked if he was too tired to continue. He said: ‘My dear child, I am not tired. I happen to be reading you a piece of medieval Italian, and I find the translation a little difficult, hence my hesitation.’

D’Arcy Thompson died in 1948, still teaching up to the age of 87, but before the advent of the computer era. He would have undoubtedly delighted in the abilities of computers, which could have empowered him to make his vision – still not generally accepted in its entirety – into an overwhelming case. Perhaps that might yet ensue, and his name once more regain its former eminence.