Morphogenesis Part 1 – Goethe, D’Arcy Thompson & Turing


‘Art forms in Nature’ by Ernst Haeckel, with its spectacular (and sometimes speculative) illustrations and ‘On Growth and Form’ by D’Arcy Thompson have fuelled a surge of interest in morphology and morphogenesis in the generative realm recently. The latter book is a rich blend of philosophy, literature, and mathematical principles, well researched from an historical point of view, leading to a poetic treatise on morphology. There no question that D’Arcy Thompson studied the work of polymath Goethe, who also was a keen observer of nature and its underlying forms. Goethe’s theory of plant metamorphosis stipulated that all plant formation stems from a modification of the leaf:

‘Furthermore I must confess to you that I have nearly discovered the secret of plant generation and structure, and that it is the simplest thing imaginable…. Namely it had become apparent to me that in the plant organ which we ordinarily call the leaf a true Proteaus is concealed, who can hide and reveal himself in all sorts of configurations. From top to bottom a plant is all leaf, united so inseparably with the future bud that one cannot be imagined without the other.’

Goethe is possibly grappling with the idea of recursion in nature, and his ‘From top to bottom a plant is all leaf’ is too much of the ‘As above so below’ – a reference to fractal geometry aside from its well known alchemical insinuations. If Goethe lead to D’Arcy Thompson, then perhaps Alan Turin might come next in the lineage, having studied ‘On growth and Form’ and becoming interested in Morphology in the last few years of his life. Turing is most known for the Turing Test, its influence on AI, and his work in cryptanalysis during the World War II. But we can only imagine what he might have discovered in the area of morphology had he not committed suicide at a relatively young age. It’s no coincidence that the ‘father’ of the modern computer was interested natural pattern formation as this field as lot of cross over’s with computational systems and models. It’s fitting that someone such as Turing, who provided an influential formalisation of the concept of the algorithm in computation, would find this topic so appealing.

Jonathon Swinton has created a very readable set of pages regarding Turing and his work on morphogenesis, and particularly his penchant for Fibonacci phyllotaxis. Turing did publish one important paper but much of his work in this area has been forgotten, Jonathon’s interest in mathematical biology and Alan Turing in general has resulted him bringing together fragments of unpublished & forgotten work, collating his findings for the benefit of interested parties.

Much of the work done by Goethe, D’Arcy Thompson & Turing, among others, lead to the formulation of ‘nature’ equations which underpin many of the algorithms generative artist employ in their works today. Nature is data.

(to be continued & expanded…)

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