Turing Patterns
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Texture is one of the pillars of aesthetic admiration for nature, for the beauty of patterns that are at once geometric and organic, in structures that convey a feeling of freedom. In biology, the process of building natural structures is called morphogenesis, a term formed from the Greek morphé (form) and genesis (origin). One of the names that helped found this field was precisely Alan Turing, also a pioneer of artificial intelligence.
Turing had a background in mathematics, but he was also an admirer and scholar of the natural world, working as a theoretical biologist, an area that mixes mathematics and biology. In 1952, he published a revolutionary article titled “The Chemical Basis of Morphogenesis.” It was with this article that the scientific concept of Turing Patterns emerged, a mathematical model to explain the formation of patterns and textures in the life forms of nature.
He published on patterns in animal skin and plant leaves, but the logic continued to be applied in various contexts. What I find most visually curious is the case of orchid petals, where imbalances in the distribution of the pattern are visible. Turing’s theory says that there is a reaction-diffusion system, which works like a dance between an activator, which releases pigment, and an inhibitor, which prevents the pigment’s action.
Just like computational thinking, this biological logic explains how simple structures can generate complex structures. And the answer is: through the interaction of opposing forces, one that expands and another that controls. A complex pattern is only possible if both sides make many continuous and balanced exchanges. If one side acts in excess, the result will be a simplistic and disordered structure, incapable of reaching a higher level of complexity.
Drawing a parallel between nature and computation, it is possible to consider that the recombination algorithm, when it generates a combination never seen before, is, for all intents and purposes, creating, since the human brain also operates using recognition and recombination of patterns, with the difference that the body uses organic senses that the machine does not have. But what happens when the human body gives up using organic sensitivity and creativity, in a scenario where only AI (mathematics) creates, and the human (organic) only controls and edits?
Thinking mathematically is not a problem, since logic and mathematics are capacities of the human mind, and this is even what distinguishes human consciousness from that of other species. But the conscious mind exists within the body, and the body is an organic structure. And what happens when a body stops acting organically?
REFERENCES
"The Chemical Basis of Morphogenesis"; Alan M. Turinghttps://ui.adsabs.harvard.edu/abs/1952RSPTB.237...37T/exportcitation
"Turing patterns in development: what about the horse part?"; Current Opinion in Genetics & Development, 2012https://www.sciencedirect.com/science/article/abs/pii/S0959437X12001438
"And growth on form? How tissue expansion generates novel shapes, colours and enhance biological functions of Turing colour patterns of Eukaryotes"; Pierre Galipot, PLOS ONE, 2025https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0305921&type=printable
"Morphogenesis (Chapter 11)"; Alan M. Turing, Cambridge University Press, 2012https://www.cambridge.org/core/books/abs/alan-m-turing/morphogenesis/C7287DF8C5923FA02F7671FD6A9CEA1A
"Turing Algorithm: Simulating Organic Morphogenesis through Data Structures"; L.P. Santos, ECA-USP, 2025https://zenodo.org/records/10006563
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