Often considered one of the fathers of modern computing, Alan Turing is widely recognized for his contributions to the field of computer science. In particular, Turing developed the Turing His Machine. A Turing machine is a virtual machine that manipulates symbols on his one-dimensional tape of infinity according to a table of rules. A Turing machine can simulate any computer his algorithm and provides a mathematical formulation of today’s digital his computer. In his 1947 lecture, Turing alluded to the concept of computer intelligence. Probably his one of the first mentions of this concept. Machines modifying their own instructions provide a mechanism for this. “¹Turing eventually proposed something called the Turing test. It is a method of determining whether a machine is capable of displaying human intelligence, and is highly influential and the subject of much debate in the field of artificial intelligence.

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Turing’s contributions in the field of mathematical biology are equally noteworthy but may be less well known. On August 14, 1952, Turing published the only research paper in biology entitled “The Chemical Basis of Morphogenesis.”², he proposed a mechanism to explain the patterns observed in nature. More specifically, Turing noted that an inherent property of biological systems is asymmetry, which does not arise from the laws of physics alone. Taking the development of the embryo as an example, he said that the embryo begins as a symmetrical mass of cells, and that in most cases the laws of physics cannot explain the development of organs such as limbs and eyes in precise locations. Instead, the development of asymmetry in biological systems occurs as a result of signaling molecules that originate from and move away from a particular source within a tissue, leading to concentration gradients and patterns within the system. Turing named these signaling molecules morphogens. However, patterns that occur in systems of molecules that move according to the fundamental laws of physics eventually vanish, leaving no observable pattern. A process is required to generate and amplify the patterns in the system in a stable manner. To explain the pattern development, Turing proposed adding instability to the linear system of molecular motion by introducing diffusion of morphogens at specific points in time. Based on theoretical calculations, the addition of diffusion led to the destabilization of the system and the development of a pattern now called the Turing-His pattern. Developing patterns through the introduction of diffusion seemed counterintuitive at the time, but this is now a widely accepted system known as the reaction-diffusion system.

Turing’s work was groundbreaking for several reasons. First, this study introduced the concept of morphogens and reaction-diffusion systems, which has had a great impact not only on the field of developmental biology, but also on various fields such as chemistry, physics and ecology. Moreover, due to its unique use of numerical analysis to study biologically observed phenomena, this work has had a significant impact on the field of mathematical biology.

Interestingly, Turing’s work on morphogenesis remained largely unknown until more than 25 years later when researchers pointed to the existence of morphogen gradients.³Nüsslein–Volhard and Wieschaus showed that mutations occur at 15 loci. Drosophila Drosophila melanogaster disrupted larval segmentation patterns, and these mutations had three different levels of spatial organization. Ultimately, the results indicated that morphological gradients were responsible for the segmental patterning of the system. Experimental confirmation of Turing patterns came even later in his 2014, allowing researchers to reproduce them in chemical cells.^Four.

However, as shown above, the application of Turing patterns is not limited to developmental biology, or biology in general. To name a few, Turing patterns describe shell structures and patterns observed in aquatic mollusks.^Fiveand they have also been used to gain insight into human settlements⁶ water filter design⁷Experimentally, Turing patterns could explain the spacing of the lateral ridges of the mammalian palate.⁸In 2021, researchers showed that a strained layer of bismuth atoms on the surface of niobium diselenide exhibits a Turing pattern.⁹, an observation that may play an important role in the development of microdevices. Interestingly, artists are using Turing patterns to create generative art.

Today, August 14, 2022, marks the 70th anniversary of the completion of the manuscript The Chemical Basis of Morphogenesis. Sadly, Turing died two years after its publication, unable to comprehend the broader implications of his work. By the looks of it, Turing has barely scratched the surface of the pattern’s potential applications.