Alan Turing was a well-known computer scientist in the early to mid 1900s. He broke the German Enigma machine’s code during World War II, greatly aiding in the Allied victory, and went on to work on the first stored program computer at the National Physical Laboratory in London after the war. Towards the end of his life, Turing researched other fields, which resulted in part in the development of his theory of morphogenesis and his theoretical discovery of Turing Patterns. His theory, simply put, says that there are two “morphogens,” one activator and one inhibitor, which diffuse into the available space and react with one another. These reactions form a predictable pattern that can produce a variety of things, including patterning on animals (e.g. zebra stripes or cheetah print), variety in cell composition that aids in the development of animal embryos, and possibly even crime pattern predictions in cities.
The math behind this theory is surprisingly simple considering its far-reaching scope: it has two main components that account for diffusion and reaction and can be subbed out for the equations related to the specific “morphogens.” The equation solves for the change in concentration over time. The diffusion part includes a diffusion constant multiplied by what can be considered the “acceleration” of the concentration in a specific location. The reaction part is solely dependent on the local concentration of each chemical, and the equations pictured in the poster serve as placeholders that are switched out when the morphogens are identified. The relative simplicity of these equations make this idea relatively accessible to people outside the physics and math fields, meaning that biologists and chemists can incorporate it into their work. Turing’s theory serves as a bridge between the three big fields of science as well as math, and is gaining traction currently as an important research topic in areas of study such as biophysics.
