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One Dimensional Rings of Coupled Oscillators - Turing's Theory Realized
Alan Turing is most well know for his work in computation and artificial intelligence but he also made dramatic contributions to many other scientific disciplines. In this work we look into one of his lesser known but equally important contributions to the field of pattern formation in biological systems. Using a customized Programmable Illumination Microscope (PIM) and the Belousov-Zhabotinsky (BZ) reaction we have the ability to modulate and perturb a large system of nearest neighbor coupled nonlinear oscillators. The BZ reactants are put into an emulsion environment and subjected to external inhibitory illumination while undergoing realtime observation and analysis. This system allows for selective phase perturbations and oscillation cessations as well as global modulation of reaction rate and coupling strength. The active feedback system allows for manipulating the system into desired attractor states and the creation of arbitrary boundary conditions. These tools have been used to create one dimensional rings of oscillators as theorized by Turing in The Chemical Basis of Morphogenesis (1952). We present the patterns and dynamical attractors observed in these experiments and compare to two theoretical models; a single variable phase model as well as a Turing analysis of an oscillatory reaction scheme.