Significance Turing proposed that intercellular reaction-diffusion of molecules is responsible for morphogenesis. The impact of this paradigm has been profound. We exploit an abiological experimental system of emulsion drops containing the Belousov–Zhabotinsky reactants ideally suited to test Turing’s theory. Our experiments verify Turing’s thesis of the chemical basis of morphogenesis and reveal a pattern, not previously predicted by theory, which we explain by extending Turing’s model to include heterogeneity. Quantitative experimental results obtained using this artificial cellular system establish the strengths and weaknesses of the Turing model, applicable to biology and materials science alike, and pinpoint which directions are required for improvement.

We investigate the Belousov–Zhabotinsky (BZ) reaction in an attempt to establish a basis for computation using chemical oscillators coupled via inhibition. The system consists of BZ droplets suspended in oil. Interdrop coupling is governed by the non-polar communicator of inhibition, Br2. We consider a linear arrangement of three droplets to be a NOR gate, where the center droplet is the output and the other two are inputs. Oxidation spikes in the inputs, which we define to be TRUE, cause a delay in the next spike of the output, which we read to be FALSE. Conversely, when the inputs do not spike (FALSE) there is no delay in the output (TRUE), thus producing the behavior of a NOR gate. We are able to reliably produce NOR gates with this behavior in microfluidic experiment.

Methods for creating custom planar networks of diffusively coupled chemical oscillators and perturbing individual oscillators within the network are presented. The oscillators consist of the Belousov-Zhabotinsky (BZ) reaction contained in an emulsion. Networks of drops of the BZ reaction are created with either Dirichlet (constant-concentration) or Neumann (no-flux) boundary conditions in a custom planar configuration using programmable illumination for the perturbations. The differences between the observed network dynamics for each boundary condition are described. Using light, we demonstrate the ability to control the initial conditions of the network and to cause individual oscillators within the network to undergo sustained period elongation or a one-time phase delay.

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to k peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky ∼100µm emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength; (i) unlocked ; uncorrelated phase shifts between all oscillators, (ii) locked ; arm-hubs synchronized in-phase with a k-dependent phase shift between the arm and central hub, and (iii) center silent; central hub stopped oscillating and the arm-hubs oscillated without synchrony. We compare experiment to theory. For case (ii), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.