Fig. 5: Two-dimensional chemically instantiated probabilistic automaton.

a Snapshots of the two-dimensional experimental platform showing propagation and replication events starting with a single Chemical Entity (see Supplementary Video 4). b The basic construct of the experimental Chemit demonstrates propagation (1), replication (2), competition (3–5), and random selection (6) between multiple events in a 5 × 5 array using the 2D-CCA state machine as a proof-of-principle. PWM states \({{S}}_{{0}},{{S}}_{{1}},{{S}}_{{2}},{{S}}_{{3}}\) are shown in white, orange, red, and blue. c Conceptual design of closed-loop chemically instantiated probabilistic automaton, where CNN, FSM, and PWM stand for convolutional neural network, finite state machine, and pulse width modulation, respectively. d Population dynamics of Chemits on two-dimensional experimental step (7 × 7 cells) vs. oscillatory time steps. e Number of high chemical states vs. time from which Chemits are derived based on pulse width modulation (PWM) logic. f Average population dynamics of Chemits with different domain sizes. g Shows the time evolution of the average number of Chemits with different initial conditions which converge at a steady state depending on the available resource space. All simulations were run 25 times and the mean population at different time steps was estimated (n = 25). The numerical simulation time step is dimensionless.