Fig. 4: Implementation of one-dimensional chemical cellular automata and configuration space quantification.

a, b Representation of hybrid electronic–chemical state machine working in deterministic and probabilistic computational modes. (Black arrow: deterministic, red arrow: probabilistic). Here, D, P, C and T represent digital, physical, chemical and transfer state machines and \({{{{{{\rm{CS}}}}}}}_{{{{{{\rm{a}}}}}}}\), \({{{{{{\rm{CS}}}}}}}_{{{{{{\rm{d}}}}}}}\) and represent analogue chemical state, digital chemical state, and digital state respectively. c Top: Implementation of elementary cellular automata (CA) (rule 30) in deterministic mode (see Supplementary Video 3) and probabilistic modes demonstrating one-to-one and many-to-one mappings (light blue: 0, blue: 1), bottom: observed oscillations with convolutional neural network (CNN) states in the background while running CA with colours representing red, light blue and dark blue oscillatory states. d Top left and bottom show examples of deviations from one-to-one mapping in single and multiple cells (H and L represent high and low pulse width modulation (PWM) states). Top right shows the average peak intensity observed at different PWM levels. center points and error bars represent the mean value and standard deviation from two independent runs (n = 2). This data is qualitative in nature; however, it demonstrates the presence of nonlinear behaviour of observed intensities on the application of different PWM levels (see Supplementary Information Fig. 26 for more details).