## Biological Basis of the Computational Model The code provided is a simulation of excitable media using a cellular automata approach, which mimics the dynamics of excitable systems such as neural or cardiac tissues. The primary biological concepts being modeled in the code are excitation, refractory periods, and external stimulation governed by a Poisson process. Below are the key biological aspects that are mirrored in this computational model: ### Excitable Cells - **Cellular Excitability**: The model represents excitable cells, which have the ability to undergo an action potential. Excitable cells, like neurons or cardiac muscle cells, react to stimuli and propagate electrical signals. In the code, an excited state is represented by a `1`, indicating the cell has "fired". ### Refractory Periods - **Recovery and Refractory Periods**: After excitation, cells enter a refractory state where they cannot be re-excited immediately. This is akin to the physiological refractory periods observed in action potentials. The code models this by assigning a negative value to cells post-excitation, which gradually returns to zero (the resting state) over time. The refractory period can vary based on the connectivity of the cell, reflecting biological variability in recovery phases. ### Connectivity - **Cellular Connections**: The model considers the connectivity between cells. Biologically, this can be thought of as synaptic connections in neurons or gap junctions in cardiac tissues. Cells with four connections have a longer refractory period, demonstrating how structural connectivity can affect functional dynamics. This may represent, for example, certain cells in the brain or heart that are more interlinked and therefore have altered electrophysiological properties. ### Stochastic Stimulation - **External Stimulation and Poisson Process**: The code includes stochastic external stimulation modeled as a Poisson process. This represents random excitatory input that cells might receive from external sources, akin to spontaneous neural activity or random synaptic inputs. The probability of stimulation is determined by the rate parameter (`lambda`) of the Poisson process, which controls the mean stimulation rate. ### Neighbors Influencing Excitation - **Propagation of Excitation**: The function `next_to_excited` assesses whether a cell's neighbor is excited, allowing for potential excitation in the current cell. This mimics the biological propagation of electrical signals where the excitation of one cell can trigger the excitation of adjacent cells, contributing to the spread of action potentials across tissue. Overall, this model captures fundamental biological principles of excitable media, emphasizing how cell connectivity, refractory periods, and external stimuli contribute to the dynamics of cellular excitability.