Quorum Sensing: Spatial Autoinducer Diffusion Front (2D)

This is the 2D companion to the 3D well-mixed quorum-sensing simulator, and it is deliberately built on different physics rather than a flattened view of the same scene. Instead of one pooled concentration shared instantly across the whole chamber, this version solves a real reaction-diffusion PDE on a spatial grid: each bacterium secretes autoinducer into the medium at its own location, the signal spreads outward at a finite diffusion rate, and every cell only ever senses the concentration directly beneath it. That locality lets genuinely spatial phenomena emerge — a dense pocket of cells can ignite into a self-reinforcing, glowing patch long before the population as a whole reaches quorum, and that patch can then spread outward as an activation front, or stay stubbornly isolated if diffusion is too slow or the medium is flushed too fast. Tune cell density, the diffusion coefficient, dilution rate, receptor threshold and feedback gain to watch local quorum ignition, spreading fronts, and — at high diffusion — convergence back onto the same well-mixed balance the 3D model predicts.