If you literally want a visual representation, there are systems of differential equations that model biological/chemical reaction-diffusion. Roughly speaking,

If you literally want a visual representation, there are systems of differential equations that model biological/chemical reaction-diffusion. Roughly speaking, this gives you a bridge between cellular automata, reaction-diffusion and morphogenesis by defining chemicals, states, species - whatever - as a system of differential equations. These produce organic and natural looking patterns!