Diffusion equation

In an appropriate limit the density distribution for cellular automaton (d) appears to satisfy the usual diffusion equation ∂_{t}f[x, t] c ∂_{xx}f[x, t] discussed on page 163. The solution to this equation with an impulse initial condition is Exp[-x^{2}/t], and with a block from -a to a it is (Erf[(a - x)/Sqrt[t]] + Erf[(a + x)/Sqrt[t]])/a.