where C(x, t) is the concentration of the ink at a location away from the origin at distance x and at elapsed time t from time zero, and D is the famous diffusion coefficient often a constant in a homogeneous solution. The equation says that the slope of the concentration changing over time is proportional to the slope of the slope (2 nd derivative) of the concentration gradient at that location, a similar formula in the Schrödinger equation for quantum mechanics. The official analytical solution for this problem when D is a constant is a Gaussian curve spreading over space and broadening over time 𝐶(𝑥, 𝑡) =