Simulation of 3D Diffusion Using the Monte Carlo Method

Using a Monte Carlo method, this Demonstration simulates the diffusion process in three dimensions, which obeys the equation

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At time , the square of points at the bottom of the box represents the initial condition. At each time step, these points will diffuse by a random walk (Monte Carlo simulation) in three dimensions , , and . Each dimension can have a different diffusion coefficient, but in this Demonstration the three diffusion coefficients are assumed equal. You can also change the range of the initial square.