The Diffusion Game—Using Symbolic Mathematics Software To Play the Game on a Large Scale

The primary goal of the activities in this document is to observe how the statistical "microscopic" behavior of individual particles ultimately determines a certain "macroscopic" behavior in a large system. Diffusion provides a simple example; a particle on one side of a container, through random kinetic collision events, is either kicked to the opposite side of the container or remains on its current side (assuming the container is split into two halves). This behavior is simulated here for a large number of particles by using a Mathcad random number generator. An interactive process is carried out whereby a random integer is generated during each step for each particle, and the particle is moved to the other side if a certain pre-selected outcome is obtained. By carrying out the simulation in Mathcad, one can easily alter the ultimate number of steps in the simulation, the number of particles in the simulation, and the "probability criterion" that is used to determine whether a particle switches sides. ...