This paper describes a random walk simulation using a number cube and a lattice of concentric rings of tiled hexagons. At the basic level, it gives beginning students a concrete connection to the concept of stochastic diffusion and related physical quantities. A simple algorithm is presented that can be used to set up spreadsheet files to calculate these simulated quantities and even to “discover” the diffusion equation. Lattices with different geometries in two and three dimensions are also presented. This type of simulation provides fertile ground for independent investigations by all levels of undergraduate students.
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Information about the listed shapes can be found at the Wolfram Website, for example, <http://mathworld.wolfram.com/TruncatedIcosahedron.html> or <http://mathworld.wolfram.com/TruncatedOctahedron.html> or <http://mathworld.wolfram.com/Space-FillingPolyhedron.html>.
© 2013 American Association of Physics Teachers.
2013
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