Random Walk on a Lattice 

Visualize a symmetric random walk in 2D.

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X SeedRandom[1234]; data2d = RandomFunction[RandomWalkProcess[0.5], {0, 10^3}, 2];

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X Graphics[Line[Transpose@data2d["States"]], AspectRatio -> Automatic]

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Visualize a symmetric random walk in 3D.

In[3]:=

X data3d = RandomFunction[RandomWalkProcess[0.5], {0, 10^3}, 3];

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X Graphics3D[Line[Transpose@data3d["States"]], BoxRatios -> Automatic]

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