State Transition Graphs for Integer Torus Maps

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The state transition graph formed by taking each point {x,y} in an integer grid of size n and mapping it to the point obtained by iteratively applying the transformation Mod[{{a,b},{c,d}}.{x,y},n] the specified number of times.

Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

When the matrix {{a,b},{c,d}} is invertible, every point in the grid maps to a distinct point, so that the state transition graph contains only cycles.



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