Arnold’s Cat Map.
The discrete map acting on a two-dimensional lattice {x, y} where x and y are restricted to the integer values 0, 1, ..., c-1.
Its solution introduces Fibonacci integers.
It should be clear that these three expressions are equivalent the latter because of the following identity :
Periodic solutions of the continuous map (period N) :
The discrete map acting on a two-dimensional lattice {x, y} where x and y are restricted to the integer values 0, 1, ..., c-1.
Its solution introduces Fibonacci integers.
Prediction of the period as a function of c :
