cycle detection methods in Mathematica
CycleFixedPoint.m implements the function CycleFixedPoint
, which can be used to detect cycling in an iterative process.
The function implements both the algorithms of Floyd and Brent to detect cycles.
Some examples:
CycleFixedPoint[Mod[7 # + 3, 11] &, 2, Method -> "Brent"]
{4, 9, 0, 3, 2, 6, 1, 10, 7, 8}
CycleFixedPoint[Mod[7 # + 3, 11] &, 2, Method -> "Floyd"]
{2, 6, 1, 10, 7, 8, 4, 9, 0, 3}
CycleFixedPoint[3.5 # (1 - #) &, 0.2, Method -> "Brent"]
{0.826941, 0.500884, 0.874997, 0.38282}
CycleFixedPoint[3.5 # (1 - #) &, 0.2, Method -> "Floyd"]
{0.826941, 0.500884, 0.874997, 0.38282}
See the package for more details.