3 different methods now yield the same numerical results and are in agreement with other sources

Henon map (discrete dynamical system) was used to test validity of software algorithm models.

Also RPS (Rock Paper Scissors game) computations were re-done yielding correct Lyapunov Exponent spectrum for the game, verifying that the game can be modeled by chaotic attractor (just the same as Henon map) despite its random probabilistic trajectories phase space.

In the summary following 3 different algorithms were used:

1. Wolf method for system of differential equations (see ref. 1 appendix A and ref. 2)

2. Wolf method for discrete time series (without ODE model)  (see ref. 1 appendix B)

3. Sano Sawada method (see ref 3)

In all above cases Lyapunov exponents converge and oscillate around .42, in the full agreement with quoted sources.

In addition a new source of algorithms and application tools can be found in ref. 4

Hope is that we can use these tools to run thru some discretized form of lottery data , let it be frequency/number transition or some other reformulated time series.

As the tool-set is expanding we will be adding computation algorithms and models for Local Lyapunov Exponents, Entropy and Entropy Filtering.

Attempt is to first verify that we follow to best degree possible existing body of research and agree on the numerical results before tackling on lottery number distributions.&nbsp....

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