Coarse-Graining the Data

Logistic Map Examples: Mean-Centered Bins

Here is the time series y₂ - y₁, y₃ - y₂, ..., y₁₀₀₀ - y₉₉₉ generated by successive differences of 1000 iterates of the logistic map with mean-centered bin lines drawn, and the corresponding driven IFS.

We must use differences because the logistic map values y_k all lie between 0 and 1, so mean-centered bins will be of no use for the y_k.

Here the bin boundaries B1 and B3 are placed one-quarter of the standard deviation of difference values below and above the mean.

Here the bin boundaries are half the standard deviation below and above the mean.

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