Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Zero-Centered Bins - Example 2

Here we use the cartoon with generator having turning points (3/9, 2/3) and (5/9, 1/3). The bin boundary B2 is set to 0, and B1 and B3 are one tenth of the range below and above B2.

Here are the successive differences of the cartoon data. Note most differences lie in bin2 and bin3, but bin1 and bin4 are more fully occupied than we saw when B1 and B3 are one-quarter of the range. Here is the IFS driven by these differences as data points. The only obvious feature is the cluster of IFS points along the diagonal between (1,0) and (0,1). The superdiagonal (between (1,1/2) and (1/2,1)) contains a faint echo of the diagonal, but the subdiagonal (between (1/2,0) and (0,1/2)) appears relatively empty.

Return to zero-centered bins.