Logistic Map Histograms and Bifurcation Diagram


Width: Height: Histogram Height: Data point intensity (0-1):

Iterations: Data points per r: Min r: Max r: Min x displayed: Max x displayed:

Histogram - click the bifurcation diagram to display

Another view of logistic map - the iteration of xn+1 = rxn(1-xn)

This version displays the results of doing lots of iterations from random values of x0 (chosen from a uniform distribution 0-1). The final value (after the specified number of iterations) is plotted on the chart. The x-axis represents r, and the y-axis represents the value of x reached. Essentially, each column of the chart acts like a histogram, where brighter colours represent more data points landing there. You can also see the histograms, as histograms, by clicking the chart.

This approach has the effect of plotting the famous bifurcation diagram. To get a more faithful representation, try increasing the number of iterations - 1000 is a good number, although it may be a little slow.

Other logistic map plotters - Logistic Map Graph and Logistic Map Pixmap

Peter Corbett, 2014

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