Iterations: Min r: Max r: Min x0: Max x0:
A view of the logistic map - the iteration of xn+1 = rxn(1-xn)
This version displays different values of r along the x-axis, different values of x0 along the y-axis, and represents xn as pixel colour - black = 0, white = 1. If you click and drag on the canvas you can zoom in. Try altering the iteration count; working through values of 0 to 20 should give you an idea of how the map works, and 100 iterations should be fine if you don't zoom in too far.
This diagram - like so many others - shows the connection between chaos and fractals. It plots the outcomes from a chaotic system, and the result is a fractal... or at any rate tends towards being fractal as the number of iterations increases. There's a lot of self-similarity in the diagram.
Other logistic map plotters - Logistic Map Graph and Logistic Map Histograms and Bifurcation Diagram
Peter Corbett, 2014
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