Bifurcation Diagram

A bifurcation diagram is a pretty fractal that demonstrates how very simple functions can give rise to chaotic behaviour.

In this applet we take a function f and iterate it to form a series:

y0 = 0.5
yn+1 = r * f(yn)
Moving horizontally through the image the constant r is slowly varied and for that vertical slice a new series of y values is calculated and plotted.

If you pick f(x) = x * (1 - x) then you'll end up with the Logistic Equation version of the bifurcation diagram. This applet starts with this funciton, but by clicking the "Edit Function" button you can edit the plot of f and create your own bifurcation diagram.

The interesting thing about this fractal is that a whole range of functions give rise to chaotic behaviour.

More details: Wikipedia, Paul Bourke.

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My other fractals: