Logistic map bifurcation diagram image gallery

These images of regions of the logistic map bifurcation diagram at various magnifications were created by the WBif.cpp program using its features that make it easy to apply different coloring schemes that bring out different aspects of the diagram. The latest version of the program is for Microsoft Visual C++ .NET.

The diagrams are produced from left to right as vertical slices. In the full bifurcation diagram (see below), the X (horizontal) axis plots values from 0 to 4.0. The Y axis plots the equation's results for the values of X through many sequential iterations. The color of each point is determined by how many times it was hit while the slice was being calculated, so the hardest hit areas get colored lighter or darker depending on the palette used.

The blank windows are areas where the equation produces only a few unique values. Farther right, the number of values doubles. After a "1" region comes a "2" region, then a "4", and so on. This is called period doubling. The most filled-in regions are where the values exhibit chaos, not repeating and thus not falling into a cycle.

Click any thumbnail to view the full size image. Image sizes range from 60 KB to 300 KB.

The full bifurcation diagram from X=0 to 4. The full size image has detail that the thumbnail does not.	Full diagram with different coloring.