The logistic map and the
tent map are really families
of functions: both depend on a parameter s. For each s, we get a different function. The
values of the iterates of a point certainly can depend on s, and the bifurcation diagram
is a method of organizing this data. |

Specifically, the bifurcation
diagram is a graph of the s-values on the horizontal axis, and above each s-value
the iterates of some value, plotted vertically. |

To emphasize the long-range behavior,
sometimes the points are plotted only after a number of transients
are computed but not plotted. |

Selecting the s-values on the left, we see the bifurcation diagram for s up to that
value, together with the graphical iteration plot and
histogram at that s-value. |