These images are excerpts from the bifurcation diagrams of
various one-dimensional maps (…). Each of these dynamical
systems model various physical phenomena in the real world. For
example, the logistic map is a crude model of population
dynamics with reproduction and limited resources, and it is
often used as an example of the period-doubling route to chaos.
Typical of chaotic systems, many regions in these figures
exhibit self-similarity and reflect the order that emerges outof
chaos. These images were generated numerically by iterating the
discrete-time maps above as a bifurcation parameter is varied.
The bifurcation parameter is plotted as the y-axis (elevation),
and at each elevation, the stratified layer represents the
attracting set of the dynamical system for that particular
choice of bifurcation parameter. Bifurcation refers to a
qualitative change in the behavior or topology of a dynamical
system as a parameter is varied.