Math Art

Logistic Map

The Logistic map is x_t+1 = a x_t(1 - x_t), with the initial condition x₀ = 0.5.

Think of t = 0, 1, 2, ... as an integer time. The long time behaviour depends in a very complicated way on the parameter a. The mural shows the ``attractor'' in the interval 0 < x < 1, for the parameter 2 < a < 4.
full Bifurcation diagram
detail

Takashi Kanamaru's Logistic Map Site.

Takashi Kanamaru's Bifurcation Diagram for the Logistic Map Site.

Takashi Kanamaru's Chaos Site (The parent of the previous sites.)

Here is the cobweb app that Mark Haferkamp at NAU wrote.

Menger Sponge Cross section

Here is a youtube video, Menger Sponge Cross Section

Menger Star at level 5

Text of the EPS file used to make the level 5 Menger Star

Blank page. Jim Swift's home page Department of Mathematics NAU Home Page
e-mail: Jim.Swift@nau.edu