1DMaps icon 1DMaps 1.4

About 1D Maps

1DMaps is a Macintosh application for displaying the dynamics of some one dimensional, discrete dynamical systems (i.e. maps!). The latest version requires Mac OS X 10.2 or later, but version 1.1, still available, should run under Mac OS 8.6-10.1 If you have an old version of the MacOS you might need the OpenGL library, and the Carbon Library, which you can download from apple.

Latest version (Mac OS 10.2-10.14) 1DMaps 1.4.4
Version 1.1 (Mac OS 8.6-10.1) 1DMaps 1.1
Logistic Map

Bifurcation diagram for the logistic map. This one of 7 different maps, and 5 types of dynamical displays in 1DMaps.

Using the Program

This program still has a few quirks and user interface problems. Printing and "cut", "copy" and "paste" are not yet implemented for graphics, alas! (though they work for the text). Use "Cmd-Shift-3" or "Cmd-Shift-4" to create a picture file of the graphics window (Cmd is the "apple key").

A Help file is coming soon. For now you will have to simply explore the menus! You can choose from 7 dynamical systems in the "Choose" Menu item. Multiple windows can be open at once: so you can have more than one system displayed, or display one system in multiple ways.

Show Menu The "Show" Menu allows you to change the type of data being displayed in the frontmost window.

  • "Cobweb" to show the function and iterations using the cobweb diagram. Click in the plot window to change the initial condition. Use the spacebar to interate one step. Set the number of iterates and parameters using the "Set Paramters" menu.
  • "Bifurcation" to show the bifurcation diagram (varying one parameter of the system);
  • "Invariant Density" to show the average occupation number in a histogram of a particular orbit
  • "Lyapunov Exponent" to compute the stability of the given initial condition as a function of parameter
  • "Exit Time" to compute the time that initial conditions take to escape to "infinity." (onlyt meaningful when the map has orbits that are unbounded, e.g. the Logistic map for μ>4)

For more information on 1D dynamics

  • Strogatz, S. (1994), Nonlinear Dynamics and Chaos (Addison-Wesley, Reading)
  • Devaney, R. L. (1986), An Introduction to Chaotic Dynamical Systems (Benjamin/Cummings, Menlo Park).
  • Alligood, K., T. Sauer and J. Yorke (1997), Chaos. An introduction to dynamical systems (Springer-Verlag, New York).

Keyboard Options



Iterate the map one step (used for Cobwebs)

  Up/Down Arrow:

Increment or decrement the parameter "mu"

  Right/Left Arrow:

Increment or decrement the "n", to display the function f^n(x)


  Command (Apple) .:

Cancel long operations (for example if you set the number of iterations too large)

Last updated: Nov 11, 2019
This program is based upon work supported by the National Science Foundation under Grant DMS-0202032 and DMS-0707659.