Chaos Lab #3, Help

Critical curves of 2D iterations: the MQ family

This family of 2D endomorphisms has been much studied by Prof. Christian Mira (Toulouse, France) and is treated in Ch. 4 of the book, JPX.
  • u(x,y) = a*x + y
  • v(x,y) = b + x^2
  • The two control parameters here, a and b, are to be set with the sliders at the top of the Tcl/Tk screen. Many choices may result in malfunction of the script.

    The buttons

    • Next LC: the first LC (from the french for "critical curve") is shown in the initial graphic. With each click of this button, the image of the latest LC under the action of the map is drawn.
    • Puff: (from "Puff, the magic dragon") starts from the initial point (set to (0.5, 0.5) at the top of the script) and plots 500 iterates (as red dots) under the iterated map. Each successive puff adds another 500 points to the orbit.
    • Clear: removes the red dots, saving the current endpoint of the trajectory.

    Suggested experiments

    Corresponding to Ch. 4 of JPX, set a = 0.7, and decrease b from -0.4 to -1.0.
    Revised 16 Sept 2002 by Ralph Abraham