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.
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