We continue our work with 2D iterations.
- A few critical curves of the MQ map
family define an absorbing area.
-
Maple script for an MQ map
- This is a text version of the Maple script
which was used to draw Fig. 4-01.
We have not included it here as you will draw your own
with our Tcl script.
- Critical curves of the MQ map family
- Crit curves of MQ
- Download this ASCII file and save it on your hard disk,
- Open the Wish program, and select this script
Instructions for the curves program
- On openning:
- We draw the critical curves of rank -1 and of rank 0
with the default values of the map family parameters,
a = 0.7, and b = -0.8 (the sliders show zero)
- Sliders for map parameters a and b
- These come into use after clicking the Clear button
- Clear button:
- This clears the screen, reads the two sliders,
and draws the fundamental critical curve of rank -1
- Puff button:
- Thus puffer computes 500 iterates of the standard
initial point, (-0.5, -0.5), then another 500 iterates,
etc., with each press of the button
- NextLC button:
- This button draws the next critical curve segment
- Snap a Pic button
- This will create a printable file ("canvas.ps")
on the hard drive in the folder which contains the
program "Wish" (probably "Tcl/Tk Folder") which may
be printed on a Postscript printer
Try variations of the map parameters following the figures
in the text, Chs. 4, 5, and 6, and notice how the critical
curves locate the attractor.
References for 2D maps:
- Chaos in Discrete Dynamical Systems,
Chs. 4,5,6.
- All books by Mira
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