Orbits of Martin's Map
Orbits are generated by iterating the map times using different initial points. The map parameters , , and can be varied manually or a random set can be launched. Three orbits are plotted initially, starting from three different initial points marked by locator objects "". You can drag these initial points or add and/or delete new ones (Alt+Click on Windows) inside the plot. Three orbit colors are used cyclically.
All locator objects can be hidden for a "cleaner" plot. The plot range can be changed to full to include all points from all orbits.
The Martin map equations were taken from:
M. Trott, The Mathematica GuideBook for Programming, New York: Springer‐Verlag, 2004 pp. 347–349.
B. Martin, "Graphic Potential of Recursive Functions,"J. Landsdown, R. A. Earnshaw, eds., Computers in Art, Design and Animation, New York: Springer–Verlag, 1989 pp. 109–129.
The Martin Map is also called the "Hopalong-Attractor".
See also: Hopalong Image Generator and a German website: Huepfer.
"Orbits of Martin's Map"
Wolfram Demonstrations Project
Published: September 24 2009