# Orbits of the Hopalong Map

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This Demonstration plots a number of orbits of the two-dimensional iterative map known as the Hopalong map. The Hopalong map can be represented by the recursion equations: , , with and ranging over the reals and equal to either 0 or +1.

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Contributed by: Erik Mahieu (July 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The Martin map equations were taken from [1] and [2].

The simplified, two-parameter equations for the map were suggested to the author by Barry Martin.

The Martin map is also called the "Hopalong-Attractor".

See also the German website: Huepfer.

References

[1] M. Trott, *The Mathematica GuideBook for Programming*, New York: Springer–Verlag, 2004 pp. 347–349.

[2] B. Martin, "Graphic Potential of Recursive Functions," in *Computers in Art, Design and Animation *(J. Landsdown and R. A. Earnshaw, eds.), New York: Springer–Verlag, 1989 pp. 109–129.

## Permanent Citation

"Orbits of the Hopalong Map"

http://demonstrations.wolfram.com/OrbitsOfTheHopalongMap/

Wolfram Demonstrations Project

Published: July 18 2011