Hopalong Attractor
Main Concept
Hopalong attractors are fractals introduced by Barry Martin of Aston University in Birmingham, England.
The point-plot for this application is generated by iterating the following equations, also known as the Martin map:
starting from a choice of three initial points , , and then plotting all the , point pairs.
The following application allows you to explore the Hopalong by varying the parameters , , and as well as (the number of iterations), the symbol size of the iterates, and the background color choice. You can also change the starting values , of each of the three orbits by dragging the handles (which are solid green diamonds by default).
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More MathApps
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References
Barry Martin, Computer Recreations, Scientific American, Sept 1986.
Paul Bourke, An Introduction to Fractals, http://paulbourke.net/fractals/fracintro/
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