Hopalong Attractor - Maple Help

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:

${x}_{k+1}={y}_{k}-\mathrm{sign}\left({x}_{k}\right)\cdot \sqrt{\left|b\cdot {x}_{k}-c\right|}$

${y}_{k+1}=a-{x}_{k}$

starting from a choice of three initial points ${x}_{1}$, ${y}_{1}$, and then plotting all the ${x}_{i}$, ${y}_{i}$ point pairs.

The following application allows you to explore the Hopalong by varying the parameters $a$, $b$, and $c$ as well as $n$ (the number of iterations), the symbol size of the iterates, and the background color choice. You can also change the starting values ${x}_{1}$, ${y}_{1}$ of each of the three orbits by dragging the handles (which are solid green diamonds by default).

Hopalong Attractor

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