Hopalong Attractor

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).

	References
	Barry Martin, Computer Recreations, Scientific American, Sept 1986.   Paul Bourke, An Introduction to Fractals, http://paulbourke.net/fractals/fracintro/