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Hopalong Attractor

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Hopalong Attractor


Dave Linder

Software Architect, Mathematical Software



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]-sign(x[k])*sqrt(abs(b*x[k]-c))

         y[k+1] = a-x[k]


starting from a choice of three initial points `#msub(mi("x"),mi("1"))`, `#msub(mi("y"),mi("1"))`, and then plotting all the `#msub(mi("x"),mi("i"))`, `#msub(mi("y"),mi("i"))` point pairs.


The application below allows you to explore the Hopalong by varying the parameters a, b and c as well as n the number of iterations, the iterates' symbol size, and the background color choice. You can also change the starting values  `#msub(mi("x"),mi("1"))`, `#msub(mi("y"),mi("1"))` of each of the three orbits by dragging the cross symbols appearing in the plot, but you may need to set the background color to white and reduce n the number of iterations in order to see the crosses more clearly.


Hopalong Attractor




This Application requires at least Maple 18 or the Maple Player 18 in order run.


Application creation with Explore



Legal Notice: © Maplesoft, a division of Waterloo Maple Inc. 2014. Maplesoft and Maple are trademarks of Waterloo Maple Inc. This application may contain errors and Maplesoft is not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact Maplesoft for permission if you wish to use this application in for-profit activities.