| Dave Linder Software Architect, Mathematical Software Maplesoft 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))](/view.aspx?si=153557/b947d6992478731b1b453b9aa909aae2.gif) ![y[k+1] = a-x[k]](/view.aspx?si=153557/ba5ba1c6b06730b7bdd48b8f7164951d.gif) starting from a choice of three initial points  , and then plotting all the  point pairs. The application below allows you to explore the Hopalong by varying the parameters  ,  and  as well as  the number of iterations, the iterates' symbol size, and the background color choice. You can also change the starting values  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  the number of iterations in order to see the crosses more clearly.  This Application requires at least Maple 18 or the Maple Player 18 in order run. 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. | 
