Martin's Map Artwork

This Demonstration explores further the artistic possibilities of Martin's map. It requires the support of a C compiler.
The map can be simplified to , , where and are real and is either or . Barry Martin [1] proved that all possible orbits of the map can be explored with these parameter values.
The graphics show up to 1000 colored orbits generated by up to 5000 iterations started from random initial values. Some initial values around the center are added to improve the overall appearance.
Change the zoom rate and drag the locator to explore new areas of this beautiful iterative mapping. More ways to explore Martin's map can be found in [2].

SNAPSHOTS

  • [Snapshot]
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DETAILS

References
[1] B. Martin, "Theory of the Simplified Hopalong Equations," Jan 12, 2010. www.dropbox.com/s/ae84a49cbx9hitk/Theory%20 of %20 the %20 simplified %20 Simplified %20 Hopalong.pdf?dl=0.
[2] I. Sassarini, "An Interactive Flight through Attractor Orbits Generated Using Martin's Hopalong Formula," Chrome Experiments. (Apr 22, 2016) www.chromeexperiments.com/experiment/webgl-attractors-trip.
[3] I. Sassarini, "Barry Martin's Hopalong Orbits Visualizer." (Apr 22, 2016). iacopoapps.appspot.com/hopalongwebgl.
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