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
are real and
. Barry Martin  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 .