dorband

Instructions may be found below the applet interface.

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view/download model file: dorband.nlogo

WHAT IS IT? ----------- This is a mathematical model that demonstrates discrete dynamical systems in the plane, generated by iteration of a single map (endomorphism). In this particular case, the map is selected from a one-parameter family of maps, called the Dorband Map Family (after John Dorband), by setting a control parametr, 'c", between zero and one. HOW IT WORKS ------------ A set of "test particles" (chosen by user actions) will be advanced along trajectories by repeated application of the map. HOW TO USE IT -------------

SETUP: Clears the screen and gets ready. PLACE-PARTICLES: Puts the program into the mode in which you can position green test-particles by clicking anywhere in the graphics window. GO: Runs the simulation to show the trajectories in red, hides the test particles. Pressing the "go" button again will stop the action. CLEAR: Erases the red trajectories, restores green visibility to the test particles. After stopping the action, clearing the screen, and resuming GO, you may judge if the trajectory has actually arrived close enough to the attractor.

THINGS TO NOTICE ---------------- Try to identify all attractors for a given setting of "c". CREDITS AND REFERENCES ---------------------- This model derived from: Wilensky, U. (1998). NetLogo Vector Fields model. http://ccl.northwestern.edu/netlogo/models/VectorFields. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. Author: Ralph Abraham, UCSC, January, 2005.