callahan@mimsy.umd.edu (Jack Callahan) (10/06/90)
I'm looking for a plotting package that will draw orbit diagrams for iterated functions for viewing things like bifurcations. I heard of something called MAPPER, but haven't be able to locate it. Something else that would nice is a plotting package that displays the function and then shows the behavior of the iterated of a particular point (specified by the user). It might even draw the lines from f(x) to the line x=y back to f(x), etc. used to illustrate the effects of attracting and repelling fixed points and their basins. Thanks for any feedback. BCNU, -- jack -- Jack Callahan - callahan@brillig.umd.edu Computer Science Department University of Maryland, College Park <insert a cute and witty disclaimer here>
scavo@cs.uoregon.edu (Tom Scavo) (10/06/90)
In article <26866@mimsy.umd.edu> callahan@mimsy.umd.edu (Jack Callahan) writes: >I'm looking for a plotting package that will draw orbit >diagrams for iterated functions for viewing things like >bifurcations. I heard of something called MAPPER, but >haven't be able to locate it. Fractint ver. 14 includes a few routines that draw orbit diagrams for the logistic function and a trigonometric mapping (type = bifurcation, biflambda, bif+sinpi, bif=sinpi). That's the only noncommercial package that I know of (anybody else know of others?). Although I haven't seen it, I understand that the program Chaos in the Classroom by Dynamical Systems, Inc. will do bifurcation diagrams for eight different mappings. If you care to program yourself, see chapter 4 of _Chaos,_Fractals,_and_Dynamics_ by R.L. Devaney for an elegant algorithm in Basic. The basic idea of an orbit diagram is incredibly simple. >Something else that would nice is a plotting package that >displays the function and then shows the behavior of the >iterated of a particular point (specified by the user). >It might even draw the lines from f(x) to the line x=y >back to f(x), etc. used to illustrate the effects of >attracting and repelling fixed points and their basins. Chaos in the Classroom claims to be able to do this for its menu of eight mappings, and so will Phaser for just about any function you can think of. Also, there's an algorithm (again in Basic) in Barnsley's _Fractals_ _Everywhere_ (and again in chapter 4) that will draw the "stair step" or "web" diagram that you ask for. Hope this helps. -- Tom Scavo <scavo@cs.uoregon.edu> ---------