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> ---------
riddle@mathcs.emory.edu (Larry Riddle) (10/07/90)
>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. > Richard Parris at Philips Exeter Academy has written a program for the IBM-PC called feedback that can draw the web diagram for any function typed in by the user. The program will also display the iteration count and the current x value. The user can set any initial seed. The program will also do bifurcation diagrams, but rather slowly. Zooming is possible on both the web diagram and the bifurcation. And the best part is that the program is FREE. All you have to do is write Richard at Philips Exeter Academy (it's somewhere in New Hamphsire, sorry can't remember the exact address) and enclose a blank disk and a return stamped mailer. -- Larry Riddle | riddle@mathcs.emory.edu PREFERRED Agnes Scott College | {decvax,gatech}!emory!riddle UUCP Dept of Math | riddle@emory.bitnet NON-DOMAIN BITNET Decatur, GA 30030 | (404) 371-6222 AT&T