Re: Cobweb Plot
- To: mathgroup at smc.vnet.net
- Subject: [mg27513] Re: Cobweb Plot
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sat, 3 Mar 2001 03:39:56 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <97l3cs$jfm@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, something like this ? http://www.mathconsult.ch/showroom/pubs/MathProg/htmls/p2-1.htm Buy the book by Romand Maeder http://www.amazon.com/exec/obidos/ASIN/0124649920/mathconsdrrmder/107-1760968-0378115 Regards Jens Jon Joseph wrote: > > I have been experimenting with chaotic systems and have been trying to > produce a "Cobweb Plot". A description of this type of plot, taken from > "CHAOS An Introduction to Dynamical Systems" by Alligood, Sauer, Yorke, is > > "A cobweb plot illustrates convergence to an attracting fixed point of > g(x)=2x(1-x). Let x0=0.1 be the initial condition. Then the first iterate is > x1=g(x0)=0.18. Note that the point (x0,x1) lies on the function graph, and > (x1,x1) lies on the diagonal line. Connect these points with a horizontal > dotted line to make a path. Then find x2=g(x1)=0.2952, and continue the > path with a vertical dotted line to (x1, x2) and with a horizontal dotted > line to (x2, x2). An entire orbit can be mapped out this way." > > I can create the data in a procedural program and then plot the list that > results. Can anyone think of a more elegant, Mathematica oriented, > approach? Thanks in advance > > Dr. Jon Joseph > VP of Advanced Technology > Nicolet Biomedical > 5225 Verona Road > Madison WI 53711 > jjoseph at nicoletbiomedical.com