Cobweb Plot
- To: mathgroup at smc.vnet.net
- Subject: [mg27494] Cobweb Plot
- From: "Jon Joseph" <pokemon at tds.net>
- Date: Thu, 1 Mar 2001 03:53:20 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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
- Follow-Ups:
- Re: Cobweb Plot
- From: Tomas Garza <tgarza01@prodigy.net.mx>
- Re: Cobweb Plot