MathGroup Archive 2001

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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



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