Thurston's method for real polynomials

As discussed in the paper The W. Thurston Method for Real Polynomial Maps by A.Bonifant, J.Milnor, and S.Sutherland, the maple code used to implement Thurston's Method for real polynomials and to produce most of the figures in the paper can be found below.

• If you would like to just run the maple code here, enter the combinatorics in the box below. Specifying the dynamics of the critical orbits will completely determine a post-critically finite polynomial on the unit interval. To do so, enter a sequence of n+1 integers between 0 and n, separated by commas, satisfying the following rules:
  • Two consecutive integers must always be different
  • The first and last entries must be either 0 or n
  • There must be at least one "turning point"; that is, the sequence cannot be strictly monotone.

  For example, entering "0,3,2,1,0" will find the quadratic map of the form ax(1-x) where the critical point has a period two orbit (and also list the fixed point between them), while "8,7,6,5,2,1,3,4,0" will determine a cubic polynomial with both critical points in a period 7 orbit, framed by the (repelling) period 2 orbit 0↔1.
  The interface on this page only supports maps with simple critical points, and allows less control of the process and the resulting graphics than Maple program below.

  ThurstonMethod([ ]);
• The maple routines are in the file RealThurstonMethod.mpl, which should be loaded into a maple session using a command like read(RealThurstonMethod.mpl); (Save this file in the same directory as you will run your Maple session from). This file is readable as regular text, in case you would like to see the details of the implementation but don't have immediate access to Maple.
• Here is a maple worksheet illustrating its use. This requires a copy of the maple routines above in order to run. You might also want the worksheet used to produce (some of) the figures in the paper, but there is no explanation there.