What follows is the highlighted source code with comments. You can also download this file directly: PlanarMapDemo.java.

/* * This work by W. Patrick Hooper <wphooper@gmail.com> is free of known copyright restrictions. * The work is in the public domain. * * Author's website: <a href="http://wphooper.com">http://wphooper.com</a>. */ package geometry; import number.Complex; /** * This class is just meant to demonstrate the utility of interfaces. * * @author W. Patrick Hooper */ class PlanarMapDemo { /** * Apply the map f one hundred times to the point z and return the result. */ static Complex applyOneHundredTimes(PlanarMap f, Complex z) { for (int i = 0; i < 100; i++) { z = f.map(z); } return z; } public static void main(String[] args) { Complex z=new Complex(0.5, 0.8); System.out.println("The complex number z="+z); Similarity f=new Similarity(new Complex(0,0.75),new Complex(1)); System.out.println("The map f is given by "+f+"."); System.out.println("We have f^100(z)="+applyOneHundredTimes(f,z)+"."); System.out.println("That should be pretty close to the fixed point of f."); ComplexPolynomial g=new ComplexPolynomial(new Complex(0), new Complex(0), new Complex(1)); System.out.println("The map g is given by "+g+"."); System.out.println("We have g^100(z)="+applyOneHundredTimes(g,z)+"."); System.out.println("That should be close to zero, since |z|<1."); // The point of this is that we could write the method applyOneHundredTimes // once, rather than writing a version for each type of function. } }

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