path
Class SubstitutionFractal

java.lang.Object
  path.SubstitutionFractal

All Implemented Interfaces:

Path

public class SubstitutionFractal
extends Object
implements Path

A substitution fractal is the limit of a sequence of polygonal approximations. It is obtained by the following construction. Let p be an arbitrary polygonal path. This will be the first polygonal approximation of our path. Let gamma be a polygonal path which starts at zero and ends at one. We call this the substitution path. The second polygonal approximation is obtained by replacing each edge of p by the image of gamma under a similarity sending the endpoints of gamma to the endpoints of the edge. The third approximation is obtained by applying the same process to the second approximation, and so on.

Constructor Summary

SubstitutionFractal(PolygonalPath gamma)
Construct a Substitution path with gamma serving as both the first polygonal approximation and the substitution path.

SubstitutionFractal(PolygonalPath p, PolygonalPath gamma)
Construct a Substitution path with a given first polygonal approximation p and a substitution path gamma.

Method Summary

Complex	endingPoint() Return the ending point of the path
PathIterator	iterator() Return an iterator over the sub-paths
Complex	startingPoint() Return the starting point of the path

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SubstitutionFractal

public SubstitutionFractal(PolygonalPath p,
                           PolygonalPath gamma)

Construct a Substitution path with a given first polygonal approximation p and a substitution path gamma.

SubstitutionFractal

public SubstitutionFractal(PolygonalPath gamma)

Construct a Substitution path with gamma serving as both the first polygonal approximation and the substitution path.

Method Detail

iterator

public PathIterator iterator()

Return an iterator over the sub-paths

Specified by:

iterator in interface Path

endingPoint

public Complex endingPoint()

Return the ending point of the path

Specified by:

endingPoint in interface Path

startingPoint

public Complex startingPoint()

Return the starting point of the path

Specified by:

startingPoint in interface Path