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java.lang.Object path.SubstitutionFractal
public class SubstitutionFractal
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 | |
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SubstitutionFractal(PolygonalPath gamma)
Construct a Substitution path with gamma serving as both the first polygonal approximation and the substitution path. |
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SubstitutionFractal(PolygonalPath p,
PolygonalPath gamma)
Construct a Substitution path with a given first polygonal approximation p and a substitution path gamma. |
Method Summary | |
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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 |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public SubstitutionFractal(PolygonalPath p, PolygonalPath gamma)
public SubstitutionFractal(PolygonalPath gamma)
Method Detail |
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public PathIterator iterator()
iterator
in interface Path
public Complex endingPoint()
endingPoint
in interface Path
public Complex startingPoint()
startingPoint
in interface Path
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