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1. As Curve 1 we enter the vertical line segment x=0 with y ranging
between -.1 and .1.
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2. Here is the graph of Curve 1.
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3. Function 1 is the contraction mapping f(x,y)=(x/3,y).
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4. Function 2 is the contraction mapping g(x,y)=(x/3+2/3,y).
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5. Setting P(F1) and P(F2) to both be one means that on average, the
value of the function FC will be given by F1 half of the time and F2
the other half of the time.
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6. We select the probabilistic composition FC
to be applied to Curve 1 and set the iterations for FC to range
from 1 to 1000.
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7. After selecting 1000 iterations for FC we need to
click the "Calculate" button to calculate a random list of 1000 1's and
2's to provide a sequence for the function composition.
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8. Clicking the "GraphCurves" button draws us a thickened Cantor set.
This set is the unique invariant set for the iterated function system
defined by F1 and F2.
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