Here we will learn to recognize the visual signature of IFS driven by cyclic data, that is, numbers that repeat a particular pattern.
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The simplest repeated sequence is constant, just repeat the same number. |
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Constant sequences generate sequences of points that converge to the fixed point of the corresponding transformation. |
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The next simplest repeated sequence is a 2-cycle, it alternates between two values. |
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Here we find the addresses of the 2-cycle points. |
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Here we find the coordinates of the 2-cycle points. |
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How do the limiting points depend on the choice of initial point? |
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Repeating a pattern of three transformations produces a 3-cycle. |
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Here we find the addresses of the 3-cycle points. |
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Here we find the coordinates of the 3-cycle points. |
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What happens if we apply the 3-cycle transformations in a different order? |
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General cycles |
Return to Driven IFS.