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Fractals are selfsimilar patterns found in chaos from "summary" of Chaos by James Gleick

Fractals offer a way of seeing chaos. They are shapes that look almost the same at different levels of magnification. To understand them is to understand the essential structure of chaos. Fractals are the mathematical language of chaos, revealing its patterns. They are shapes that contain an infinite complexity, yet are generated by simple rules. Their self-similarity means that no matter how closely you examine them, you see the same patterns repeated over and over again. This property gives them a unique beauty and power. Fractals can be found in many natural phenomena, from coastlines to clouds to the branching of trees. They are the fingerprints of chaos in the natural world. The complexity of these natural forms can be captured and understood through the lens of fractals. By studyi...
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    Chaos

    James Gleick

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