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Exploring Self-Similarity in Fractals and Nature

Discover the concept of self-similarity in fractals like the Koch Curve and Mandelbrot Set, and see how nature exhibits self-similarity across scales, from plant growth to rugged terrains. Explore how zooming in or out reveals similar patterns in diverse contexts and ponder the beauty of this phenomenon.

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Exploring Self-Similarity in Fractals and Nature

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  1. Self-Similarity Some examples

  2. Self-Similarity in the Koch Curve Fractals usually possess what is called self-similarity across scales. That is, as one zooms in or out the geometry/ image has a similar (sometimes exact) appearance.

  3. Self-Similarity in the Mandelbrot Set

  4. Self-similarity in Nature

  5. Natural: A picture of a fern How do plants do it? Mathematical: plant growth as simulated by a simple iterative procedure.

  6. Is this a large piece of rugged terrain photographed from an aeroplane, or the side of a mountain, or a patch of dirt on the scale of a few meters, or a magnification of the surface of a rough rock? Whichever it is, it could also easily be imagined to be any one of the others. So one could start at the large scale view from the air and apply successive zooms down to a microscopic scale, the surface maintains self similarity across those scales.

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