Self-similarity
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In mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show th
Close-up of a Romanesco broccoli
Fractal
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In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals
Self-similarity
…coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole…
Highly magnified area on the boundary of the Mandelbrot set
The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
Mandelbrot set with 12 encirclements
2x 120 degrees recursive IFS