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A fractal is a geometric shape that can be subdivided into parts such that each of these parts is exactly or approximately equal to the whole.

Examples of fractals are the Mandelbrot set, Cantor set, Sierpinski triangle, Peano curve, Koch snowflake and Lorenz attractor.

Fractals can be used to describe many highly irregular real-world objects, such as clouds, mountains, turbulence, and coastlines.

Fractals possess as their defining characteristic a kind of symmetry known as "self-similarity under scale". "Symmetry" here means invariance under some operation. For instance, a bilaterally symmetric object is invariant under the operation of reflection -- hold it in front of a mirror and it "looks the same". Fractal object are invariant under scaling operations. Magnify or shrink a fractal, and it looks the same.

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