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Fractal Geometry

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Mandelbrot Set

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A set of complex numbers for which the function f(z)=z2+cf(z) = z^2 + c does not diverge when iterated from z=0z=0, where cc is a complex parameter.

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Julia Set

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For a given complex number cc, the Julia set is the boundary of the set of points that do not escape to infinity under iteration of the complex quadratic polynomial f(z)=z2+cf(z) = z^2 + c.

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Sierpinski Triangle

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A self-similar fractal object with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.

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Koch Snowflake

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Initiated from an equilateral triangle, each iteration replaces the middle third of a line segment with a pair of lines that form a smaller equilateral triangle.

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Cantor Set

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The Cantor set is created by iteratively deleting the open middle third from each segment of a line segment, starting with a single line.

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Menger Sponge

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A three-dimensional fractal curve. It is a generalization of the two-dimensional Sierpinski carpet and the one-dimensional Cantor set, formed by recursively removing cubes.

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Barnsley Fern

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A fractal that uses four affine transformations to mimic the appearance of a natural fern. The transformations are chosen probabilistically at each iteration to plot points on a plane.

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Dragon Curve

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A recursively generated fractal curve where each iteration is formed by folding a line in half, which suggests the shape of a dragon.

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