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Fractal Geometry
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Mandelbrot Set
A set of complex numbers for which the function does not diverge when iterated from , where is a complex parameter.
Julia Set
For a given complex number , the Julia set is the boundary of the set of points that do not escape to infinity under iteration of the complex quadratic polynomial .
Sierpinski Triangle
A self-similar fractal object with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
Koch Snowflake
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.
Cantor Set
The Cantor set is created by iteratively deleting the open middle third from each segment of a line segment, starting with a single line.
Menger Sponge
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.
Barnsley Fern
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.
Dragon Curve
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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