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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.

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

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

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

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

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

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.