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Zephyr’s Kiss (Fractal vase - Julia set)

Swirls settle gently into a seductive silky form, giving rise to a spectacle of morphing fractals.

Designed as a stack of quadratic Julia sets, where each set is similar to the sets immediately above and below it. The sets are defined as the set of all complex points z which do not diverge to infinity under the transformation:

z -> z^2 + c,

where c is some complex number. If we sample c at regular intervals along a smooth path inside the Mandelbrot set, we obtain a series of connected Julia sets locally similar enough to form a continuous surface when stacked. By choosing an appropriate path for c, the Julia sets consist of a closed curve without self-intersections at each stage, producing a surface with printable overhangs.

Inspired by:

https://www.thingiverse.com/virtox/collections/julia-vase

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