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Where absolute values create mathematical flames
Unlike the Mandelbrot set which uses z² + c directly, the Burning Ship takes the absolute value of the real and imaginary parts before squaring. This seemingly small change transforms the smooth Mandelbrot into a fractal resembling a ship engulfed in flames.
The Mandelbrot set is symmetric about the real axis because complex conjugation preserves the iteration. But the absolute value operation breaks this symmetry in a surprising way—the Burning Ship is asymmetric, yet still infinitely detailed and self-similar at every scale.
The Burning Ship was discovered by Michael Michelitsch and Otto Rössler in 1992. Unlike the Mandelbrot set (discovered 1978), it received less attention despite its striking appearance. It belongs to a family of "non-analytic" fractals created by using absolute values.
Just as the Mandelbrot set contains infinite copies of itself (mini-Mandelbrots), the Burning Ship contains mini-ships at various scales. Zoom into the boundary regions to discover these embedded copies, each slightly distorted but maintaining the characteristic ship shape.