Lab
Burning Ship fractal
The Burning Ship fractal takes the Mandelbrot iteration and adds a twist: before squaring, it takes the absolute value of each component. This small change breaks the Mandelbrot set's symmetry and produces an asymmetric, ship-like fractal filled with dramatic masts, smoke, and hull structures.
zₙ₊₁ = (|Re(zₙ)| + i|Im(zₙ)|)² + c · drag to pan · scroll to zoom
200
inferno
interesting locations
The Burning Ship fractal was first described by Michael Michelitsch and Otto Rössler in 1992. Its defining feature is the use of absolute values: where the Mandelbrot set iterates zₙ₊₁ = zₙ² + c, the Burning Ship takes absolute values of the real and imaginary parts before squaring. This small modification breaks the left-right symmetry of the Mandelbrot set and produces an entirely different geometry — one that looks uncannily like a ship on fire, complete with masts, rigging, and a hull.
The coloring here uses a smooth escape-time algorithm. Rather than counting whole iterations, it uses the fractional escape count ν = n − log₂(log₂|z|) to produce continuous gradients between iteration bands. This eliminates the banding artifacts common in naive escape-time coloring and reveals the fine filament structure near the boundary.
Like the Mandelbrot set, the Burning Ship has infinite detail at every scale. Zoom into the antenna structure above the main body to find miniature copies of the ship; explore the hull to find spiraling filaments. The boundary between the inside and outside is, as with all fractals in this family, infinitely complex — a set of measure zero that nevertheless contains all the visual interest.