Explore a variant of the Mandelbrot set - unique flame shape through absolute value transformation
The Burning Ship fractal is a famous variant of the Mandelbrot set, discovered by Michael Michelitsch and Otto E. Rössler in 1992. Unlike the standard Mandelbrot set z_{n+1} = z_n² + c, the Burning Ship takes the absolute value of both the real and imaginary parts before each iteration, creating a unique "burning ship" shape with flame-like self-similar structures.
The Burning Ship iteration formula is z_{n+1} = (|Re(z_n)| + i|Im(z_n)|)² + c with z_0 = 0. This absolute value operation reflects all four quadrants of the complex plane into the first quadrant before squaring. This creates an asymmetric fractal with a spectacular burning ship appearance at its bottom. The escape time algorithm colors each point: if it escapes within finite iterations (|z| > 2), color by escape speed; if it remains in the set, display as black.
The most famous region of the Burning Ship fractal lies between real part [-1.8, -1.7] and imaginary part [-0.08, 0.01], presenting a spectacular vision of a ship burning in water. The absolute value operation creates an "origami" effect, folding and mapping different parts of the complex plane to produce unique geometric structures. Compared to the Mandelbrot set, Burning Ship has sharper details with more vertical and horizontal edge characteristics.
The Burning Ship fractal has the richest details at the bottom of the ship (negative imaginary region). Try exploring between real parts -1.74 to -1.76 where you can discover infinitely nested self-similar structures. Increasing iterations reveals finer details but reduces rendering speed. Try different color palettes - the fire palette best captures the meaning of its name.