Question 1

What is the Burning Ship fractal?

Accepted Answer

The Burning Ship fractal, discovered by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating z_{n+1} = (|Re(z)| + i|Im(z)|)² + c. Taking absolute values of both real and imaginary parts before squaring 'folds' the plane into the positive quadrant at each step, breaking the rotational symmetry of the Mandelbrot set and producing an asymmetric fractal that — when viewed upside-down — resembles a sailing ship ablaze.

Question 2

How does the Burning Ship differ from the Mandelbrot set?

Accepted Answer

The Mandelbrot set uses z_{n+1} = z_n² + c. The Burning Ship replaces z_n with (|Re(z_n)| + i|Im(z_n)|), which flips all four quadrants into the first quadrant before squaring. This destroys conjugate symmetry (the Mandelbrot set is symmetric about the real axis; the Burning Ship is not) and produces qualitatively different boundary behaviour despite the same escape criterion |z| > 2.

Question 3

What are Burning Julia sets?

Accepted Answer

Just as the Mandelbrot set parameterises Julia sets for f_c(z)=z²+c, the Burning Ship parameterises 'Burning Julia sets' for g_c(z)=(|Re(z)|+i|Im(z)|)²+c. For a fixed c, each pixel z₀ is iterated under g_c and coloured by whether the orbit escapes. Burning Julia sets have an even more jagged, asymmetric appearance than classical Julia sets, with intricate filament structures near the ship boundary.

Question 4

What notable features should I zoom into?

Accepted Answer

Use the bookmark buttons to explore: the 'Main Mast' around c ≈ (−1.755, −0.029) shows the primary vertical spike from which the ship's name derives; 'Hull Detail' near (−0.348, −0.658) reveals intricate spiral decorations; 'Mini Ship' near (−1.940, 0.001) contains an embedded miniature copy of the entire fractal; 'Rigging' at extreme zoom near (−2.000, 0.00015) shows infinite self-similar filaments. The bookmarks in the simulator load all these views automatically.

🧪 Burning Ship Fractal Explorer

What did you find?