Burning Ship fractal

High-quality overview image of the Burning Ship fractal

High-quality image of the large ship in the left antenna

High-quality deep-zoom image of a small ship in the armada in the left Western antenna of the main ship structure

Burning Ship Deep Zoom to 2.3e-50

The Burning Ship fractal

A zoom-in to the lower left of the Burning Ship fractal, showing a "burning ship" and self-similarity to the complete fractal.

A zoom-in to line on the left of the fractal, showing nested repetition (a different colour scheme is used here).

High quality image of the Burning Ship fractal.

The Burning Ship Fractal featured in the 1K intro "JenterErForetrukket" by Youth Uprising; a demoscene production.

The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:

$z_{n+1} = (|\operatorname{Re} \left(z_n\right)|+i|\operatorname{Im} \left(z_n\right)|)^2 + c, \quad z_0=0$

in the complex plane $\mathbb{C}$ which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy–Riemann equations.

See also

• Mandelbrot set
• Julia set
• Fractal

External links

• About properties and symmetries of the Burning Ship fractal, featured by Theory.org,
• Burning Ship Fractal, Description generated by a C source code.
• Burning Ship with its Mset of higher powers and Julia Sets
• Burningship, Video,
• Fractal webpage includes the first representations and the original paper cited above on the Burning Ship fractal.
• 3D representations of the Burning Ship fractal