The Burning Ship fractal

Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

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


in the complex plane

Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...

  which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set

Mandelbrot set

The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable two-dimensional fractal shape...

 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.

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