Draft:Celtic Fractal

The Celtic Fractal.

The Celtic Fractal is an escape time fractal that is generated from the equation: $z_{n+1}=(|\operatorname {Re} \left(z_{n}^{2}\right)|+\operatorname {Im} \left(z_{n}^{2}\right))+c,\quad z_{0}=0$.

In the Mandelbrot set, both real and imaginary parts are not turned into their absolute values, while in the Burning Ship fractal, both parts are turned into their absolute values. The Celtic only does this for its real part, making it share characteristics with both the Mandelbrot set and the Burning Ship fractal.

A similar image of the Celtic Fractal in another color pallete.

Ditto.

Similarities with the Mandelbrot Set

• It is bilaterally symmetrical.
• It has the main body repeated to the left much like how the Mandelbrot set has bulbs.

Similarities with the Burning Ship fractal

• It is a non-analytical function.
• It has a similar shape.
• This fractal can be found in the Burning Ship fractal.