The Bailout condition is given by the following formula:

\; \begin{matrix} {|z \colon \Bbb{C}| = \sqrt{b}} \\ \Downarrow \\ {\sqrt{\Re{^2 z}+\Im{^2 z}} = \sqrt{b}} \\ \Downarrow \\  {\Re{^2 z}+\Im{^2 z} = b} \end{matrix} \;

The default value for this condition is usually 4. Questo valore indica un cerchio con centro \; O(0; 0) \; avente raggio \; \sqrt{b}=2 \; .

How does the Bailout condition function?

The Bailout condition makes the points, iterated n times, don't reach infinite. It helps to develop a limited number of iterations. Programs such as GNU Xaos, the iterable point colours vary according to the computable iterations within this condition.

Colore iterazioni

In GNU Xaos, the point colours (with x e iy coordinates) of an specific area alter according to computable iterations

Effects on fractals during the change of the Bailout condition

During the variation of this condition, the appearance of fractal will change radically. Let's take, for example, the Mandelbrot fractal, modifying the Bailout condition Calculation>Bailout to 1:

Mandelbrot con Bailout 1

Mandelbrot set with bailout value "1"

Have you noticed? The appearance of the Mandelbrot set is completely altered. Now it's a completely different fractal with new details to be explored. The same thing certainly will be true for other fractals too.

Comments are closed.