In the dynamical space, the parameter $\overset { o }{ c }=({ c }_{ 0 };{ c }_{ 1 },{ c }_{ 2 }) $ is fixed and $\overset { o }{ \varphi } _{ 0 } $ is varied (see quadratic mapping) in the real scators set. It's important that the mentioned parameter has the component $ { c }_{ 2 } $ with a non zero value, this way the fractal behavior can be observed, otherwise although will be interesting behavior, (watch escape velocity) this will not be fractal. In the galery below you can be appreciated dynamical space images, from which you can get the Julia set (named by the mathematician Gastón Julia) for real scators.
The previous images represents the s-x plane, i.e. these are a "y" hyperaxis section, in the second image you can be observed that the square's origin it's localized in $s=-0.0001; x=0$ iterating 10 times, and can be noted that to higher iterations the image location remains in the same place, but not it's behavior which changes with increasing number of iterations. We can note, that the previous images haven't fractal behavior and this is because that were obtained in the "y" hyper-axis origin. The next image contains the link to visualize the gallery directly.
