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escape velocity

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By mfg, 9 November, 2017

In the previous page (hun: 2D dynamic) displayed images in which we can appreciate hyperbolas, but when the iterations number increases a square figure appears inscribed in them.

10y40
hyper-axis "y" sections, (left) iterating 10 times and (right) iterating 40 times.

  

The inscribed figure in the hyperbolas it becomes more noticeable for larger iterations, this is because ht real scator metric is used.  In hun: 2D dynamic section, the necessary condition to observe a fractal behavior was mentioned, in fact according with this condition the previous images aren't fractals. The confined condition is $f{}_{0}^{2}-f{}_{1}^{2}\leq\varepsilon$ (hyperbola's equation) since that the presented sections are localed at the origin of the hyper-axis "y", the images are formed by the points that have a low bailout because it can't escape from confinement. The points that can escape have a high bailout and the previous condition don't apply for them, this can be observe increase the iterations number in the  quadratic mapping.

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