Important Notice: Our web hosting provider recently started charging us for additional visits, which was unexpected. In response, we're seeking donations. Depending on the situation, we may explore different monetization options for our Community and Expert Contributors. It's crucial to provide more returns for their expertise and offer more Expert Validated Answers or AI Validated Answers. Learn more about our hosting issue here.

What are orbits?

April 26, 2017orbits

0

10 Posted

What are orbits?

1 Answer

0

10 Posted

When a complex polynomial is iterated, the point representing z runs through successive positions which define a trajectory, named the orbit of the point. The properties of the orbit can be used to color the point of the complex plane used to do the iteration (see question 5Ba and following). For example, Fractint offers a very nice option to see the orbit of a point: strike the key, then the key when the Mandelbrot or a Julia set is displayed on the screen and place the cursor on different points of the image. It is easy to see that the orbit never escapes when the cursor is in the set, and that it escapes out of the limits of the window (in fact, towards infinity) when the cursor is on a brightly colored zone outside the set.