# mandelbrot_orbit

mandelbrot_orbit, a Python code which computes the Mandelbrot iterates arising from a single starting point.

The Mandelbrot set is a set of points C in the complex plane with the property that the iteration

```        z(0) = c
z(n+1) = z(n)^2 + z(0), for n = 0, 1, ...
```
remains bounded.

The function mandelbrot_orbit() computes up to n iterates for a given starting point, but stops immediately if the iterates exceed 2 in norm. If the iterates stay bounded, a plot may show a pattern in which successive iterates spiral in towards a limit point, or in which they bounce back and forth among several limits.

### Languages:

mandelbrot_orbit is available in a MATLAB version and an Octave version and a Python version.

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### Source Code:

Last revised on 09 February 2023.