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.


The computer code and data files described and made available on this web page are distributed under the MIT license


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.