mandelbrot_orbit


mandelbrot_orbit, an Octave 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.

Licensing:

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

Languages:

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

Related Data and Programs:

mandelbrot_orbit_test

caustic, an Octave code which generates an image of a caustic, by drawing n equally spaced points in a circle, and then connecting specific pairs of points using a spacing parameter m.

epicycloid, an Octave code which plots an epicycloid curve.

fern, an Octave code which displays the Barnsley fractal fern.

fibonacci_spiral, an Octave code which displays points on a Fibonacci spiral, suggesting the arrangement of seeds in a sunflower, for instance.

hilbert_curve, an Octave code which computes the sequence of discrete Hilbert curves whose limit is a space-filling curve.

julia_set, an Octave code which computes and plots a Julia set, the set of points in the complex plane that remain bounded under a mapping of the form f(z) = z^2+c.

mandelbrot, an Octave code which generates an image of the Mandelbrot fractal set;

Source Code:


Last revised on 05 September 2022.