**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.

caustic, a Python 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, a Python code which plots an epicycloid curve.

fern, a Python code which displays the Barnsley fractal fern.

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

henon_orbit, a Python code which computes the orbit of the Henon map for various sets of initial data.

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

julia_set, a Python 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, a Python code which generates an image of the Mandelbrot fractal set;

- mandelbrot_orbit.py, the source code.
- mandelbrot_orbit.sh, runs all the tests.
- mandelbrot_orbit.txt, the output file.

- mandelbrot_orbit_test1.png
- mandelbrot_orbit_test2.png
- mandelbrot_orbit_test3.png
- mandelbrot_orbit_test4.png
- mandelbrot_orbit_test5.png
- mandelbrot_orbit_test6.png
- mandelbrot_orbit_test7.png
- mandelbrot_orbit_test8.png