Mandelbrot Orbit

This program generates the orbit for a given Mandelbrot point. Something like:

That's the orbit of point (-1.3,0) which has period 4.

Math

This is the Mnadelbrot Set basic formula:

f(z) = z² + c

where z and c are complex number.

The Mandelbrot set is the set of complex numbers c for which the function does not diverge when iterated from z=0. Than means, given a c complex number, if you apply the formula to that number n times using the previous result as the new z number, that c belongs to Mandelbrot Set if the sequence does not diverge.

This python script plots the series for a given complex point.

Prerequisites

Python 3.6.9
pytest-5.3.5

Usage

Install:

./bin/install

Run:

mandelbrot-orbit '{ZX}' '{ZY}' {NUM_ITERATIONS} {OUPUTFILE}
mandelbrot-orbit -0.1 0.7 100 ./mandelbrot_orbit.png

The script generates an image: mandelbrot-orbit.png

Development

Setup:

./bin/dev-setup

Running the tests:

./bin/test

Run:

./bin/run '-0.1' '0.7' 100 ./output/mandelbrot_orbit.png

Troubleshooting

You could see this error:

/home/josecelano/.local/lib/python3.6/site-packages/matplotlib/backends/backend_gtk3.py:195: Warning: Source ID 8 was not found when attempting to remove it
  GLib.source_remove(self._idle_draw_id)

It seems to be a known issue pending to release:

https://stackoverflow.com/questions/29540845/how-can-i-deactivate-warning-source-id-510-was-not-found-when-attempting-to-re

TODO

• Although calculations are done with an arbitrary precision library, we use matplotlib to generate the graph and that package uses a float type for data source so we cannot plot a point with greater precision than the language float precision.