https://github.com/robaina/mandeltravel
Travelling across the Mandelbrot set
https://github.com/robaina/mandeltravel
Last synced: 5 months ago
JSON representation
Travelling across the Mandelbrot set
- Host: GitHub
- URL: https://github.com/robaina/mandeltravel
- Owner: Robaina
- Created: 2017-07-22T10:33:44.000Z (almost 9 years ago)
- Default Branch: master
- Last Pushed: 2017-07-22T10:56:29.000Z (almost 9 years ago)
- Last Synced: 2025-10-27T15:57:29.721Z (8 months ago)
- Language: Matlab
- Size: 2.01 MB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# MandelTravel
Travelling across the Mandelbrot set
This project aims at developing an application which allows the user to travel the Mandelbrot set.
The Mandelbrot set can be regarded as a parameter space of the Julia sets, in which each complex number
in the Mandelbrot set defines a Julia set.
The idea is to select a path on the set. Then a video will show a movie of the succesion of Jualia sets
corresponding to the parameter values traversed through the path. At the same time the user can follow the
path on the set. This gives an idea of how the population of Julia sets looks like on the Mandelbrot set.
A further implementation would allow to reconstruct 3D images composed of the several secctions of Julia sets
obtained througout the path,
Currenlty only a first version is provided in MATLAB code. This version allows to select a path on the Mandelbrot
set and see the movie generated by the Julia sets. To this end, the function
"W = mandelbrot(n)"
must be used first obtain matrix W where the Mandelbrot set is encoded.
The entries w_kj in the matrix correspond to the value of the iteration
Zn+1 = zn^2 + c_kj
with z0 = 0
c_kj = k + i*j
That is, the complex plane has been discretize with a grid (details in the function "mandelbrot")
The parameter "n" controls the number of iteration and hence the resolution of the Mandelbrot set.
After W is generated, the function mandeltravel(W) can be called. The path is selected by left-clicking
with the mouse. Once the path is chosen press enter to generate the movie.
The MATLAB code will be substituted by open source code. Also, possible a version in Java, which can
be run in an standalone way would be preferred.