attractors 1.1.0

Simulation and visualization of strange attractors

Attractors is a package for simulation and visualization of strange attractors.

For complete documentation, see the repository docs at https://github.com/Vignesh-Desmond/attractors

Installation

The package is currently hosted on PyPi and can be installed with pip:

pip install attractors

Alternatively, the package can be installed locally after cloning by the following command:

python -m pip install .

Note:

The package requires FFMPEG as a prerequisite for generating visualization output. For installation, see here

Dependencies

• Python (3.8+)

• NumPy (1.21.0+)

• Matplotlib (3.4.2+)

Usage

The package is intended to be used mainly via the command-line interface. The simplest way to visualize an Lorenz attractor is given below:

attractors -p 100000 -s 100 -t multipoint lorenz

-p : Number of points for the simulation

-s : Simulation time

-t : Type of visualization

There are two types of visualizations:

multipoint visualization can simulate multiple initial coordinates, useful to infer the chaotic nature of the attractors. Use --n to set the number of initial points.

gradient visualization uses gradient color for the 3D plot, given a specific axis.

By default, the visualization output will be saved in an MPEG4 encoded video. To show a live plot, use the --live flag (only supported for multipoint).

The full list of possible settings can be obtained by the help command: attractors -h

usage: attractors [-v] [-h] -t {multipoint,gradient}
                  [--des {euler,rk2,rk3,rk4,rk5}] [--width WIDTH]
                  [--height HEIGHT] [--dpi DPI] [--theme THEME] -s SIMTIME -p
                  SIMPOINTS [--bgcolor BGCOLOR] [--cmap CMAP] [--fps FPS]
                  [--n N] [--rk2 {heun,imp_poly,ralston}] [--outf OUTF]
                  [--live]
                  ATTRACTOR ...

optional arguments:
  -v, --version         show program's version number and exit
  -h, --help            show this help message and exit

required arguments:
  -t {multipoint,gradient}, --type {multipoint,gradient}
                        choose simulation type
  -s SIMTIME, --simtime SIMTIME
                        set the simulation time
  -p SIMPOINTS, --simpoints SIMPOINTS
                        set the number of points to be used for the simulation

other arguments:
  --des {euler,rk2,rk3,rk4,rk5}
                        set the Differential Equation Solver. Default: rk4
  --width WIDTH         set width of the figure Default: 16
  --height HEIGHT       set height of the figure Default: 9
  --dpi DPI             set DPI of the figure Default: 120
  --theme THEME         choose theme (color palette) to be used
  --bgcolor BGCOLOR     Background color for figure in hex. Overrides theme
                        settings Default: #000000
  --cmap CMAP           Matplotlib cmap for palette. Overrides theme settings
                        Default: jet
  --fps FPS             Set FPS for animated video (or interactive plot)
                        Default: 60
  --n N                 Number of initial points for Multipoint animation
                        Default: 3
  --rk2 {heun,imp_poly,ralston}
                        Method for 2nd order Runge-Kutta if specified to used.
                        Default: heun
  --outf OUTF           Output video filename Default: output.mp4
  --live                Live plotting instead of generating video.

Attractor settings:
  Choose one of the attractors and specify its parameters

  ATTRACTOR
    lorenz              Lorenz attractor
    rabinovich_fabrikant
                        Rabinovich Fabrikant attractor
    lotka_volterra      Lotka Volterra attractor
    rossler             Rossler attractor
    wang_sun            Wang Sun attractor
    rikitake            Rikitake attractor
    nose_hoover         Nose Hoover attractor
    aizawa              Aizawa attractor
    three_cell_cnn      Three Cell CNN attractor
    bouali_type_1       Bouali Type 1 attractor
    bouali_type_2       Bouali Type 2 attractor
    bouali_type_3       Bouali Type 3 attractor
    finance             Finance attractor
    burke_shaw          Burke Shaw attractor
    moore_spiegel       Moore Spiegel attractor
    sakarya             Sakarya attractor
    dadras              Dadras attractor
    halvorsen           Halvorsen attractor
    hadley              Hadley attractor
    chen                Chen attractor
    chen_lee            Chen Lee attractor
    chen_celikovsky     Chen Celikovsky attractor

Each attractor also has its own parameters to set. The settings for each attractor can be obtained by the help command: attractors ATTRACTOR -h

The help message for Lorenz attractors will be as follows:

usage: attractors lorenz [-h] [--sigma SIGMA] [--beta BETA] [--rho RHO]
                         [--initcoord INITCOORD] [--xlim XLIM] [--ylim YLIM]
                         [--zlim ZLIM]

optional arguments:
  -h, --help            show this help message and exit

Lorenz attractor parameters:
  --sigma SIGMA         Parameter for Lorenz attractor Default: 5
  --beta BETA           Parameter for Lorenz attractor Default: 2.66667
  --rho RHO             Parameter for Lorenz attractor Default: 28
  --initcoord INITCOORD
                        Initial coordinate for Lorenz attractor. Input format:
                        "x,y,z" Default: [0.1, 0.1, 0.1]
  --xlim XLIM           x axis limits for figure. Input format: "xmin,xmax"
                        Default: [-20, 20]
  --ylim YLIM           y axis limits for figure. Input format: "ymin,ymax"
                        Default: [-30, 30]
  --zlim ZLIM           z axis limits for figure. Input format: "zmin,zmax"
                        Default: [5, 45]

License

This package is licensed under the MIT License