Basic Usage

A simple code snippet using the attractors package

from attractors import Attractor

obj = Attractor("lorenz").rk3(0, 100, 10000) #rk3(starttime, endtime, simpoints)

In the above snippet, obj is an generator instance yielding an attractor instance with X, Y, and Z attributes. The generator reaches StopIteration after iterating simpoints (number of points used for the simulation) times.

The parameters of each attractor can be given as kwargs as follows:

attr = Attractor("lorenz", sigma = 5, rho = 28.5, init_coord = [0.2,0.1,0.1])

When parameters are not given, the default parameters are loaded for each attractor. In the above example, since beta is not given, the default value of 2.66667 is loaded.

To obtain the 3D coordinates of an attractor, we need to solve (usually) 3 non-linear ODE, one for each dimension. The solution can be derived via approximation using the Runge-Kutta methods. Currently, this package consists of the following iterative explicit RK methods:

  • Euler

  • RK2 (Heun, Ralston, Improved Polygon)

  • RK3

  • RK4

  • RK5

For 2nd order Runge-Kutta, the method can be specified via the positional argument rk2_method

obj = attr.rk3(0, 100, 10000, rk2_method="heun")
 #methods = "heun", "ralston", "imp_poly"

A list of attractors and ODE solvers can be obtained via the static methods list_attractors() and list_des() respectively.