Plotting and Animation

The attractors package also comes with plotting and animation functions using Matplotlib. There are 2 plotting types, Multipoint and Gradient.

Plot

Multipoint plot can be used to visualize multiple attractor objects which can be used to demonstrate the chaotic nature based on perturbances in initial conditions and parameters

The following sample code shows the usage of plot_multipoint()

from attractors import Attractor
import numpy as np

n = 3
a = "rossler"
simtime = 100
simpoints = simtime * 100

# Create a list of n attractor instances
attrs = [Attractor(a) for _ in range(n)]

# Change the initial coordinates randomly for n-1 objects
for attr in attrs[1:]:
    attr.coord += np.random.normal(0, 0.01, size=3)

# Solve the ODE equations and store the generators
objs = []
for a in attrs:
    func = getattr(a, "rk3")
    objs.append(func(0, simtime, simpoints))

# Use plot_multipoint with necessary kwargs
ax = Attractor.plot_multipoint(
    *objs,
    dpi=240,
    bgcolor="#FFFFFF",
    palette=["#616161", "#7a7a7a", "#2e2e2e", "#1c1c1c"],
    linekwargs={"linewidth": 0.5, "alpha": 0.7},
    pointkwargs={"markersize": 1}
)

plot_multipoint() is a class method that requires 2 arguments:

index : timestep of the attractor objects on plot
*objs : generator list

Additionally, it also takes in multiple kwargs that

set the figure parameters: width, height, dpi
set the axes limits: xlim, ylim, zlim
set line and point parameters via linekwargs, pointkwargs (pass to matplotlib kwargs)
set color
- by theme
- by manually by specifying bgcolor (single hexcode) and palette (list of hexcodes). Overrides theme settings if given.

The figure parameters, axes limits and theme can also be set via set_figure(), set_limits() and set_theme() methods respectively

plot_gradient() is similar to plot_multipoint(), however it can only take one generator as input. And it also takes an extra kwarg: gradientaxis to specify the axis along which the gradient is applied. (X, Y or Z).

Both plot_gradient() and plot_multipoint() returns an Matplotlib.axes object which can be used to display or save the figure and also change axes parameters after plotting.

Animate

The Animate functions set_animate_multipoint() and set_animate_gradient() are similar to their plot function counterparts. By default, the visualization output will be saved in an MPEG4 encoded video. An example for gradient animation is as follows

from attractors import Attractor

obj = Attractor("dequan_li").rk3(0, 10, 10000)

Attractor.set_animate_gradient(obj,
    width=10,
    height=10,
    theme="nord").animate(outf="example.mp4")

The above code generates a video example.mp4 in the directory that it was run from. animate() is a class method acting on the Attractor class instance. It has no required argmunents and it takes the following kwargs

live: boolean arg to show the animated plot in a window interactively or save as output video.
fps: frames per second of animation
outf: filename of output video if generated
show: boolean arg to disable plt.show() and return the Matplotlib.FuncAnimation instance (only when live is True)

Both set_animate_gradient() and set_animate_multipoint() have 2 additional parameters: elevationrate and azimuthrate which control the rate of change of elevation and azimuth angle for the duration of the animation respectively.