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Visualization utilities

In this page we document several plotting utility functions that have been created to make the visualization of the output of Attractors.jl seamless. See the examples page for usage of all these plotting functions.

Note that most functions have an out-of-place and an in-place form, the in-place form always taking as a first input a pre-initialized Axis to plot in while the out-of-place creates and returns a new figure object.

E.g.,

heatmap_basins_attractors(grid, basins, attractors; kwargs...)
heatmap_basins_attractors!(ax, grid, basins, attractors; kwargs...)

Common plotting keywords

Common keywords for plotting functions in Attractors.jl are:

  • ukeys: the basin ids (unique keys, vector of integers) to use. By default all existing keys are used.
  • access = [1, 2]: indices of which dimensions of an attractor to select and visualize in a two-dimensional plot. Only these ids will be visualized. By default all are used.
  • colors: a dictionary mapping basin ids (i.e., including the -1 key) to a color. By default the JuliaDynamics colorscheme is used if less than 7 ids are present, otherwise random colors from the :darktest colormap.
  • markers: dictionary mapping attractor ids to markers they should be plotted as
  • labels = Dict(ukeys .=> ukeys): how to label each attractor.
  • add_legend = length(ukeys) < 7: whether to add a legend mapping colors to labels.
Attractors.shaded_basins_heatmap — Function
shaded_basins_heatmap(grid, basins, attractors, iterations; kwargs...)

Plot a heatmap of found (2-dimensional) basins of attraction and corresponding attractors. A matrix iterations with the same size of basins must be provided to shade the color according to the value of this matrix. A small value corresponds to a light color and a large value to a darker tone. This is useful to represent the number of iterations taken for each initial condition to converge. See also convergence_time to store this iteration number.

Keyword arguments

  • show_attractors = true: shows the attractor on plot
  • maxit = maximum(iterations): clip the values of iterations to

the value maxit. Useful when there are some very long iterations and keep the range constrained to a given interval.

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Attractors.plot_basins_curves — Function
plot_basins_curves(fractions_curves, prange = 1:length(); kwargs...)

Plot the fractions of basins of attraction versus a parameter range, i.e., visualize the output of continuation. See also plot_basins_attractors_curves.

Keyword arguments

  • style = :band: how to visualize the basin fractions. Choices are :band for a band plot with cumulative sum = 1 or :lines for a lines plot of each basin fraction
  • separatorwidth = 1, separatorcolor = "white": adds a line separating the fractions if the style is :band
  • axislegend_kwargs = (position = :lt,): propagated to axislegend if a legend is added
  • series_kwargs = NamedTuple(): propagated to the band or scatterline plot
  • Also all common plotting keywords.
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Attractors.plot_basins_attractors_curves — Function
plot_basins_attractors_curves(
    fractions_curves, attractors_info, a2rs [, prange]
    kwargs...
)

Convenience combination of plot_basins_curves and plot_attractors_curves in a multi-panel plot that shares legend, colors, markers, etc. This function allows a2rs to be a Vector of functions, each mapping attractors into real numbers. Below the basins fractions plot, one additional panel is created for each entry in a2rs. a2rs can also be a single function, in which case only one panel is made.

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Video output

Attractors.animate_attractors_continuation — Function
animate_attractors_continuation(
    ds::DynamicalSystem, attractors_info, fractions_curves, prange, pidx;
    kwargs...
)

Animate how the found system attractors and their corresponding basin fractions change as the system parameter is increased. This function combines the input and output of the continuation function into a video output.

The input dynamical system ds is used to evolve initial conditions sampled from the found attractors, so that the attractors are better visualized. attractors_info, fractions_curves are the output of continuation while ds, prange, pidx are the input to continuation.

Keyword arguments

  • savename = "attracont.mp4": name of video output file.
  • framerate = 4: framerate of video output.
  • Δt, T: propagated to trajectory for evolving an initial condition sampled from an attractor.
  • Also all common plotting keywords.
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