Contour Plots

The easiest way to get started with contour plots is to use the PythonPlot backend. PythonPlot requires the PythonPlot.jl package which can be installed by typing ] and then add PythonPlot into the REPL. The first time you call pythonplot(), Julia may install matplotlib for you. All of the plots generated on this page use PythonPlot, although the code will work for the default GR backend as well.

Let's define some ranges and a function f(x, y) to plot. Notice the ' in the line defining z. This is the adjoint operator and makes x a row vector. You can check the shape of x' by typing size(x'). In the tutorial, we mentioned that the @. macro evaluates whatever is to the right of it in an element-wise manner. More precisely, the dot . is shorthand for broadcasting; since x' is of size (1, 100) and y is of size (50, ), z = @. f(x', y) will broadcast the function f over x' and y and yield a matrix of size (50, 100).

using Plots; pythonplot()

f(x, y) = (3x + y^2) * abs(sin(x) + cos(y))

x = range(0, 5, length=100)
y = range(0, 3, length=50)
z = @. f(x', y)
contour(x, y, z)
2023-02-02T10:06:13.316545 image/svg+xml Matplotlib v3.6.3, https://matplotlib.org/

Much like with plot! and scatter!, the contour function also has a mutating version contour! which can be used to modify the plot after it has been generated.

With the pythonplot backend, contour can also take in a row vector for x, so alternatively, you can define x as a row vector as shown below and PythonPlot will know how to plot it correctly. Beware that this will NOT work for other backends such as the default GR backend, which require x and y to both be column vectors.

x = range(0, 5, length=100)'
y = range(0, 3, length=50)
z = @. f(x, y)
contour(x, y, z)

Common Attributes

Let's make this plot more presentable with the following attributes:

  1. The number of levels can be changed with levels.
  2. Besides the title and axes labels, we can also add contour labels via the attribute contour_labels, which has the alias clabels. We'll use the LaTeXStrings.jl package to write the function expression in the title. (To install this package, type ] and then add LaTeXStrings into the REPL.)
  3. The colormap can be changed using seriescolor, which has the alias color, or even c. The default colormap is :inferno, from matplotlib. A full list of colormaps can be found in the ColorSchemes section of the manual.
  4. The colorbar location can be changed with the attribute colorbar, alias cbar. We can remove it by setting cbar=false.
  5. The widths of the isocontours can be changed using linewidth, or lw.

Note that levels, color, and contour_labels need to be specified in contour.

using LaTeXStrings

f(x, y) = (3x + y^2) * abs(sin(x) + cos(y))

x = range(0, 5, length=100)
y = range(0, 3, length=50)
z = @. f(x', y)

contour(x, y, z, levels=10, color=:turbo, clabels=true, cbar=false, lw=1)
title!(L"Plot of $(3x + y^2)|\sin(x) + \cos(y)|$")
xlabel!(L"x")
ylabel!(L"y")
2023-02-02T10:06:15.652647 image/svg+xml Matplotlib v3.6.3, https://matplotlib.org/

If only black lines are desired, you can set the color attribute like so:

contour(x, y, z, color=[:black])

and for alternating black and red lines of a specific hex value, you could type color=[:black, "#E52B50"], and so on.

To get a full list of the available values that an attribute can take, type plotattr("attribute") into the REPL. For example, plotattr("cbar") shows that it can take either symbols from a predefined list (e.g. :left and :top), which move the colorbar from its default location; or a boolean true or false, the latter of which hides the colorbar.

Filled Contours

We can also specify that the contours should be filled in. One way to do this is by using the attribute fill:

contour(x, y, z, fill=true)

Another way is to use the function contourf, along with its mutating version contourf!:

contourf(x, y, z, levels=20, color=:turbo)
title!(L"(3x + y^2)|\sin(x) + \cos(y)|")
xlabel!(L"x")
ylabel!(L"y")
2023-02-02T10:06:18.970277 image/svg+xml Matplotlib v3.6.3, https://matplotlib.org/

If you are using the GR backend to plot filled contours, there will be black lines separating the filled regions. If these lines are undesirable, you can set the line width to 0: lw=0.

Logarithmic Contour Plots

Much like with line and scatter plots, the X and Y axes can be made logarithmic through the xscale and yscale attributes. If both axes need to be logarithmic, then you can set scale=:log10.

It will be easier for the backend to generate the plot if the attributes are specified in the contourf command directly instead of using their mutating versions.

g(x, y) = log(x*y)

x = 10 .^ range(0, 6, length=100)
y = 10 .^ range(0, 6, length=100)
z = @. g(x', y)
contourf(x, y, z, color=:plasma, scale=:log10,
    title=L"\log(xy)", xlabel=L"x", ylabel=L"y")
2023-02-02T10:06:21.076498 image/svg+xml Matplotlib v3.6.3, https://matplotlib.org/

It is often desired that the colorbar be logarithmic. The process to get this working correctly is a bit more involved and will require some manual tweaking. First, we define a function h(x, y) = exp(x^2 + y^2), which we will plot the logarithm of. Then we adjust the levels and colorbar_ticks attributes.

The colorbar_ticks attribute can take in a tuple of two vectors (tickvalues, ticklabels). Since h(x, y) varies from 10^0 to 10^8 over the prescribed domain, tickvalues will be a vector tv = 0:8. We can format the labels with superscripts by using LaTeXStrings again. Note that the string interpolation operator changes from $ to %$ when working within L"..." to avoid clashing with $ as normally used in LaTeX.

h(x, y) = exp(x^2 + y^2)

x = range(-3, 3, length=100)
y = range(-3, 3, length=100)
z = @. h(x', y)

tv = 0:8
tl = [L"10^{%$i}" for i in tv]
contourf(x, y, log10.(z), color=:turbo, levels=8,
    colorbar_ticks=(tv, tl), aspect_ratio=:equal,
    title=L"\exp(x^{2} + y^{2})", xlabel=L"x", ylabel=L"y")
2023-02-02T10:06:23.630298 image/svg+xml Matplotlib v3.6.3, https://matplotlib.org/

If you want the fill boundaries to correspond to the orders of magnitude, levels=8. Depending on the data, this number may require some tweaking. If you want a smoother plot, then you can set levels to a much larger number.