Complex Polya Field

using CairoMakie

x = y = -2:0.005:2
f(z) = 1 / (z * (z^2 - z - 1 - 3im))
fvals = [f(u + 1im * v) for u in x, v in y]
fvalues = abs.(fvals)
fargs = angle.(fvals)
polya(x, y) = Point2f(real(f(x + 1im * y)), -imag(f(x + 1im * y)))

fig = Figure(resolution = (900, 400))
axs = [Axis(fig[1, i], aspect = 1) for i in 1:2]
cmap = :roma
streamplot!(axs[1], polya, -2 .. 2, -2 .. 2, colormap = [:black, :red],
        gridsize = (40, 40), arrow_size = 6, linewidth = 1)
pltobj2 = heatmap!(axs[2], x, y, fargs, colorrange = (-π, π), colormap = cmap)
streamplot!(axs[2], polya, -2 .. 2, -2 .. 2, colormap = [:black, :black],
        gridsize = (40, 40), arrow_size = 6, linewidth = 1)
Colorbar(fig[1, 3], pltobj2, ticks = ([-π, -π / 2, 0, π / 2, π],
        [L"-\pi", L"-\pi/2", L"0", L"\pi/2", L"\pi"]))
limits!(axs[1], -2, 2, -2, 2)
limits!(axs[2], -2, 2, -2, 2)
colsize!(fig.layout, 1, Aspect(1, 1.0))
colsize!(fig.layout, 2, Aspect(1, 1.0))
fig

Warning

This example was autogenerated using:

using Pkg
Pkg.status(["CairoMakie"])
Status `~/work/BeautifulMakie/BeautifulMakie/docs/Project.toml`
  [13f3f980] CairoMakie v0.10.6

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