ComplexPhasePortrait.jl

This package is a Julia implementation of the phase portrait ideas presented in Elias Wegert's book "Visual Complex Functions".

Installation

From the Julia command prompt:

Pkg.clone("git://github.com/JuliaHolomorphic/ComplexPhasePortrait.jl.git")

There is so far one exported function, portrait, and here I will try to detail its use. First we need function data over a grid.

using ComplexPhasePortrait

nx = 1000
x = range(-1, stop=1, length=nx)
Z = x' .+ reverse(x)*im

f = z -> (z - 0.5im)^2 * (z + 0.5+0.5im)/z
fz = f.(Z)

Now a basic phase plot.

img = portrait(fz)

Now for a basic plot using NIST coloring.

img = portrait(fz, ctype="nist")

Lines of constant phase are given by

img = portrait(fz, PTstepphase)

Lines of constant modulus are given by

img = portrait(fz, PTstepmod)

Finally, a conformal grid is given by

img = portrait(fz, PTcgrid)