Would appreciate it if @cormullion (or others) could make a tutorial for (colorful) hyperbolic plots
Sounds like your domain not mine… 
I was wondering about the image you tweeted, Fatou is not necessarily hyperbolic… but you’re right, it might be interesting to view fractals in a hyperbolic plane
Oh, yes! That is kind of hyperbolic, I was trying to draw vectors on a Poincaré disk, but I put it to one side when I had problems at the edges (which are supposed to be infinite but weren’t, for some reason?). This one is a bit more graphic design-y… 
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Now I provided an option to use Poincare disk / half-plane in Fatou iteration
using Fatou, PyPlot
newton(:(z^5-1),∂=2π,n=700,plane=true,iter=true) |> fatou |> plot
Fatou is also plotting beyond the boundary of the disk, which is at radius of 1
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