There is an additional difficulty: settings that look good on screen will look bad when saved to PNG, and vice versa.
The following functions do a fair job on my system in the range from 10 to 1 million points, with dpi=100 for the screen display and dpi=600 for saving the figure to PNG.
using Distributions, StatsBase, Plots; gr()
# get normalised ranks :
pseudos(sample) = [ordinalrank(sample[i,:])./(size(sample,2)+1) for i in 1:size(sample,1)]
make_plot(dat,N; kwargs...) = scatter!(pseudos(dat[:,1:N])...;kwargs...)
data = rand(LogNormal(0,1), (2,1_000_000))
data[2,:] .+= rand(1_000_000) .* data[1,:].^2
dpi = 100 # use dpi=100 for default screen display, and dpi=600 to savefig as PNG
sf = dpi/100
ms(n) = 0.1*sf + 4exp(-sf*5e-5*n)
ma(n) = 0.02*sf + exp(-3e-5*n/sf)
N = [10^n for n in 1:6]
p = plot(layout=(2,3), size = (1800, 1200), legend=:bottomright, dpi=dpi)
[make_plot(data, N[n], ms=ms(N[n]), ma=ma(N[n]), label=string(N[n]), msw=0, msc=:auto, subplot=n) for n in 1:length(N)]
p
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Screen display (dpi=100):
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Savefig as PNG (dpi=600):
