Gradual increasing of step size for a range of values

You could use an appropriate pair of inverse functions to do the smooth mapping.

A simple example using square root and power of 2:

using Plots
n = 100
x1, x2 = 0.0, 5000.0
x = LinRange(√x1, √x2, n).^2
plot(scatter(x), scatter(diff(x)))
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