How to set an axis with arbitrary, but equally spaced, scaling.

Hello,

I am attempting to replicate the following plot in a textbook using my own numerical solver. I am having trouble with replicating the x-axis in the plot for comparison since it is a bit odd. See the axes below:

I am aware that you can use Xtick to choose where ticks are located, but this does not affect the spacing of the ticks such that they are equally spaced like in the example above. The closest I am able to get is shown below:

Log scaling does slightly better, but is still not evenly spaced like I would hope:

Unfortunately I have not been able to find a way to change the scaling to be something other than linear or log. I am using MATLAB R2023a.

Does anyone know a way to create the evently spaced type of scaling seen in the first set of axes?

NOTE:-

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You could not plot versus the numbers 0,1,2,3, but then set the x-tick labels as you wish?

x = [1/3 1/2 1 inf];
xfake = [0 1 2 3];

y = [2 3 5 7];
plot(xfake,y,'-or')
set(gca,Xtick = [0 1 2 3],XTickLabel = x)

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How to set an axis with arbitrary, but equally spaced, scaling.

How to set an axis with arbitrary, but equally spaced, scaling.