# Logarithmic x-axis for ListPlot?

I have a list of points that I am trying to plot. Is there a way to make a ListPlot where the y-axis increases normally by 1 every interval but the x-axis increases by $x^2$, i.e., 1, 4, 9, 16, etc.?

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• closely related, unfortunately my answer doesn't seem to work in V10. – Kuba Jun 4 '15 at 20:49
• of course the requested power law interval is not logarithmic. You ought to edit the question or title to clarify what you mean. – george2079 Jun 16 '15 at 19:47

This is precisely what ListLogLinearPlot achieves--logarithmic $x$ and linear $y$ axes:

ListLogLinearPlot[Table[{n, Sqrt[n]}, {n, 100}]]


You need to make custom ticks and transform the data:

 list = Table[ {x, Log[x]} , {x, 1, 25} ];
ListPlot[{Sqrt[#[[1]]], #[[2]]} & /@ list ,
Ticks -> {{#, #^2} & /@ Range[1, 5], Automatic} ]


To do this, you can define your own ticks marks when you do the plot.

   data = Table[{i, i}, {i, 1, 50, 1}]
SpecialTicks = Table[{i^2, i}, {i, 1, 50, 1}];
ListPlot[data, Frame -> True, FrameTicks -> {{Automatic, None}, {SpecialTicks, All}}]


Here, I've added "All" just to show the linear tick marks at the top of the graph, but you can remove them.

• I changed from ListLinePlot to ListLogLinearPlot but it didn't connect the data points anymore. So I had to add ,Joined -> True. I also had to fiddle with axis origin to remove a vertical line that appeared. – simon Dec 12 '19 at 18:13