# Can we make a labelled parametric plot in which the parameter is integer? [closed]

Can we make a labelled parametric plot in which the parameters are integers?

I'm just using Wolfram Alpha but could equally use Mathematica Online, and want something like here.

I want to plot values of $$x\cdot \exp{(2\pi i\log_{-1/3}x)}$$ in the complex plane for integers $$x$$.

This is only possible in Desmos by sending the complex and real parts to the x and y axes manually. However, I want to replace the base $$2/3$$ log with a base $$-1/3$$ logarithm, and that will either require putting a complex number into the formula or taking a base negative log, neither of which Desmos allows.

I can make a similar parametric plot in Wolfram like this but not with labels, and what I really need are the a) integer $$u$$ only, b) with the base $$-1/3$$ logarithm and c) labelled.

• I'm voting to close this question as off-topic because it does not concern Mathematica (Wolfram|Alpha is a separate system). – Szabolcs May 16 '19 at 13:17
• You could try community.wolfram.com – Szabolcs May 16 '19 at 13:18
• It is also slightly unclear what, exactly is being asked. – kirma May 16 '19 at 13:20
• @Szabolcs does that edit fix it? – samerivertwice May 16 '19 at 13:20
• Please do show what you tried, at the minimum typing up the expressions in Mathematica syntax. I assume you searched the documentation and found ParametricPlot. Did you try it? Discrete points can be highlighted with the Mesh option that has many examples in the docs. – Szabolcs May 16 '19 at 13:39

Here's one approach to plot a connected list of labeled values of a complex-valued equation for integer values of x:

ComplexListPlot[
Table[Labeled[x Exp[2 Pi I Log[-1/3, x]], x], {x, 1, 20}],
Joined -> True, PlotMarkers -> Automatic, PlotRangePadding -> Scaled[.2]] A little prettier one with different base of Log:

ComplexListPlot[
Table[Labeled[x Exp[2 Pi I Log[3, x]], x], {x, 1, 20}],
Joined -> True, PlotMarkers -> Automatic, PlotRangePadding -> Scaled[.1]] • Top job, thanks. – samerivertwice May 16 '19 at 15:20