# 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.

## closed as off-topic by Szabolcs, Roman, m_goldberg, Coolwater, MarcoBMay 23 at 14:14

• The question does not concern the technical computing software Mathematica by Wolfram Research. Please see the help center to find out about the topics that can be asked here.
If this question can be reworded to fit the rules in the help center, please edit the question.

• 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 at 13:17
• You could try community.wolfram.com – Szabolcs May 16 at 13:18
• It is also slightly unclear what, exactly is being asked. – kirma May 16 at 13:20
• @Szabolcs does that edit fix it? – samerivertwice May 16 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 at 13:39

## 1 Answer

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 at 15:20