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.

  • 3
    $\begingroup$ I'm voting to close this question as off-topic because it does not concern Mathematica (Wolfram|Alpha is a separate system). $\endgroup$ – Szabolcs May 16 '19 at 13:17
  • $\begingroup$ You could try community.wolfram.com $\endgroup$ – Szabolcs May 16 '19 at 13:18
  • $\begingroup$ It is also slightly unclear what, exactly is being asked. $\endgroup$ – kirma May 16 '19 at 13:20
  • $\begingroup$ @Szabolcs does that edit fix it? $\endgroup$ – samerivertwice May 16 '19 at 13:20
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    $\begingroup$ 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. $\endgroup$ – 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:

 Table[Labeled[x Exp[2 Pi I Log[-1/3, x]], x], {x, 1, 20}], 
 Joined -> True, PlotMarkers -> Automatic, PlotRangePadding -> Scaled[.2]]

enter image description here

A little prettier one with different base of Log:

 Table[Labeled[x Exp[2 Pi I Log[3, x]], x], {x, 1, 20}], 
 Joined -> True, PlotMarkers -> Automatic, PlotRangePadding -> Scaled[.1]]

enter image description here

| improve this answer | |
  • $\begingroup$ Top job, thanks. $\endgroup$ – samerivertwice May 16 '19 at 15:20

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