# A possible bug about ParametricPlot in version 13.3

## example 1

ParametricPlot3D[{x, y, 0}, {x, y} ∈ MengerMesh[2, 2]] // AbsoluteTiming


## example 2

With[{regmem = RegionMember[MengerMesh[2, 2]]},
ParametricPlot[{x, y}, {x, 0, 1}, {y, 0, 1}, PlotPoints -> 50,
RegionFunction ->
Function[{x, y}, regmem@{x, y}]]] // AbsoluteTiming


## example 3

ParametricPlot[{x, y}, {x, 0, 1}, {y, 0, 1}, PlotPoints -> 30,
RegionFunction ->
Function[{x, y}, {x, y} ∈
MengerMesh[2, 2]]] // AbsoluteTiming


but

## example 4

ParametricPlot[{x, y}, {x, y} ∈ MengerMesh[2, 2]] // AbsoluteTiming


It take long time to get this picture(need 148). When I test version 11.3, it only need 0.8

$Version (* 11.3.0 for Microsoft Windows (64-bit) (March 27, 2018) *) ParametricPlot[{x, y}, {x, y} ∈ MengerMesh[2, 2]] // AbsoluteTiming  • Can you be explicit? What do you regard as a bug here? Jul 12, 2023 at 1:25 • Could you use Show[Region[MengerMesh[2, 2], Frame -> True]] instead? Jul 12, 2023 at 1:39 • @ChrisK Since I want to transform a region, for example ParametricPlot[{x - y^2/2, y - x^2/2}, {x, y} ∈ MengerMesh[2, 2]], and at usually, ParametricPlot is faster then TransformedRegion. Jul 12, 2023 at 1:43 • @herbertfederer Thanks, I'm not familiar with the 2D version of ParametricPlot. Jul 12, 2023 at 1:46 • @ChrisK - the Show in your code doesn't contribute anything. Region[MengerMesh[2, 2], Frame -> True] produces the same result. Jul 12, 2023 at 1:52 ## 2 Answers Fixed in version 13.3.1 $Version
ParametricPlot[{x, y}, {x, y} ∈
MengerMesh[2, 2]] // AbsoluteTiming


• where did you get 13.3.1 from? I went to my portal at Wolfram and it is still says 13.3 latest. I went to the cloud and it says 13.3 there also. Was this even announced? When was it released? Aug 14, 2023 at 13:39
• @Nasser Some user can update to 13.3.1 now, maybe release soon :) Aug 14, 2023 at 14:24
• I got an email about Wolfram Desktop 13.3.1. I have not received an email about Mathematica 13.3.1. Aug 19, 2023 at 15:53

Somebody has forgotten to set the plot point number

ParametricPlot[{x,y}, {x,y} ∈ MengerMesh[2, 2],
PlotPoints -> 4] // AbsoluteTiming


• (+1)Thanks, since PlotPoints->0 also work. It indicate that it is actually a bug. Jul 12, 2023 at 10:35