2 added 209 characters in body

## Mathematica, 134134 131 bytes

N.B. This solution is no longer valid, as the question was later edited to require r to be measured in pixels. Thanks to Martin Ender for helping me shave off a few bytes in the comments.

r=Input[];RegionPlot[And@@((Abs[y+I x-#]^2<3r^2)&/@Table[r Exp[2@Table[Exp[2n I Pi n/3]3Pi]r,{n,3}]),{x,-1,1},{y,-1,1},Frame->False,BoundaryStyle->None]


The input value must be scaled between 0 and 1 for this code to work. Note that almost a quarter of this code is required to display the shape "in isolation", as this is not Mathematica's default.

## Mathematica, 134 bytes

r=Input[];RegionPlot[And@@((Abs[y+I x-#]^2<3r^2)&/@Table[r Exp[2 I Pi n/3],{n,3}]),{x,-1,1},{y,-1,1},Frame->False,BoundaryStyle->None]


The input value must be scaled between 0 and 1 for this code to work. Note that almost a quarter of this code is required to display the shape "in isolation", as this is not Mathematica's default.

## Mathematica, 134 131 bytes

N.B. This solution is no longer valid, as the question was later edited to require r to be measured in pixels. Thanks to Martin Ender for helping me shave off a few bytes in the comments.

r=Input[];RegionPlot[And@@((Abs[y+I x-#]^2<3r^2)&/@Table[Exp[2n I/3Pi]r,{n,3}]),{x,-1,1},{y,-1,1},Frame->False,BoundaryStyle->None]


The input value must be scaled between 0 and 1 for this code to work. Note that almost a quarter of this code is required to display the shape "in isolation", as this is not Mathematica's default.

1

## Mathematica, 134 bytes

r=Input[];RegionPlot[And@@((Abs[y+I x-#]^2<3r^2)&/@Table[r Exp[2 I Pi n/3],{n,3}]),{x,-1,1},{y,-1,1},Frame->False,BoundaryStyle->None]


The input value must be scaled between 0 and 1 for this code to work. Note that almost a quarter of this code is required to display the shape "in isolation", as this is not Mathematica's default.