2 added 209 characters in body
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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N.B. This solution is no longer valid, as the question was later edited to require r to be measured in pixels.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]

enter image description here

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]

enter image description here

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N.B. This solution is no longer valid, as the question was later edited to require r to be measured in pixels.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]

enter image description here

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
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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]

enter image description here

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.