I don't know if it is worth posting an answer, but nevertheless here it goes (code adopted by a discussion with David Park several years ago; then working with Mathematica 5.2. I tried to upgrade it in order to fit Graphics structure of recent versions):
partitionfunction[d_][q_] := Piecewise[{ {Sin[(Pi*q)/(2*d)]^2, Inequality[0, LessEqual, q, Less, d]}, {1, Inequality[d, LessEqual, q, Less, 2*Pi - d]}, {Sin[(Pi*(2*Pi - q))/(2*d)]^2, 2*Pi - d <= q <= 2*Pi}}] radius[d_][q_] := 1 + 1.5*partitionfunction[d][q]*BesselJ[5, (13/(2*Pi))*q + 5] curve[d_][q_] := radius[d][q]*{Cos[q], Sin[q]} g = ParametricPlot[curve[1][q], {q, 0, 2*Pi}, Axes -> False, PlotPoints -> 50, PlotStyle -> Thickness[0.007], Exclusions -> None]; line = Cases[g, l_Line :> First@l, Infinity]; Graphics[ {Opacity[0.4], Darker @ Orange, EdgeForm[Darker @ Orange], Polygon[line]}, Options[g]] 
This question and answer is related to the reply I wanted to give here
Thanks to ybeltukov for pointing out Exclusions (which I should have known that it has to be applied here).
