Authors can always make edits to a Demonstration. They should edit the published author notebook, then send the new version to demonstrations@wolfram.com, or to me directly (edp@ ...).
To avoid jaggedness in the Autorun, PerformanceGoal -> "Quality" should be used.
There are many guideline suggestions available. I should have caught the jitteryness of this Autorun, fixable by adding an increment to the range, as in the below.
Manipulate[
PolarPlot[
r + (2 a - (f2percent a/50)) Sin[
f1 (x - f1fs/180 \[Pi])] + (f2percent a/50) Sin[
f2 (x - f2fs/180 \[Pi])], {x, 0, 2 rev \[Pi]},
PlotStyle -> {Black}, PlotRange -> Automatic,
ImageSize -> 1.15 {400, 400}, PlotPoints -> 25,
PerformanceGoal -> "Quality"
],
{{r, 1, Style["r", Italic]}, 1, 10, 1, Appearance -> "Labeled", ImageSize -> Tiny},
"",
{{a, 6, Style["a", Italic]}, 1, 10, 1, Appearance -> "Labeled", ImageSize -> Tiny},
"",
"frequency \!\(\*SubscriptBox[\(f\), \(1\)]\) of wave 1",
{{f1, 0.5, ""}, 0, 6, Appearance -> "Labeled", ImageSize -> Tiny},
"",
"frequency \!\(\*SubscriptBox[\(f\), \(2\)]\) of wave 2",
{{f2, 0.52, ""}, 0, 6, .001, Appearance -> "Labeled",
ImageSize -> Tiny},
"",
"cycles",
{{rev, 12, ""}, 1, 100, Appearance -> "Labeled", ImageSize -> Tiny},
"",
"morph wave 1 \[Rule] 2",
{{f2percent, 50, ""}, 0, 100, Appearance -> "Labeled",
ImageSize -> Tiny},
"",
"phase shifts",
"wave 1",
{{f1fs, 0, ""}, 0, 360, Appearance -> "Labeled", ImageSize -> Tiny},
"wave 2",
{{f2fs, 0, ""}, 0, 360, Appearance -> "Labeled", ImageSize -> Tiny},
TrackedSymbols :> {f2},
AutorunSequencing -> {{4, 1200}, {6, 20}, {7, 20}, {8, 20}}]
