intothecontinuum:

r = 0.995
0.83687 ≤ a ≤ 0.83987
s = 200
Mathematica code:
Manipulate[Graphics[Line[   Table[{-r^n*Sin[n*2*Pi/a], r^n*Cos[n*2*Pi/a]}, {n, 0, s}]],  PlotRange -> 1.3], {r, .1, 1}, {a, 0.001, 4*Pi, .0001}, {s, 1,500, 1}]

intothecontinuum:

r = 0.995

0.83687 ≤ a ≤ 0.83987

s = 200

Mathematica code:

Manipulate[Graphics[Line[
Table[{-r^n*Sin[n*2*Pi/a], r^n*Cos[n*2*Pi/a]}, {n, 0, s}]],
PlotRange -> 1.3],
{r, .1, 1}, {a, 0.001, 4*Pi, .0001}, {s, 1,500, 1}]
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