No fancy math this time. Here’s what happens when you connect points on edges two apart in a regular octagon by straight lines, then let the odd-numbered vertices of the octagon go to the origin and let even-numbered vertices move away from the origin (plus various other bits of nonsense).
Code:
In[]:=
DynamicModule[{cols,r,u,verts},cols=RGBColor/@{"#35342f","#f1f2f0"};​​Manipulate[r=1/2-Cos[s]/2;​​u=If[s<π,s,s+2π];​​verts=Table[(1-r(-1)^(If[s<π,i+1,i])){Cos[2πi/8-u/8-π/8],Sin[2πi/8-u/8-π/8]},{i,0,7}];​​Graphics[{Thickness[.005],CapForm["Round"],cols[[1]],Table[Line[{tverts[[i]]+(1-t)RotateRight[verts][[i]],tRotateLeft[verts][[i]]+(1-t)RotateLeft[verts,2][[i]]}],{i,1,7,2},{t,0,1,1/8}]},PlotRange->3,ImageSize->540,Background->cols[[2]]],{s,0.,2π}]]
Out[]=
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