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[GiF] Dancing or juggling patterns of complex polynomial roots?

GROUPS:

I've seen Henry Segerman just posted a link to a nice visualization (i think original is actually here). I recognized Mathematica color schemes and right away wanted to recreated it. You can see the result below, and the WL code under the animation. Animation is showing the roots of the polynomials

$$x^5 + tx + 1 <=> x^5 + tx^2 + 1 <=> x^5 + tx^3 + 1$$

as t varies along a circle around 0 in the complex plane (with radius 1 and 2).Code could be a bit shorter, but I was in a rush. But why to use the same color function, if we can improvise, right?

enter image description here

plfn[f_,R_]:=ContourPlot[f,{x,-R,R},{y,-R,R},
PlotPoints->50,Contours->25,Frame->False,PlotRange->{{-R,R},{-R,R},5{-1,1}},
ImageSize->300,ColorFunction->"SunsetColors"]

frames=ParallelTable[Grid[
{{plfn[Abs[(x+I y)^5+ 1 Exp[I a](x+I y)+1],1.85],
plfn[Abs[(x+I y)^5+ 2 Exp[I a](x+I y)+1],1.85]},
{plfn[Abs[(x+I y)^5+ 1 Exp[I a](x+I y)^2+1],1.85],
plfn[Abs[(x+I y)^5+ 2 Exp[I a](x+I y)^2+1],1.85]},
{plfn[Abs[(x+I y)^5+ 1 Exp[I a](x+I y)^3+1],1.85],
plfn[Abs[(x+I y)^5+ 2 Exp[I a](x+I y)^3+1],1.85]}},
Spacings->{0, 0}],{a,{0}}]
Attachments:
POSTED BY: Vitaliy Kaurov
Answer
1 year ago

I'm not sure what I'm seeing but it is very hypnotising...

POSTED BY: Sander Huisman
Answer
1 year ago

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