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

GROUPS:
 Vitaliy Kaurov 7 Votes 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? 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:
2 years ago
 Sander Huisman 2 Votes I'm not sure what I'm seeing but it is very hypnotising...