(*Fuzzy Sphere scaling to 5 part lemniscate with 6 steps printed for 5x5 matrices. Each step is in 6ths for  the images.  Increase step to create the video,
Finally, one can compress the video in linux via
ffmpeg -i F5scale.avi-vcodec msmpeg4v2-q:v 7 F5scale_cmprsd.avi
*)
n=2;
(a = {{2,0,0,0,0},{0,1,0,0,0},{0,0,0,0,0},{0,0,0,-1,0},{0,0,0,0,-2}}) // MatrixForm
(b= {{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0},{0,0,0,0,1},{0,0,0,0,0}}) // MatrixForm ;
(b2=(1/(2*n))*(ConjugateTranspose[b]+b)) // MatrixForm
(c= (1/(2*n))*I*(ConjugateTranspose[b]-b))// MatrixForm
sigma1 = {{0,1}, {1,0}};
sigma2 = {{0,-I},{I,0}};
sigma3 = {{1,0},{0,-1}};
loclzr = KroneckerProduct[sigma1, r*a - x*IdentityMatrix[5]] + 
KroneckerProduct[sigma2, b2-y*IdentityMatrix[5]]+ 
KroneckerProduct[sigma3, c-z*IdentityMatrix[5]] ;
MatrixForm[loclzr]
charpoly = FullSimplify[Det[loclzr]]

step = 1/6;

plots2 = ParallelTable[ContourPlot3D[-((x^2)/256)-16 (r^8) ((x^2)+(y^2)+(z^2))+(r^6) (1+4 (x^2)+40 (x^4)-40 (y^4)-4 (z^2)-40 (z^4)-4 (y^2) (1+20 (z^2)))+(1/4) (r^4) (1-132 (x^6)+(y^2)+(z^2)-4 ((((y^2)+(z^2)))^2) (5+33 (y^2)+33 (z^2))-4 (x^4) (9+35 (y^2)+35 (z^2))-(x^2) (-1+140 (y^4)+24 (z^2)+140 (z^4)+8 (y^2) (3+35 (z^2))))+(1/32) (-32 (x^10)-32 ((((y^2)+(z^2)))^5)-32 (x^8) (1+5 (y^2)+5 (z^2))-4 (x^6) (3+80 (y^4)+24 (z^2)+80 (z^4)+8 (y^2) (3+20 (z^2)))-(x^2) ((y^2)+(z^2)) (1+160 (y^6)+6 (z^2)+32 (y^4) (1+15 (z^2))+(y^2) (6+64 (z^2)+480 (z^4))+32 ((z^4)+5 (z^6)))-2 (x^4) (1+160 (y^6)+9 (z^2)+48 (z^4)+160 (z^6)+48 (y^4) (1+10 (z^2))+(y^2) (9+96 ((z^2)+5 (z^4)))))+(1/64) (r^2) (1+640 (x^8)+4 (y^2)+4 (z^2)+128 (x^6) (3+10 (y^2)+10 (z^2))+8 (x^4) (11+56 (y^2)+56 (z^2))-4 ((((y^2)+(z^2)))^2) (-1+160 (y^4)+16 (z^2)+160 (z^4)+16 (y^2) (1+20 (z^2)))+4 (x^2) (3+15 (z^2)-5 (64 (y^6)+192 (y^4) (z^2)+64 (z^6)+3 (y^2) (-1+64 (z^4)))))== 0, {x,-2,2}, {y,-.5, .5}, {z, -.5, .5},BoxRatios->Automatic,Contours->{{1,LightBlue}},PlotPoints->50],{r,step,1,step}]

Export["FuzzySphere1.eps",plots2[[3]],ImageSize->3.2*72];

Export["FuzzySphere2.eps",plots2[[4]],ImageSize->3.2*72];

Export["FuzzySphere3.eps",plots2[[5]],ImageSize->3.2*72];

Export["FuzzySphere4.eps",plots2[[6]],ImageSize->3.2*72];

plotsall=Join[plots2,Reverse[plots2]];

Export["F5scale.avi",plotsall,ImageResolution->300,"FrameRate"->30]