(* This is a program for animating parametrized solutions            *)
(* of polynomials, with mathematica. f[z_,w_] is the                 *)
(* branch curve, where z will be taken as parameter,                 *)
(* and we solve for w. To run it, type <<filename                    *)
(* Note that the speed is now slowing down towards the end           *)

i = \[ImaginaryI];
f[z_,w_] := 128000*z^12-76800*z^11*w+92160*z^10*w^2-108544*z^9*w^3-258048*z^8*w^4+86016*z^7*w^5-112640*z^6*w^6+141312*z^5*w^7+211968*z^4*w^8-25600*z^3*w^9+36864*z^2*w^10-49152*z*w^11-65536*w^12-391307*z^8+180632*z^7*w+1940*z^6*w^2-503112*z^5*w^3-2102866*z^4*w^4+457512*z^3*w^5-122764*z^2*w^6-102904*z*w^7-251483*w^8+399430*z^4-106312*z^3*w-155028*z^2*w^2-53752*z*w^3-320858*w^4-136161;

degreef = 12;

steps = Input["Number of steps (integer) ?"];
scale = Input["Z-W range of the plot (real number) ?"];
center = Input["Center of the plot (complex number, e.g. 1.0+2.0*i) ?"];

points = {};
source = Input["Starting point (complex number) ?"];
target = Input["Endpoint (complex number) ?"];
Do[
  l = 1-(k-1)^2;
  points = Append[points, l*target + (1-l)*source],
{k,0,1,1/steps}
];

plane = {};
plotcommand = {};
Do[
  l=1-(k-1)^2;
  g[w_] := Expand[f[points[[k]],w]];
  zeros = w /. N[Solve[g[w] == 0, w]];
  partial = {};
  Do[
    pair = {Re[zeros[[q]]],Im[zeros[[q]]]};
     partial = Append[partial,pair]
    ,{q,1,degreef,1}
  ];
  plane = Append[plane,partial]
  ,{k,1,steps+1,1}
];

myplot = Table[ListPlot[plane[[t]], Axes->False, ImageSize->Full,
  PlotStyle->PointSize[0.002],
  PlotRange->{{-scale+Re[center],scale+Re[center]},
  {-scale+Im[center],scale+Im[center]}}, AspectRatio->1],{t,1,steps+1,1}];

ListAnimate[myplot]