import geometry;
import animate;
animation A;

size(15cm);

int nAnim=75;
int nCircle=6;
real astep=360/nAnim;

inversion inv=inversion((-1,-2),1);
line L1=line(N,S);
circle C=inv*L1;
point center=C.C;

for (int i=-nAnim; i < nAnim; ++i) {
  real r;
  r=0.001+4*(i/nAnim)^2;
  line L2=shift(2*r*E)*L1;
  transform T=shift(0,-2*r);
  transform R=rotate(astep*i,center);
  circle C0=circle(r*E+nCircle/2*sqrt(r)*N,r);
  circle[] Ci=sequence(new circle(int i){return T^i*C0;}, nCircle);

  fill(R*(path)C, 0.3*blue);
  circle Cl=R*(inv*L2);
  transform dsh=shift(Cl.r/3*unit(center-Cl.C));
  radialshade((path)Cl,white,dsh*Cl.C,0,black,dsh*Cl.C,Cl.r);
  for (int i=0; i < Ci.length; ++i) {
    circle Ct=inv*Ci[i];
    transform dsh=shift(Ct.r/3*unit(center-Ct.C));
    radialshade(R*(path)Ct,red,dsh*R*Ct.C,0,black,dsh*R*Ct.C,Ct.r);
  }
  A.add();
  erase();
}

A.movie(BBox(2mm,Fill(black)));