Construct an animated gif file showing the formation of the astroid.

> restart;

> with(plots):

Warning, the name changecoords has been redefined

> a1:=plot([4*cos(t),4*sin(t),t=0..2*Pi],scaling=constrained,color=cyan,axes=none):

> a2:=animate([3*cos(t)-cos(s),3*sin(t)-sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,color=yellow,axes=none,frames=50,thickness=2):

> x1:=3*cos(t)-cos(3*t):y1:=3*sin(t)+sin(3*t):

> a3:=animate([(1-s)*3*cos(t)+s*x1,(1-s)*3*sin(t)+s*y1,s=0..1],t=0..2*Pi,scaling=constrained,color=green,axes=none,frames=50):

> a4:=plot([x1,y1,t=0..2*Pi],scaling=constrained,color=red,axes=none):

> display(a1,a2,a3,a4);

>