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

> restart;

> with(plots):

Warning, the name changecoords has been redefined

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

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

> x1:=2*cos(t)-cos(2*t):y1:=2*sin(t)-sin(2*t):

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

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

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

>