English: Generated in MAPLE using the following code:

with(plots): p1:=animate(polarplot, [1-cos(theta), theta=0..t,axes = none, numpoints=10000, colour=red], t=0..2*Pi, frames=125):

p2:=polarplot(-cos(theta), theta=0..2*Pi, colour=blue): p3:=animate(implicitplot, [(x-sin(u)+0.5)^2+(y+cos(u))^2=0.5^2, x=-2..1, y=-1.5..1.5,colour=black, numpoints=50000], u=Pi/2..5/2*Pi, frames=125): p4:=animate(pointplot,[coords=polar, [1-cos(t),t], colour=red, symbol=solidcircle], t=0..2*Pi, frames=125): display(p1,p2,p3,p4);