Galaxy: Rotations and Dilatations
GeoGebra Script
A = (-1, 0)
B = (1, 0)
C = (0.68, 0.74)
c = Ellipse(A, B, C)
a = Slider(0, 1, 0.01, 1, 200, false, true, false, false)
Execute(Sequence("A"+k+"="+k+"/2", k, 1, 20))
f(x) = (1 - a) * (x) + a * (-x)
Execute(Sequence("B"+k+"=Rotate(Dilate(c, A"+k+", (0, 0)), f(A"+k+" / 4), (0, 0))", k, 1, 20))
Execute(Sequence("ShowLabel(B"+k+", false)", k, 1, 20))
Execute(Sequence("SetDynamicColor(B"+k+", "+k+"/20, 1, 1)", k, 1, 20))Note
The animation actually shows a variation of colors (HSV) using the expression:
1/"+k+"