Descent

A very simple idea: just a bunch of octagons in the plane, shrinking. I ended up deciding that the 4:3 aspect ratio, while less symmetric than my usual square, actually made it more clear what is going on.

Here's the code:

With[
 {cols = RGBColor /@ {"#DFF09D", "#295E62"}},
 Manipulate[
    Graphics[
     {cols[[If[r < 2.5, 1, -1]]],
      Table[
       RegularPolygon[3^i {Cos[t], Sin[t]}, {Mod[r, 2.5]^2, 0}, 8], {t, 0, 2 Pi - Pi/8, 2 Pi/8}, {i, -4, 2}]
      },
     PlotRange -> {{-8, 8}, {-6, 6}}, ImageSize -> {800, 600}, Background -> cols[[If[r < 2.5, -1, 1]]]],
    {r, 5. - #, #, -#}] &[5./399]
 ]