Cata1[k_] := Plot[{F[x, k + 1], G[x,k + 1]}, {x, 2^-(k + 1), 2^(1/3 (-2 - 3 k))}, Filling -> 1 -> {2}]

Cata2[k_] := Plot[{G[x, k], G[x, k + 1]}, {x, 2^(1/3 (-2 - 3k)), 2^(1/3 (-1 - 3 k))}, Filling -> 1 -> {2}]

Cata3[k_] := Plot[{G[x, k], F[x,k]}, {x, 2^(1/3 (-1 - 3 k)), 2^-k}, Filling -> 1 -> {2}]