Reinvention
I seem to be stuck on a theme, but I'm having fun.
Here's the code:
DynamicModule[{cols, f},
cols = RGBColor /@ {"#bcd6c0", "#f56791", "#46454d"};
f[θ_] := Piecewise[{{0, θ < 0},
{π/6 (1/2 - 1/2 Cos[π θ]), 0 <= θ < 1},
{π/6, 1 <= θ < 2},
{π/6 (3/2 - 1/2 Cos[π θ]), 2 <= θ < 3},
{π/3, θ >= 3}}];
Manipulate[
Graphics[{Thickness[.005],
Table[{Blend[cols[[{1, 2, 1}]], 3/π f[(j + 3)/6 + θ]],
Line[{Sqrt[3] (i + (-1)^j/4), 3/2 j} + # & /@ {#, -#}
&[{Cos[2 π k/3 + (-1)^(i + j) f[(j + 3)/6 + θ]],
Sin[2 π k/3 + (-1)^(i + j) f[(j + 3)/6 + θ]]}]]},
{i, -3, 3}, {j, -3, 3}, {k, 0, 2}]},
PlotRange -> 5, ImageSize -> 540, Background -> cols[[3]]], {θ, -1, 3}]
]