I present a slight variation. Not as concise, but surprisingly fluid:
With[{m = 7, n = 7, r = 6, c1 = RGBColor["#00EAFF"], c2 = RGBColor["#F37EF9"], cb = RGBColor["#020438"]},
Manipulate[Graphics[With[{? = ? Sin[?]/r},
Table[{Directive[AbsoluteThickness[2], Blend[{c1, c2}, Haversine[r ?]]],
Line[TranslationTransform[{j, k}] @
{{0, 0}, (Haversine[?] + Haversine[{? + ?/2, ? - ?/2}])/2, {1, 1}/2,
(Haversine[? + ?] + Haversine[{? - ?/2, ? + ?/2}])/2, {1, 1}}],
Line[TranslationTransform[{j, k}] @
{{0, 1}, (Haversine[{?, ? + ?}] + Haversine[? - ?/2])/2, {1, 1}/2,
(Haversine[{? + ?, ?}] + Haversine[? + ?/2])/2, {1, 0}}]},
{j, 0, m - 1}, {k, 0, n - 1}]],
Background -> cb], {?, 0, 2 ?}]]