-- learn some short cut aliases:
ul |*> #=> up left |_self>
u |*> #=> up |_self>
ur |*> #=> up right |_self>
l |*> #=> left |_self>
r |*> #=> right |_self>
dl |*> #=> down left |_self>
d |*> #=> down |_self>
dr |*> #=> down right |_self>

-- learn our difference operators:
diff-R |*> #=> pos( dr -0.125 old-R ul |_self> + d -0.125 old-R u |_self> + dl -0.125 old-R ur |_self> + r -0.125 old-R l |_self> + old-R |_self> + l -0.125 old-R r |_self> + ur -0.125 old-R dl |_self> + u -0.125 old-R d |_self> + ul -0.125 old-R dr |_self>)
diff-G |*> #=> pos( dr -0.125 old-G ul |_self> + d -0.125 old-G u |_self> + dl -0.125 old-G ur |_self> + r -0.125 old-G l |_self> + old-G |_self> + l -0.125 old-G r |_self> + ur -0.125 old-G dl |_self> + u -0.125 old-G d |_self> + ul -0.125 old-G dr |_self>)
diff-B |*> #=> pos( dr -0.125 old-B ul |_self> + d -0.125 old-B u |_self> + dl -0.125 old-B ur |_self> + r -0.125 old-B l |_self> + old-B |_self> + l -0.125 old-B r |_self> + ur -0.125 old-B dl |_self> + u -0.125 old-B d |_self> + ul -0.125 old-B dr |_self>)

-- copy values to old-values:
|null> => map[R,old-R] rel-kets[R] |>
|null> => map[G,old-G] rel-kets[G] |>
|null> => map[B,old-B] rel-kets[B] |>

-- apply our operators:
|null> => map[diff-R,R-2d-differences] rel-kets[old-R] |>
|null> => map[diff-G,G-2d-differences] rel-kets[old-G] |>
|null> => map[diff-B,B-2d-differences] rel-kets[old-B] |>