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Notes about colormapping

terminal color encoding

To increase the resolution of rendering images in the y-axis, each terminal row is divided into two pixels using the unicode characters █, , ▄, and ▀, labeled as const.FULL_1, const.FULL_0, const.HALF_01, and const.HALF_10 respectively. A pair of these "pixels" being rendered as a single character I call a "patch".

curses has 255 slots for foreground/background color pairs. We assign each SLOT to a (F, B) color where SLOT is a number between 1 and 255 inclusive representing a curses color slot, and F and B are numbers between 0 and 255 inclusive representing terminal colors for the foreground and background respectively. F and B must come from the set of K colors in a colormap.

To increase the capacity of colors per colormap, we note that we never need to use a slot where F == B since we can always just use █ colored by (F, *), or colored using (*, B). Similarly, we never need to use a slot for F < B. If we wanted a slot colored as ▄ (F, B) with F < B, we can replace it with ▀ (B, F).

Thus we have the following solution so that every possible patch can be encoded in the colormap using a combination of one of █, , ▄, and ▀ and one of our stored (F, B) pairs.

COLORS are the K color values in the color map indexed from 0 to K-1 inclusive
SLOTS are the 255 slots from 1 to 255 inclusive
PATCH is a (X0, X1) pair where X0 and X1 are the indices into COLORS that we want to render

PATCH = (X0, X1)	(COLORS, CHAR)	(SLOT, CHAR)
(0, 0)	(COLORS[K-1], COLORS[0]), " ")	(K-1, " ")
(1, 0)	(COLORS[1], COLORS[0]), "▀")	(1, "▀")
(2, 0)	(COLORS[2], COLORS[0]), "▀")	(2, "▀")
...	...	...
(K-1, 0)	(COLORS[K-1], COLORS[0]), "▀")	(K-1, "▀")
(0, 1)	(COLORS[1], COLORS[0]), "▄")	(2, "▄")
(1, 1)	(COLORS[1], COLORS[0]), "█")	(2, "█")
(2, 1)	(COLORS[2], COLORS[1]), "▀")	(K, "▀")
...	...	...
(K-1, 1)	(COLORS[K-1], COLORS[1]), "▀")	(2K-1, "▀")
(0, 2)	(COLORS[2], COLORS[0]), "▄")	(3, "▄")
(1, 2)	(COLORS[2], COLORS[1]), "▄")	(K+1, "▄")
(2, 2)	(COLORS[2], COLORS[0]), "█")	(3, "█")
(3, 2)	(COLORS[3], COLORS[2]), "▀")	(2K, "▀")
...	...	...
(K-1, 2)	(COLORS[3], COLORS[2]), "▀")	(3K-4, "▀")
...	...	...
(K-1, K-1)	(COLORS[K-1], COLORS[0]), "█")	(K-1, "█")

The formula for this is

SLOT = (X1 * (K - 1)) - (X_1 * (X_1 - 1)) // 2 + X0 - X1