Every level is balanced, which is why there is nothing to take

Every level is balanced, which is why there is nothing to take

A wavelet tree splits each node's values at their midpoint, so a level's bits are as near half ones as the point set allows — by construction, not by accident. Over 3,612 points the zero-order entropy runs from 0.987 to 1.000 bits a bit, and a uniform permutation of the same size gives 0.997. A coding that compresses to zero-order entropy is being handed the one input it cannot help, and what little it does gain comes from the imbalance of individual nodes rather than of levels.

Drawn at 700 × 430, wide on the page. Everything above is what compressed-grid returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

4 essays call compressed-grid. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.