Bits per symbol as one symbol takes over the stream

Bits per symbol as one symbol takes over the stream

An alphabet of 8, with the first symbol appearing at the probability on the horizontal axis and the rest sharing what is left. The entropy falls toward zero. Arithmetic coding follows it within a hundredth of a bit everywhere. Huffman flattens at exactly 1.000, because the shortest word a prefix code has is one bit and it must be spent on every symbol — at p = 0.99, that is 8.7 times what the stream is worth.

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

2 essays call skew-staircase. 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.