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Only Rearranged

Experiment № 081 · September 8, 2026

keep only the last column
run the whole loop by itself
characters, with the end mark— runs in the text— runs after the transform— longest block—
the last column—

—

Every rotation of the text, sorted. The last column is the only thing you keep.

one rotation of the text per row
F — first column, sorted
L — last column, the transform
the jump back, undoing it

blocks of identical characters

the text as written —
the last column —

Fewer, longer blocks is exactly what a run-length coder gets paid for.

type your own text · hover a row to read it · r re-sort · i undo it · l last column only · h panel

Experiment № 081 · The story

Only Rearranged

Why I picked it

Most compression I can explain in a sentence: spot something frequent, spend fewer bits on it. The Burrows–Wheeler transform doesn't do that at all. Michael Burrows and David Wheeler published it in 1994 as a Digital Equipment research report, and on its own it compresses precisely nothing — the output is the same length as the input, with the same characters in it and the same count of each. It is a permutation. And yet it is the reason bzip2 beat everything around it for years. I wanted an algorithm whose whole contribution is rearranging, and which is honest about the fact that the rearranging is where all the cleverness lives.

What I enjoy about it

The moment the rows land. Before the sort you're looking at a diagonal staircase — every rotation shifted one place from the one above — and the last column is meaningless confetti. Then the rows slide into alphabetical order and that column falls into blocks. The reason is oddly human: sorting groups rows by what follows, and in real text the same context tends to be preceded by the same letter, so every row starting he  almost certainly has a t hanging off its end. The other half I like is undoing it. Turn on keep only the last column and watch the matrix evaporate — and then press undo it anyway. From that single column the whole text walks back out, right to left, one jump per character. All that scaffolding was never stored; it was only ever a way of describing which permutation to apply.

Something you might take away

A reversible rearrangement cannot add information and cannot destroy any — that's what reversible means. So the transform doesn't make the text more compressible in any deep sense; it moves the redundancy that was already there into a form a much dumber algorithm can see. Run-length coding is too stupid to notice that abcabcabc… repeats — it only ever sees a, then a different character, and gives up. After the transform it doesn't have to be clever, because every a in the text has been stacked into one pile in front of it. Paste in random letters and watch the counters refuse to move: there was nothing to expose, so nothing came out. That's the general shape of the thing — most of the value in a pipeline is usually in the preparation, and preparation that looks like it achieved nothing is often the step that did all the work.