← Range ArcadeWORLD Nº 052 · ONE THREAD BACK
⟲ rewind loomREAD YESTERDAY'S ROW WITHOUT LOOKING AT MOST OF TODAY'S

A ROW OF RULE 30. THE ROW BEFORE IT IS HIDDEN.

Find a 0·1·0.
Then everything below is forced.

Uncover threads of this row one at a time. Read 0, 1, 0 above the marked thread
and the loom's memory resets; from there the row before it unwinds by itself.

THE LOOMROW 1 / 6
THIS ROW, GENERATION GTHE ROW BEFORE IT, HIDDEN
⟲

One thread
of the row before.

This row was woven from a hidden row before it. You will be asked about one thread of that hidden row.
Uncover threads of this row one at a time, as few as you can. Find the telltale dark, lit, dark and the thread below is settled. Then answer: lit or dark.

0 POINTS← → CHOOSE · ENTER UNCOVER · 1 LIT · 0 DARKWIND IT BACK

The inverse of rule 30 is a three-state machine, and the word 0,1,0 sends every state to the same place: ntmc.cell_sync reads a predecessor cell in O(1) cells.

ANOTHER SET OF ROWS

Words choose which generations come off the loom.

HOW THE LOOM REWINDS

Reading a row backwards.

Rule 30 makes each new cell from three old ones: new = left XOR (centre OR right). Run that backwards from the top of a row and each hidden cell is forced by the two hidden cells above it and the visible cell between them. The loom keeps that pair as its memory, and the memory has only three states worth telling apart.

Reading the threads 0, 1, 0 from above sends all three states to the same one, so from there the hidden row unwinds without knowing anything higher up. Uncover the threads from the marked one upward until you see 0·1·0; the loom fills in the rest and the marked thread is proved.

A proved answer is 30 points, a guess that happens to be right is 15, and every thread beyond the nearest 0·1·0 costs two. Three stars is six rows proved with at most one spare thread each. Rows woven from a single seed have exactly one row before them; the check runs rule 30 forward on the answer to be sure.

SIX ROWS REWOUND

⟲

You read yesterday
without looking at today.

A FEW ROWS FOR A FRIEND

Rewind these rows with me.