← Range ArcadeWORLD Nº 055 · CALL THE EDGE, THEN STOP
◐ edge fortuneKNOW WHAT THE CARRY DECIDES. KNOW WHERE IT STOPS DECIDING.

GENERATION ONE QUINTILLION. NO SIMULATION. STILL KNOWN.

The carry decides
exactly this many bits.

Read g+1 in binary. However many low bits carried, that is v, and v alone fixes the first bits of the edge:
a run of ones, a zero, a plateau. Call them, then stop before the first bit nobody can know from v.

THE EDGEFORTUNE 1 / 8
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Eight fortunes
at the edge of the pattern.

Each fortune is a spot on a growing pattern, far too big to ever draw. A few of its edge bits can still be known for certain.
Call them, lit or dark, from the outside in, and stop before the first one nobody can know.
Five points a known bit, fifteen for a perfect stop. A wrong call ends the fortune.

0 POINTS1 LIT · 0 DARK · ENTER STOPTELL ME THE EDGE

prefixlaw: bit b of the edge has period 2^p(b) from generation zero, so v2(g+1) = v pins every bit with p(b) ≤ v+1, and the next one genuinely varies.

OTHER GENERATIONS

Words choose which generations the fortune teller reads.

THE FORTUNE TELLER'S LADDER

What v2(g+1) knows, and what it cannot.

Every bit of rule 30's light-cone edge is exactly periodic with a period that is a power of two, from generation zero. So which bits are fixed by g+1's carry is a matter of divisibility: if 2^v divides g+1, every bit with p(b) ≤ v+1 is pinned, and the bit after that takes both values as the odd part of g+1 changes.

The pinned prefix is always a run of ones (the edge run, A094604), then a zero, then a short plateau pattern that depends only on v. The ladder in the first level shows the run and the whole pinned prefix per rung; later levels ask you to read v off the counter and remember.

Calling past the pinned bits is gambling: the game looks each bit up honestly, and a lucky call scores two, but a slip ends the fortune. The encore asks for the centre column at a small generation, where no lookup exists at all; the game has to simulate, and so would anyone.

EIGHT FORTUNES READ

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You knew
where knowledge ends.

A FORTUNE FOR A FRIEND

Read these edges with me.