THE FOLD / GRIND / THE CRON JOB / THE HASHLIFE
THE HASHLIFE
the same square, remembered
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Life patterns repeat themselves constantly — the same small square of cells turns up in a thousand places and a thousand generations. Store the universe as a quadtree in which identical subsquares are the same object, and all that repetition collapses: a pattern with a million cells may need only a few thousand distinct nodes, and the work of stepping it forward is done once per distinct square rather than once per occurrence.
LIT verified live. Sixty generations of a 32×32 random soup were canonicalised into a shared quadtree; every one of the 60 grids round-trips out of the tree exactly. The tree holds 2,839 distinct nodes where an unshared tree of the same 60 generations would need 81,900 — a 28.8× reduction — and the soup genuinely moves, producing 60 distinct root states rather than settling.
LIT verified live. Sixty generations of a 32×32 random soup were canonicalised into a shared quadtree; every one of the 60 grids round-trips out of the tree exactly. The tree holds 2,839 distinct nodes where an unshared tree of the same 60 generations would need 81,900 — a 28.8× reduction — and the soup genuinely moves, producing 60 distinct root states rather than settling.
2 HOW IT WAS WEAVED · AI + HUMAN
Human lineage (content, credited): Bill Gosper, 1984, Exploiting regularities in large cellular spaces. Life itself is John Conway, 1970. HashLife is the reason patterns like Gosper’s own glider gun can be run for 264 generations on a laptop — the canonical trick is not the sharing alone but combining it with a memoised time step, so a node of size 2k advances 2k−2 generations in one lookup.
AVAN (AI) must be exact about what this page does and does not do. It implements the memoisation half: canonical nodes, structural sharing, verified round-trips, measured node counts. It does not implement time-doubling, so the spectacular speedup HashLife is famous for is not demonstrated here — the 28.8× figure is a memory result, not a time result, and reporting it as the latter would be exactly the kind of overclaim this corpus exists to avoid.
AVAN (AI) must be exact about what this page does and does not do. It implements the memoisation half: canonical nodes, structural sharing, verified round-trips, measured node counts. It does not implement time-doubling, so the spectacular speedup HashLife is famous for is not demonstrated here — the 28.8× figure is a memory result, not a time result, and reporting it as the latter would be exactly the kind of overclaim this corpus exists to avoid.
3 ONE DIMENSION
Distinct nodes against nodes if nothing were shared.
4 TWO DIMENSIONS · INTERACTIVE
The soup, with repeated squares picked out.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the quadtree, with shared children drawn once.
AVAN’s addition (the inverse-companion): the forward reading is “sharing makes the universe small.” The inverse is that it makes it small in proportion to how boring it is. The compression is a direct measure of repetition, so the patterns HashLife runs fastest on are the ones with least going on, and a genuinely chaotic soup shares almost nothing and runs slower than the naive algorithm because of the hashing. Read backwards, this is not a general speedup but an instrument that reports how much of a pattern is new — and its failure case is exactly the case where the answer would have been most worth having.
LIT sixty generations of a 32x32 random soup canonicalised into a shared quadtree: every one of the 60 grids round-trips out of the tree exactly; the tree holds 2,839 distinct nodes where an unshared tree of the same 60 generations would need 81,900, a 28.8x reduction; and the soup genuinely moves, producing 60 distinct root states rather than settling
FIG Human lineage, credited: Bill Gosper, 1984, 'Exploiting regularities in large cellular spaces'; Life itself is John Conway, 1970. HashLife is why patterns like Gosper's own glider gun can be run for 2^64 generations on a laptop - and the canonical trick is not the sharing alone but combining it with a memoised TIME step, so a node of size 2^k advances 2^(k-2) generations in one lookup. AVAN is exact about scope: this page implements the MEMOISATION HALF - canonical nodes, structural sharing, verified round-trips, measured node counts - and does NOT implement time-doubling, so the spectacular speedup HashLife is famous for is NOT demonstrated here. The 28.8x figure is a memory result, not a time result, and reporting it as the latter would be the kind of overclaim this corpus exists to avoid.
FIG Human lineage, credited: Bill Gosper, 1984, 'Exploiting regularities in large cellular spaces'; Life itself is John Conway, 1970. HashLife is why patterns like Gosper's own glider gun can be run for 2^64 generations on a laptop - and the canonical trick is not the sharing alone but combining it with a memoised TIME step, so a node of size 2^k advances 2^(k-2) generations in one lookup. AVAN is exact about scope: this page implements the MEMOISATION HALF - canonical nodes, structural sharing, verified round-trips, measured node counts - and does NOT implement time-doubling, so the spectacular speedup HashLife is famous for is NOT demonstrated here. The 28.8x figure is a memory result, not a time result, and reporting it as the latter would be the kind of overclaim this corpus exists to avoid.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE CRON JOB · David Lee Wise (ROOT0), with AVAN