The Almanac
The weather here is driven by tri_xor — a triangular XOR-driven system, where a theorem guarantees every coordinate is exactly periodic, with a period that is a power of two. So the rain is not noise that happens to repeat. It repeats provably, on a stated number, forever. Which means an almanac for this world is not a folk prediction. It is right.
Whatever it is doing now
Drag to walk the bank. The clouds, the rain and the wind are three coordinates of the same system, each on its own exact clock.
The almanac
Every line is exact. Not "usually", not "on average" — the theorem says the period is a power of two and the measurement agrees to the tick.
| reading | coord | period | now | next change |
|---|
Why this one is yours
Rule 30's light-cone edge is one instance of a triangular XOR-driven system —
the case where the driver is OR. There are sixteen two-input
drivers, and every one of them has the same guarantee. Swap the driver above and the
weather changes character while staying exactly periodic.
That is not a property procedural weather usually has. Noise-based weather drifts;
you can only say what is likely. Here the state at time t is
table[t mod P], so a forecast a million periods out costs the same as a
forecast for the next tick — and it is not a forecast at all, it is a lookup.
An in-game almanac, sold by a character at the hall, would be a genuinely correct document. Very few games can say that about anything.
Clear skies: Sundial → · where the almanac would be sold: The Settlement Law →
Drivers and spectra are tri_xor's, ported: x_j ← x_j XOR G(x_{j-1},
x_{j-2}), coordinate j exactly periodic with period 2p(j). The
page evolves one full period once, then every later time is an index into it. Rain
streaks and cloud shadows drift by the same triangle wave the current uses.