STREAM ORDER IS ALREADY A RULER SEQUENCE

Ruler Rivers & Flow.

Two order-n streams meet to make an order-n+1, so confluences thin out by a factor of two per order — which is v₂, exactly. This basin is grown from the edge run and nothing else. Then the water: every droplet's position is a pure function of (seed, droplet, t), so jump to t = 1,000,000 and it is already there.

On Planet One

The planet's rivers keep the counting but live on the address: a trunk in every 4,096-cell valley, alive only where its own signal says so, and tributaries leaving on the rows where v₂(j+1) ≥ 1 — longer for higher order. That is this basin's law, laid onto a cube-sphere. Open Planet One →