Transport

Ordinary proposal

B3/S24567

Birth rule

Survival rule

Birth: 3. Survival: 2, 4, 5, 6, 7. This frozen first pass supplies every neighbor forecast.

Contraction veto

Maximum tolerated loss

Neighboring cells allowed to disappear

A loss of 0 remains permissible. A scheduled death stays alive only when its eight-neighbor forecast loses 1 or more.

Expansion veto

Maximum tolerated gain

Neighboring cells allowed to appear

A gain of 0 remains permissible. A scheduled birth stays dead only when its eight-neighbor forecast gains 1 or more.

Two-scale forecast

Fixed invariant

The secondary count covers the focal cell's same eight neighbors. Each neighbor's provisional future uses its own Moore count, so the forecast consults the sixteen-cell second ring. Forecasts never recurse into other veto decisions, and every final state commits synchronously.

013GOL

Second Thought

Every cell first proposes an ordinary Life transition, then forecasts the ordinary futures of its eight neighbors: projected collapse can protect a life, while projected expansion can suppress a birth.

Explore the collection Rules & reproducibility

Current composition

01Every position first proposes ordinary B3/S24567 from the frozen current field.
02The same eight neighbors are counted again in that provisional field. Calculating their futures consults the second ring.
03A projected loss greater than 0 vetoes a scheduled death; otherwise ordinary death proceeds.
04A projected gain greater than 0 vetoes a scheduled birth; otherwise ordinary birth proceeds.
05The secondary rule grants no new transition. Proposals, forecasts, vetoes, and final occupancy commit synchronously without recursion or evolution randomness.

Update: Frozen Life proposal → first-ring forecast → directional veto
Field: 160 × 160 · toroidal

Selected cell

Position: (80, 80) · Dead
Current neighbors: 2 / 8
Ordinary proposal: Dead
Projected neighbors: 0 / 8
Forecast delta: -2
Veto: None · ordinary proposal permitted
Next result: No transition · dead

Experiment index013 / 100

Game of Life: Second Thought

Paused · Forecasting the first ring

160 × 160 · generation 0

Color view shows established life lime, births cream, ordinary deaths coral, protected deaths cyan, and suppressed births amber. Inspect cell outlines projected-alive first-ring neighbors in cyan, projected-dead first-ring neighbors with gray dashes, and second-ring inputs with violet dashes. Arrow keys move the cursor; Enter paints when inspection is off; P plays or pauses; S advances one generation.

Established lifeBirthOrdinary deathDeath protectedBirth suppressed

Watch ordinary Life transitions survive, hesitate, or disappear when cells forecast the direction of their neighborhood.