Transport

Standard Life

B36/S23

Birth rule

Survival rule

Birth: 3, 6. Survival: 2, 3.

Pivot triggers

Frozen source field

Living pivot · neighbor counts

Dead pivot · neighbor counts

Living triggers: 0, 1, 3, 5, 7, 8. Dead triggers: 6.

Actions by count

Nine independent assignments

Each enabled pivot count owns its assigned action. 0: Rotate 90° counterclockwise · 1: Rotate 90° clockwise · 3: Rotate 90° clockwise · 5: Rotate 90° clockwise · 6: Rotate 90° counterclockwise · 7: Rotate 90° clockwise · 8: Rotate 90° counterclockwise Horizontal means left ↔ right; vertical means top ↔ bottom.

Claim resolution

Fixed invariant

A pivot executes only when no other candidate lies within two cells in any direction. That makes every accepted 3 × 3 claim disjoint. Every overlapping candidate rests; no coordinate, scan order, or random winner is used.

010GOL

Pivot Life

Standard Life grows beneath isolated local pivots whose neighbor counts select different rotations or mirrors, while overlapping transformation claims honestly rest.

Explore the collection Rules & reproducibility

Current composition

01The frozen field applies B36/S23 everywhere to create one provisional Life generation.
02On that same frozen field, living pivots trigger at 0, 1, 3, 5, 7, 8 neighbors and dead pivots at 6.
03A candidate executes only if no other candidate lies within its two-cell claim radius. Overlapping claims all rest.
04Each accepted pivot reads the action assigned to its own neighbor count, transforms its disjoint 3 × 3 provisional block, and then the field commits atomically.

Update: Synchronous Life → disjoint local transforms
Field: 160 × 160 · toroidal

Selected cell

Position: (80, 80) · Dead
Neighbors: 1 / 8
Ordinary Life: Birth disabled · dead
Trigger: Not selected
Mapped action: Rotate 90° clockwise
Nearby candidates: 0 within the two-cell claim radius
Next pivot result: Not a candidate

Experiment index010 / 100

Game of Life: Pivot Life

Paused · Count-mapped turns

160 × 160 · generation 0

Color view marks accepted pivots amber, suppressed pivots coral, boundary-blocked pivots blue, and transformed Moore blocks violet. Inspect cell outlines the inner 3 by 3 transform block and outer 5 by 5 claim radius. Arrow keys move the cursor; Enter toggles a cell when inspection is off; P plays or pauses; S advances one generation.

Ordinary lifeAccepted pivotOverlapping claim restsTransformed block

Watch isolated pivots locally turn or mirror Life while crowded transformation opportunities honestly rest.