GOL-039 · technical companion

Pursuit Loop

One shuffled closed loop: every cell pursues the next and has one pursuer. Randomly phased escape compasses and configurable blocked waits keep trying new directions.

Open simulation →Markdown Download example JSON

At a glance

geometry: Square lattice
neighborhood: One global targeting cycle + cardinal pursuit + eight-way angular escape
states: Fixed identities, targets and pursuers + dual compasses + rotation senses + blocked waits
update: Synchronous one-square advances, later-turn angular escape, then one compass update
renderer: Canvas 2D

Targeting loop

Initialization shuffles all living identities once with seeded Fisher–Yates and links each to the next, including last to first. For two or more cells, following targets visits every cell exactly once before closing; each has exactly one pursuer. Targets and population stay fixed. One cell has no target and stays put; empty worlds remain empty. Unlike independent Pursuit assignments, there are no shared targets or separate targeting cycles.

Compasses and movement

Each cell starts with a uniformly random eight-way escape heading and independent 50/50 fixed clockwise or counterclockwise sense. A separate angular seed controls these traits. The cardinal compass aims at its target, updating after every Step, even when blocked. Preserve an equally best prior bearing; otherwise use private seeded ties. Rotate the escape compass one 45-degree notch per Step, never per advance. Wrapping uses shortest wrapped bearings and seam-crossing moves; bounded edges block outward moves.

Blocked waits

Pursuit distance 1–3 advances one square at a time. Each advance reads frozen occupancy; departing cells still block it. The first obstruction ends the turn, retaining partial progress. Blocked wait 0–16 counts extra complete waiting turns: zero permits escape on the next turn. An eligible blocked cell proposes one square in its displayed escape direction. Only unique claims to empty squares move; competing cardinal/angular claims all wait. No scans, swaps, tunneling, retries, death or retargeting. The rotating compass offers later attempts but cannot guarantee escape from a packed field.

Controls and inspection

Rule composer contains Blocked wait and Pursuit distance. Initial condition includes field and Loop seeds, density, all classic fields, size and topology. The saved targetSeed is the Loop seed. Inspector reports target, pursuer, both compass headings, fixed sense, waiting progress, proposals, conflicts and exact next turn. Follow target and Follow pursuer walk the relationship loop without adding a graph to the stage. All shared transport, presets and mobile controls remain.

Reproducibility

Version three replaces Reincarnation completely; versions one and two are rejected as different models. Complete presets and shares save both numeric rules plus field profile, pattern, density, field/target/angular seeds and topology. Default: 10% wrapped 160-square, seeds 3800038/3800039/3800040, wait zero, distance one, 16 Steps/second. All randomizers preserve angular seed, field size and wrapping, then reset and play. Loop randomization changes only the loop seed, keeping occupancy and escape traits. Reset restores the entire field, loop, headings, rotation senses and private streams. Saved defaults restore complete openings; explicit shared links override them.

Reproduce an opening

Download the example above, open the simulation, expand the controls, then use Share & reproduce → Import JSON. The example uses authored rules and a fixed seeded starting field; it is independent of the site’s editable default composition. Import starts paused at Step zero.

Share links and JSON reproduce the configured starting conditions, including hidden layers rebuilt by Reset. They do not save an evolved board, hand-painted cells, speed or display preferences. Determinism applies to the same rule version and Step sequence; real-time playback rates vary by device.

Large fields, dense populations and large interaction radii increase the work per Step. Start with a small field and radius, then increase them while paused. Read the configuration format and automated-access guide for compatibility details.