Life Simulator

Locality and emergence

Does emergence peak at an intermediate reach? The lineage-diversity sweep saw radius 4 emerge four times as often as radius 1 and five times as often as the well-mixed world. Its seven reaches, on fresh worlds, read on how often a world crosses at all.

Substrate
soup
Status
finished
Epochs per run
20,000
Runs finished
630 / 630
Transition rate
94 of 630 finished runs flagged by the detector (15%), 70 confirmed by a replicator

Findings resting on this sweep: Emergence peaks at an intermediate reach published

Transition epoch vs radius
1 3 6 well-mixed 0 5000 10000 15000 20000 Radius Transition epoch 1: emerged at epoch 17990 1: emerged at epoch 10520 1: emerged at epoch 5470 1: emerged at epoch 13000 1: emerged at epoch 10480 2: emerged at epoch 8830 2: emerged at epoch 8440 2: emerged at epoch 9830 2: emerged at epoch 3350 2: emerged at epoch 2500 2: emerged at epoch 3230 2: emerged at epoch 10030 2: emerged at epoch 16650 2: emerged at epoch 12190 2: emerged at epoch 8390 3: emerged at epoch 6480 3: emerged at epoch 7580 3: emerged at epoch 1590 3: emerged at epoch 11910 3: emerged at epoch 14800 3: emerged at epoch 18540 3: emerged at epoch 5690 3: emerged at epoch 15060 3: emerged at epoch 17300 3: emerged at epoch 8960 3: emerged at epoch 11150 4: emerged at epoch 19540 4: emerged at epoch 10520 4: emerged at epoch 3690 4: emerged at epoch 10550 4: emerged at epoch 8300 4: emerged at epoch 7590 4: emerged at epoch 18450 4: emerged at epoch 1030 4: emerged at epoch 12660 4: emerged at epoch 11890 4: emerged at epoch 4140 4: emerged at epoch 8530 4: emerged at epoch 19330 4: emerged at epoch 12560 4: emerged at epoch 13910 4: emerged at epoch 7200 4: emerged at epoch 6710 4: emerged at epoch 16780 4: emerged at epoch 17920 4: emerged at epoch 7600 6: emerged at epoch 14260 6: emerged at epoch 7690 6: emerged at epoch 4970 6: emerged at epoch 11470 6: emerged at epoch 4360 6: emerged at epoch 5400 6: emerged at epoch 17980 6: emerged at epoch 7960 6: emerged at epoch 13510 6: emerged at epoch 5130 6: emerged at epoch 4870 8: emerged at epoch 3060 8: emerged at epoch 1160 8: emerged at epoch 1590 8: emerged at epoch 5940 8: emerged at epoch 9320 well-mixed: emerged at epoch 9970 well-mixed: emerged at epoch 19910 well-mixed: emerged at epoch 18730 well-mixed: emerged at epoch 12980 well-mixed: emerged at epoch 7410 well-mixed: emerged at epoch 19650 well-mixed: emerged at epoch 13540 well-mixed: emerged at epoch 3000 2: flagged at epoch 12120, unconfirmed 2: flagged at epoch 7700, unconfirmed 3: flagged at epoch 4110, unconfirmed 3: flagged at epoch 11920, unconfirmed 3: flagged at epoch 11770, unconfirmed 4: flagged at epoch 9400, unconfirmed 4: flagged at epoch 17130, unconfirmed 4: flagged at epoch 16250, unconfirmed 4: flagged at epoch 19150, unconfirmed 6: flagged at epoch 10320, unconfirmed 6: flagged at epoch 19640, unconfirmed 6: flagged at epoch 7670, unconfirmed 6: flagged at epoch 15720, unconfirmed 6: flagged at epoch 18810, unconfirmed 6: flagged at epoch 16100, unconfirmed 6: flagged at epoch 15890, unconfirmed 8: flagged at epoch 450, unconfirmed 8: flagged at epoch 13860, unconfirmed 8: flagged at epoch 18630, unconfirmed 8: flagged at epoch 11170, unconfirmed 8: flagged at epoch 50, unconfirmed 8: flagged at epoch 2220, unconfirmed well-mixed: flagged at epoch 5590, unconfirmed well-mixed: flagged at epoch 11210, unconfirmed 1: no emergence in 20000 epochs (85 of 90 runs) 85 2: no emergence in 20000 epochs (80 of 90 runs) 80 3: no emergence in 20000 epochs (79 of 90 runs) 79 4: no emergence in 20000 epochs (70 of 90 runs) 70 6: no emergence in 20000 epochs (79 of 90 runs) 79 8: no emergence in 20000 epochs (85 of 90 runs) 85 well-mixed: no emergence in 20000 epochs (82 of 90 runs) 82

Filled dots are runs a replicator confirmed emerged in; the line joins the median per value. Hollow dots are crossings the detector flagged that nothing confirmed. Hollow markers at the top count the runs with no emergence in 20000 epochs, the flagged-only ones among them.

Arms of radius
Radius n Flagged Emerged Median epoch IQR Censored
1 90 5/90 6% 5/90 6% 10,520 10,480–13,000 85
2 90 12/90 13% 10/90 11% 8,635 flagged 8,635 4,610–9,980 80
3 90 14/90 16% 11/90 12% 11,150 flagged 11,460 7,030–14,930 79
4 90 24/90 27% 20/90 22% 10,535 flagged 11,220 7,493–14,628 70
6 90 18/90 20% 11/90 12% 7,690 flagged 10,895 5,050–12,490 79
8 90 11/90 12% 5/90 6% 3,060 flagged 3,060 1,590–5,940 85
well-mixed 90 10/90 11% 8/90 9% 13,260 flagged 12,095 9,330–18,960 82

Flagged counts the crossings the transition detector reported; emerged counts the ones the replicator census or the copy rate confirmed. The median epoch and the IQR are of the confirmed emergences, the flagged median beside them in grey; a flagged crossing nothing confirmed is censored like a run that was never flagged.

Time to emergence vs radius
0 5000 10000 15000 20000 0 0.2 0.4 0.6 0.8 1 Epoch P(no emergence) 1 — 5 of 90 emerged 2 — 10 of 90 emerged 3 — 11 of 90 emerged 4 — 20 of 90 emerged 6 — 11 of 90 emerged 8 — 5 of 90 emerged well-mixed — 8 of 90 emerged

Each line is the estimated share of runs in an arm with no self-replicator yet at that epoch. A run that never emerged is censored where it was last watched, so it holds the line up only for as long as it was actually observed.

Emergence hazard per arm of radius
Radius Runs Events Run-epochs at risk Hazard per 104 epochs (95% CI) Persisted
1 90 5 1,757,460 0.0285 (0.00924–0.0664) 3 of 5 2 relapsed
2 90 10 1,683,440 0.0594 (0.0285–0.109) 7 of 12 5 relapsed
3 90 11 1,699,060 0.0647 (0.0323–0.116) 8 of 14 6 relapsed
4 90 20 1,618,900 0.124 (0.0755–0.191) 14 of 24 10 relapsed
6 90 11 1,677,600 0.0656 (0.0327–0.117) 9 of 18 9 relapsed
8 90 5 1,721,070 0.0291 (0.00943–0.0678) 8 of 11 3 relapsed
well-mixed 90 8 1,745,190 0.0458 (0.0198–0.0903) 5 of 10 5 relapsed
All arms 630 70 11,902,720 0.0588 (0.0458–0.0743) 54 of 94 40 relapsed

Persisted counts the emergences whose world was still in the transitioned state at its last sample; the rest climbed back out of it and are counted as relapses.

Distinct lineages vs epoch, per arm of radius
0 5000 10000 15000 20000 0 5000 10000 15000 20000 Epoch Distinct lineages 1 2 3 4 6 8 well-mixed
  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • well-mixed
Share of the largest lineage vs epoch, per arm of radius
0 5000 10000 15000 20000 0 0.05 0.1 0.15 0.2 0.25 Epoch Share of the largest lineage 1 2 3 4 6 8 well-mixed
  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • well-mixed
Compressed length of the dominant tape (bytes) vs epoch, per arm of radius
0 5000 10000 15000 20000 0 20 40 60 80 Epoch Compressed length of the dominant tape (bytes) 1 2 3 4 6 8 well-mixed
  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • well-mixed
Instructions in the dominant tape vs epoch, per arm of radius
0 5000 10000 15000 20000 0 10 20 30 40 50 Epoch Instructions in the dominant tape 1 2 3 4 6 8 well-mixed
  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • well-mixed
Compressed length of the largest lineage's tape (bytes) vs epoch, per arm of radius
0 5000 10000 15000 20000 0 20 40 60 80 Epoch Compressed length of the largest lineage's tape (bytes) 1 2 3 4 6 8 well-mixed
  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • well-mixed
Instructions in the largest lineage's tape vs epoch, per arm of radius
0 5000 10000 15000 20000 0 5 10 15 20 Epoch Instructions in the largest lineage's tape 1 2 3 4 6 8 well-mixed
  • 1
  • 2
  • 3
  • 4
  • 6
  • 8
  • well-mixed
Detector against replicator census, per arm
1 3 6 well-mixed 0 5 10 15 Arm Runs 1 — flagged only: 3 of 90 sampled runs 1 — replicators only: 1 of 90 sampled runs 1 — both: 2 of 90 sampled runs 2 — flagged only: 8 of 90 sampled runs 2 — replicators only: 1 of 90 sampled runs 2 — both: 4 of 90 sampled runs 3 — flagged only: 6 of 90 sampled runs 3 — replicators only: 1 of 90 sampled runs 3 — both: 8 of 90 sampled runs 4 — flagged only: 13 of 90 sampled runs 4 — replicators only: 2 of 90 sampled runs 4 — both: 11 of 90 sampled runs 6 — flagged only: 11 of 90 sampled runs 6 — replicators only: 0 of 90 sampled runs 6 — both: 7 of 90 sampled runs 8 — flagged only: 7 of 90 sampled runs 8 — replicators only: 0 of 90 sampled runs 8 — both: 4 of 90 sampled runs well-mixed — flagged only: 7 of 90 sampled runs well-mixed — replicators only: 0 of 90 sampled runs well-mixed — both: 3 of 90 sampled runs
  • Flagged only
  • Replicators only
  • Both

The two outer bars of an arm are its disagreements: runs the detector flagged with no replicator ever counted, and runs that counted one without being flagged.

Detector against replicator census, per arm — flagged runs held compress_ratio below 0.6, replicating runs counted at least one replicator at the locked top_k 16; the wider column re-reads the stored worlds of the same runs at top_k 64 and is blank for an arm no corpus pass has measured
Arm Sampled runs Flagged Replicators Replicators at top_k 64 Both Either but not both
1 90 5 3 2 4
2 90 12 5 4 9
3 90 14 9 8 7
4 90 24 13 11 15
6 90 18 7 7 11
8 90 11 4 4 7
well-mixed 90 10 3 3 7

The pre-registered reading final

Every run of the sweep has finished. A run emerged where it has a confirmed emergence epoch and reads replicator_share of at least 50% at some sample from it on, as in the lineage-diversity sweep.

Runs per arm, counted so far. The rate is emerged over finished.
Arm Runs Finished Emerged Rate
radius 1 90 90 4 4%
radius 2 90 90 9 10%
radius 3 90 90 7 8%
radius 4 90 90 16 18%
radius 6 90 90 6 7%
radius 8 90 90 3 3%
well-mixed 90 90 3 3%

H-peak

Radius 4 emerges more often than radius 1 and than the well-mixed world: shown

Two one-sided Fisher exact tests, Holm-corrected at family level 0.05: radius 4 16/90 against radius 1 4/90: one-sided Fisher p = 0.00385, Holm 0.00385; radius 4 16/90 against well-mixed 3/90: one-sided Fisher p = 0.00135, Holm 0.00269.

H-shape

Across the finite radii, emergence peaks at an intermediate reach: shown

A logistic regression of emergence on radius and radius² over the finished runs of radius 1, 2, 3, 4, 6, and 8, read where the radius² coefficient is negative at two-sided Wald p < 0.05 and the fitted peak lies between radius 2 and 6, with 2 of those radii on each side of it. The radius² coefficient is -0.114, Wald p = 0.00407, and the fitted peak is at radius 4.1. Well-mixed is not a distance and is left out of the fit: it emerged 3 of 90.

Replicators by the orientation-aware detector

The detector reads a random sample of 256 cells of a stored world and runs each cell's tape down a chain of 5 runs against fresh noise, each copy carried into the next run. After the last run the first half holds the fourth copy, back in the tape's own orientation even for a tape that writes its reverse; the cell passes where 3/4 of its positions match the original, each position read by the majority of 5 trials. The locked census counts only same-orientation copies among the 16 commonest tapes, so it reads zero in worlds of reverse copiers. Only the worlds a run kept are read — the first and the last, one about every 1000 epochs and the one nearest the transition — so every run is read at the same cadence, and a first replicator epoch here is no finer than that. Live samples are not used. A run is measured once the corpus pass has read every world it kept; until then it counts in none of the census columns, and the pass is re-run as runs finish. A world holds replicators where at least 50% of its sampled cells pass. This is a companion reading: it relocks neither the census nor the emergence rule (#245).

Detector, emergence rule and orientation-aware census, per arm, over finished runs — the census columns count measured runs only
Arm Finished runs Measured Flagged Emerged Replicator worlds Held to the end Replicators, not emerged Emerged, no replicators Median first replicator epoch (coarse)
1 90 90 5 5 3 3 0 2 ~11,000
2 90 90 12 10 8 6 0 2 ~10,000
3 90 90 14 11 8 8 1 4 ~9,000
4 90 90 24 20 13 10 0 7 ~12,000
6 90 90 18 11 10 8 5 6 ~17,000
8 90 90 11 5 7 4 4 2 ~6,000
well-mixed 90 90 10 8 2 2 0 6 ~19,000

Download oriented census (CSV)

Runs

Download CSV Download transition report (CSV)

Seed Radius Status Priority Epochs done Transition epoch Census
151 6 finished 30 20,000 — — Run
152 6 finished 30 20,000 — — Run
153 6 finished 30 20,000 — — Run
154 6 finished 30 20,000 — — Run
155 6 finished 30 20,000 — — Run
156 6 finished 30 20,000 4,360 confirmed — detector only Run
157 6 finished 30 20,000 — — Run
158 6 finished 30 20,000 10,320 flagged — detector only Run
159 6 finished 30 20,000 — — Run
160 6 finished 30 20,000 — — Run
161 6 finished 30 20,000 — — Run
162 6 finished 30 20,000 — — Run
163 6 finished 30 20,000 18,810 flagged 360 Run
164 6 finished 30 20,000 17,980 confirmed 177 Run
165 6 finished 30 20,000 19,640 flagged — detector only Run
166 6 finished 30 20,000 — — Run
167 6 finished 30 20,000 — — Run
168 6 finished 30 20,000 — — Run
169 6 finished 30 20,000 7,670 flagged — detector only Run
170 6 finished 30 20,000 — — Run