Life Simulator

Neighbourhood radius

Does spatial locality speed emergence and stabilise diversity afterwards?

Substrate
soup
Status
finished
Epochs per run
20,000
Runs finished
40 / 40
Transition rate
6 of 40 finished runs flagged by the detector (15%), 5 confirmed by a replicator

Findings resting on this sweep: Does spatial locality buy emergence? negative

Transition epoch vs radius
1 2 4 well-mixed 0 5000 10000 15000 20000 Radius Transition epoch 1: emerged at epoch 15560 2: emerged at epoch 12330 4: emerged at epoch 11250 well-mixed: emerged at epoch 11360 well-mixed: emerged at epoch 12400 4: flagged at epoch 5910, unconfirmed 1: no emergence in 20000 epochs (9 of 10 runs) 9 2: no emergence in 20000 epochs (9 of 10 runs) 9 4: no emergence in 20000 epochs (9 of 10 runs) 9 well-mixed: no emergence in 20000 epochs (8 of 10 runs) 8

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 10 1/10 10% 1/10 10% 15,560 15,560 9
2 10 1/10 10% 1/10 10% 12,330 12,330 9
4 10 2/10 20% 1/10 10% 11,250 flagged 8,580 11,250 9
well-mixed 10 2/10 20% 2/10 20% 11,880 11,620–12,140 8

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 — 1 of 10 emerged 2 — 1 of 10 emerged 4 — 1 of 10 emerged well-mixed — 2 of 10 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 10 1 195,560 0.0511 (0.00129–0.285) 1 of 1
2 10 1 192,330 0.052 (0.00132–0.29) 0 of 1 1 relapsed
4 10 1 191,250 0.0523 (0.00132–0.291) 2 of 2
well-mixed 10 2 183,760 0.109 (0.0132–0.393) 1 of 2 1 relapsed
All arms 40 5 762,900 0.0655 (0.0213–0.153) 4 of 6 2 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.

Detector against replicator census, per arm
1 2 4 well-mixed 0 1 2 Arm Runs 1 — flagged only: 1 of 10 sampled runs 1 — replicators only: 0 of 10 sampled runs 1 — both: 0 of 10 sampled runs 2 — flagged only: 1 of 10 sampled runs 2 — replicators only: 0 of 10 sampled runs 2 — both: 0 of 10 sampled runs 4 — flagged only: 0 of 10 sampled runs 4 — replicators only: 0 of 10 sampled runs 4 — both: 2 of 10 sampled runs well-mixed — flagged only: 0 of 10 sampled runs well-mixed — replicators only: 0 of 10 sampled runs well-mixed — both: 2 of 10 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 10 1 0 0 0 1
2 10 1 0 0 0 1
4 10 2 2 0 2 0
well-mixed 10 2 2 0 2 0
Replicator census vs top_k — stored worlds re-read at each window, the last column counting the runs whose census is empty at the locked top_k of 16 and non-empty here
top_k Worlds measured Runs with replicators Median count Max count Newly positive runs
16 40 0/40 0 0 —
64 40 0/40 0 0 0
256 40 0/40 0 0 0

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 10 10 1 1 1 1 0 0 ~17,000
2 10 10 1 1 0 0 0 1 —
4 10 10 2 1 2 2 1 0 ~9,000
well-mixed 10 10 2 2 2 0 0 0 ~13,000

Download oriented census (CSV)

Runs

Download CSV Download transition report (CSV) Download rescores (CSV)

Seed Radius Status Priority Epochs done Transition epoch Census
1 1 finished 0 20,000 — — Run
2 1 finished 0 20,000 — — Run
3 1 finished 0 20,000 — — Run
4 1 finished 0 20,000 — — Run
5 1 finished 0 20,000 — — Run
6 1 finished 0 20,000 — — Run
7 1 finished 0 20,000 — — Run
8 1 finished 0 20,000 — — Run
9 1 finished 8 20,000 15,560 confirmed — detector only Run
10 1 finished 8 20,000 — — Run
1 2 finished 8 20,000 — — Run
2 2 finished 8 20,000 — — Run
3 2 finished 8 20,000 — — Run
4 2 finished 8 20,000 — — Run
5 2 finished 8 20,000 — — Run
6 2 finished 8 20,000 — — Run
7 2 finished 8 20,000 — — Run
8 2 finished 8 20,000 — — Run
9 2 finished 8 20,000 — — Run
10 2 finished 8 20,000 12,330 confirmed — detector only Run