Life Simulator

Room to grow

Is the fixed tape length what makes complexity plateau? With a cap above the length a tape starts at, a head that steps off the end of an interaction claims a fresh byte instead of wrapping, so a tape lengthens through the programs' own copying and the 64-byte ceiling no longer bounds the dominant replicator by construction.

Substrate
soup
Status
finished
Epochs per run
20,000
Runs finished
240 / 240
Transition rate
42 of 240 finished runs flagged by the detector (18%), 13 confirmed by a replicator

Findings resting on this sweep: Does complexity keep rising? open

Transition epoch vs max tape len
64 128 256 512 0 5000 10000 15000 20000 Max tape len Transition epoch 64: emerged at epoch 5030 64: emerged at epoch 7000 64: emerged at epoch 6210 128: emerged at epoch 9510 128: emerged at epoch 4170 128: emerged at epoch 10420 128: emerged at epoch 17200 128: emerged at epoch 5880 256: emerged at epoch 8170 256: emerged at epoch 7690 256: emerged at epoch 16880 256: emerged at epoch 7620 512: emerged at epoch 7610 512: flagged at epoch 600, unconfirmed 512: flagged at epoch 600, unconfirmed 512: flagged at epoch 610, unconfirmed 512: flagged at epoch 600, unconfirmed 512: flagged at epoch 630, unconfirmed 512: flagged at epoch 670, unconfirmed 512: flagged at epoch 630, unconfirmed 512: flagged at epoch 650, unconfirmed 512: flagged at epoch 620, unconfirmed 512: flagged at epoch 620, unconfirmed 512: flagged at epoch 610, unconfirmed 512: flagged at epoch 620, unconfirmed 512: flagged at epoch 630, unconfirmed 512: flagged at epoch 620, unconfirmed 512: flagged at epoch 650, unconfirmed 512: flagged at epoch 670, unconfirmed 512: flagged at epoch 660, unconfirmed 512: flagged at epoch 690, unconfirmed 512: flagged at epoch 660, unconfirmed 512: flagged at epoch 650, unconfirmed 512: flagged at epoch 640, unconfirmed 512: flagged at epoch 620, unconfirmed 512: flagged at epoch 640, unconfirmed 512: flagged at epoch 700, unconfirmed 512: flagged at epoch 650, unconfirmed 512: flagged at epoch 660, unconfirmed 512: flagged at epoch 680, unconfirmed 512: flagged at epoch 600, unconfirmed 512: flagged at epoch 630, unconfirmed 64: no emergence in 20000 epochs (27 of 30 runs) 27 128: no emergence in 20000 epochs (85 of 90 runs) 85 256: no emergence in 20000 epochs (86 of 90 runs) 86 512: no emergence in 20000 epochs (29 of 30 runs) 29

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 max tape len
Max tape len n Flagged Emerged Median epoch IQR Censored
64 30 3/30 10% 3/30 10% 6,210 5,620–6,605 27
128 90 5/90 6% 5/90 6% 9,510 5,880–10,420 85
256 90 4/90 4% 4/90 4% 7,930 7,673–10,348 86
512 30 30/30 100% 1/30 3% 7,610 flagged 635 7,610 29

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 max tape len
0 5000 10000 15000 20000 0 0.2 0.4 0.6 0.8 1 Epoch P(no emergence) 64 — 3 of 30 emerged 128 — 5 of 90 emerged 256 — 4 of 90 emerged 512 — 1 of 30 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 max tape len
Max tape len Runs Events Run-epochs at risk Hazard per 104 epochs (95% CI) Persisted
64 30 3 558,240 0.0537 (0.0111–0.157) 3 of 3
128 90 5 1,747,180 0.0286 (0.00929–0.0668) 5 of 5
256 90 4 1,760,360 0.0227 (0.00619–0.0582) 4 of 4
512 30 1 587,610 0.017 (0.000431–0.0948) 0 of 30 30 relapsed
All arms 240 13 4,653,390 0.0279 (0.0149–0.0478) 12 of 42 30 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 max tape len
0 5000 10000 15000 20000 0 5000 10000 15000 20000 Epoch Distinct lineages 64 128 256 512
  • 64
  • 128
  • 256
  • 512
Share of the largest lineage vs epoch, per arm of max tape len
0 5000 10000 15000 20000 0 0.025 0.05 0.075 0.1 0.125 Epoch Share of the largest lineage 64 128 256 512
  • 64
  • 128
  • 256
  • 512
Compressed length of the dominant tape (bytes) vs epoch, per arm of max tape len
0 5000 10000 15000 20000 0 200 400 600 Epoch Compressed length of the dominant tape (bytes) 64 128 256 512
  • 64
  • 128
  • 256
  • 512
Instructions in the dominant tape vs epoch, per arm of max tape len
0 5000 10000 15000 20000 0 20 40 60 80 Epoch Instructions in the dominant tape 64 128 256 512
  • 64
  • 128
  • 256
  • 512
Detector against replicator census, per arm
64 128 256 512 0 10 20 30 Arm Runs 64 — flagged only: 1 of 30 sampled runs 64 — replicators only: 0 of 30 sampled runs 64 — both: 2 of 30 sampled runs 128 — flagged only: 2 of 90 sampled runs 128 — replicators only: 0 of 90 sampled runs 128 — both: 3 of 90 sampled runs 256 — flagged only: 0 of 90 sampled runs 256 — replicators only: 0 of 90 sampled runs 256 — both: 4 of 90 sampled runs 512 — flagged only: 29 of 30 sampled runs 512 — replicators only: 0 of 30 sampled runs 512 — both: 1 of 30 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
64 30 3 2 0 2 1
128 90 5 3 0 3 2
256 90 4 4 0 4 0
512 30 30 1 0 1 29
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
16 119 0/119 0 0 —
64 119 0/119 0 0 0
256 119 0/119 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)
64 30 30 3 3 2 2 0 1 ~7,000
128 90 90 5 5 5 5 0 0 ~10,000
256 90 90 4 4 4 4 0 0 ~8,000
512 30 30 30 1 1 1 0 0 ~10,000

Download oriented census (CSV)

Runs

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

Seed Max tape len Status Priority Epochs done Transition epoch Census
51 128 finished 12 20,000 — — Run
52 128 finished 12 20,000 — — Run
53 128 finished 12 20,000 — — Run
54 128 finished 12 20,000 — — Run
55 128 finished 12 20,000 17,200 confirmed — detector only Run
56 128 finished 12 20,000 — — Run
57 128 finished 12 20,000 — — Run
58 128 finished 12 20,000 — — Run
59 128 finished 12 20,000 — — Run
60 128 finished 12 20,000 — — Run
61 128 finished 12 20,000 — — Run
62 128 finished 12 20,000 — — Run
63 128 finished 12 20,000 — — Run
64 128 finished 12 20,000 — — Run
65 128 finished 12 20,000 — — Run
66 128 finished 12 20,000 — — Run
67 128 finished 12 20,000 — — Run
68 128 finished 12 20,000 — — Run
69 128 finished 12 20,000 — — Run
70 128 finished 12 20,000 — — Run