Life Simulator

Instruction cost

Does paying for computation select for efficient copiers? Every instruction a cell executes draws down an energy budget that refills each epoch, so an interaction halts once its cells have spent theirs and a copier that needs fewer steps finishes more often.

Substrate
soup
Status
finished
Epochs per run
20,000
Runs finished
120 / 120
Transition rate
8 of 120 finished runs flagged by the detector (7%), 7 confirmed by a replicator

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

Transition epoch vs energy per epoch
0 2048 8192 32768 0 5000 10000 15000 20000 Energy per epoch Transition epoch 0: emerged at epoch 6210 0: emerged at epoch 5030 0: emerged at epoch 7000 32768: emerged at epoch 8620 32768: emerged at epoch 17310 8192: emerged at epoch 12900 8192: emerged at epoch 890 32768: flagged at epoch 5710, unconfirmed 0: no emergence in 20000 epochs (27 of 30 runs) 27 32768: no emergence in 20000 epochs (28 of 30 runs) 28 8192: no emergence in 20000 epochs (28 of 30 runs) 28 2048: no emergence in 20000 epochs (30 of 30 runs) 30

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 energy per epoch
Energy per epoch n Flagged Emerged Median epoch IQR Censored
0 30 3/30 10% 3/30 10% 6,210 5,620–6,605 27
32768 30 3/30 10% 2/30 7% 12,965 flagged 8,620 10,793–15,138 28
8192 30 2/30 7% 2/30 7% 6,895 3,893–9,898 28
2048 30 0/30 0% 0/30 0% — — 30

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 energy per epoch
0 5000 10000 15000 20000 0 0.2 0.4 0.6 0.8 1 Epoch P(no emergence) 0 — 3 of 30 emerged 32768 — 2 of 30 emerged 8192 — 2 of 30 emerged 2048 — 0 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 energy per epoch
Energy per epoch Runs Events Run-epochs at risk Hazard per 104 epochs (95% CI) Persisted
0 30 3 558,240 0.0537 (0.0111–0.157) 3 of 3
32768 30 2 585,930 0.0341 (0.00413–0.123) 2 of 3 1 relapsed
8192 30 2 573,790 0.0349 (0.00422–0.126) 1 of 2 1 relapsed
2048 30 0 600,000 0 (0–0.0615) —
All arms 120 7 2,317,960 0.0302 (0.0121–0.0622) 6 of 8 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.

Distinct lineages vs epoch, per arm of energy per epoch
0 5000 10000 15000 20000 0 5000 10000 15000 20000 Epoch Distinct lineages 0 32768 8192 2048
  • 0
  • 32768
  • 8192
  • 2048
Share of the largest lineage vs epoch, per arm of energy per epoch
0 5000 10000 15000 20000 0 0.025 0.05 0.075 0.1 0.125 Epoch Share of the largest lineage 0 32768 8192 2048
  • 0
  • 32768
  • 8192
  • 2048
Compressed length of the dominant tape (bytes) vs epoch, per arm of energy per epoch
0 5000 10000 15000 20000 0 20 40 60 80 Epoch Compressed length of the dominant tape (bytes) 0 32768 8192
  • 0
  • 32768
  • 8192
Instructions in the dominant tape vs epoch, per arm of energy per epoch
0 5000 10000 15000 20000 0 10 20 30 40 Epoch Instructions in the dominant tape 0 32768 8192
  • 0
  • 32768
  • 8192
Detector against replicator census, per arm
0 32768 8192 2048 0 1 2 Arm Runs 0 — flagged only: 1 of 30 sampled runs 0 — replicators only: 0 of 30 sampled runs 0 — both: 2 of 30 sampled runs 32768 — flagged only: 2 of 30 sampled runs 32768 — replicators only: 0 of 30 sampled runs 32768 — both: 1 of 30 sampled runs 8192 — flagged only: 1 of 30 sampled runs 8192 — replicators only: 0 of 30 sampled runs 8192 — both: 1 of 30 sampled runs 2048 — flagged only: 0 of 30 sampled runs 2048 — replicators only: 0 of 30 sampled runs 2048 — both: 0 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
0 30 3 2 2 1
32768 30 3 1 1 2
8192 30 2 1 1 1
2048 30 0 0 0 0
Does complexity keep rising, per arm — the median of the last decile of each emerged run's post-crossing samples against the median of its first decile. An arm keeps rising where at least half its measured runs raise dominant_instruction_count by 20% or more without their conserved core falling, and plateaus where at least half sit within 10% of where they started. An arm clearing both bars reads mixed and one clearing neither reads neither. A run is measured on its instruction count, and its conserved core is compared in bytes, so a core that reads zero at both ends counts as a core that did not fall — the post-hoc amendment of 2026-09-21; the pre-registered rule dropped those runs as unmeasured, and the pre-registered unmeasured column counts, per arm, the measured runs it dropped. A run carrying no conserved core at all over the span is unmeasured. dominant_compressed_len is printed beside them and decides nothing: it saturates at the tape cap plus zlib's envelope, and distinct_lineages is the secondary reading of sweep 10, where an arms race shows as a late-run lineage count above the control's at the same cap. An arm reads on two measured runs, or on a blank block of ten; a steal arm whose steal_rate never left zero reads as theft that never evolved, not as theft that does not help, and one never sampled on that observable reads unmeasured
Arm Emerged Measured Pre-registered unmeasured Instructions Conserved core Compressed length Distinct lineages Rising Plateau Peak steal_rate Reading
2048 0 / 30 0 0 — — — — 0 / 0 0 / 0 — barren

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)
0 30 30 3 3 2 2 0 1 ~7,000
32768 30 30 3 2 2 2 0 0 ~9,000
8192 30 30 2 2 1 1 0 1 ~13,000
2048 30 30 0 0 0 0 0 0 —

Download oriented census (CSV)

Runs

Download CSV Download transition report (CSV)

Seed Energy per epoch Status Priority Epochs done Transition epoch Census
11 2048 finished 25 20,000 — — Run
12 2048 finished 25 20,000 — — Run
13 2048 finished 25 20,000 — — Run
14 2048 finished 25 20,000 — — Run
15 2048 finished 25 20,000 — — Run
16 2048 finished 25 20,000 — — Run
17 2048 finished 25 20,000 — — Run
18 2048 finished 25 20,000 — — Run
19 2048 finished 25 20,000 — — Run
20 2048 finished 25 20,000 — — Run
21 2048 finished 25 20,000 — — Run
22 2048 finished 25 20,000 — — Run
23 2048 finished 25 20,000 — — Run
24 2048 finished 25 20,000 — — Run
25 2048 finished 25 20,000 — — Run
26 2048 finished 25 20,000 — — Run
27 2048 finished 25 20,000 — — Run
28 2048 finished 25 20,000 — — Run
29 2048 finished 25 20,000 — — Run
30 2048 finished 25 20,000 — — Run