Experiments

The Substrate Ladder

Seven substrate versions, each adding one capability, tracking whether evolution selects for it. The goal: build a substrate worth measuring.

V11: Lenia CA Evolution

Period: 2025-2026. Substrate: Continuous cellular automaton (Lenia) with evolutionary dynamics.

Versions: V11.0 (naive), V11.1 (homogeneous evolution), V11.2 (heterogeneous chemistry), V11.5 (hierarchical coupling), V11.7 (curriculum training).

Version	$\Delta\intinfo$ (drought)	Key lesson
V11.0 (naive)	-6.2%	Decomposition baseline
V11.1 (homogeneous evolution)	-6.0%	Selection alone insufficient
V11.2 (heterogeneous chemistry)	-3.8%	+2.1pp shift from diverse viability manifolds
V11.7 (curriculum training)	+1.2 to +2.7pp generalization	Only intervention improving novel-stress response

Key finding: Training regime matters more than substrate complexity. The locality ceiling: convolutional physics cannot produce active self-maintenance under severe threat. The Yerkes-Dodson pattern (mild stress increases integration, severe stress destroys it) appeared in every condition — the most robust empirical finding across the entire program.

Source code

v11_substrate.py — Lenia substrate with FFT convolution
v11_evolution.py — Evolution loop with curriculum stress
v11_run.py — CLI runner for all V11 variants
v11_affect.py — Affect measurement (Phi, robustness)

V12: Attention-Based Lenia

Addition: State-dependent interaction topology (evolvable attention kernels).

Result: $\intinfo$ increase in 42% of cycles (vs 3% for convolution). +2.0pp shift — largest single-intervention effect. But robustness stabilizes near 1.0.

Implication: Attention is necessary but not sufficient. The system reaches the integration threshold without crossing it.

Source code

v12_substrate_attention.py — Attention kernel implementation
v12_evolution.py — Evolution loop
v12_run.py — CLI runner

V13: Content-Based Coupling

Substrate: FFT convolution + content-similarity modulation. Cells couple more strongly with cells sharing state-features.

K_i(j) = K_{\text{base}}(|i-j|) \cdot \sigma\!\bigl(\langle h(s_i),\, h(s_j) \rangle - \tau\bigr)

Three seeds, 30 cycles each ( $C{=}16$ , $N{=}128$ ). Mean robustness 0.923, peak 1.052 at population bottleneck. This became the foundation substrate for all measurement experiments (Experiments 0-12).

V13 evolution trajectory showing integration, robustness, population, and parameter drift — **V13 evolution trajectory (seed 42).** Four panels: (top-left) mean Φ under baseline and stress conditions — note the collapse to ~0 during severe bottleneck at cycle 10; (top-right) stress robustness with the proportion of patterns showing Φ increase; (bottom-left) population dynamics — the pink bands mark drought cycles with 60–100% mortality; (bottom-right) content-coupling parameters τ (similarity threshold) and β (gate steepness) drifting under selection.

V13 cross-seed robustness trajectories compared to historical baselines — **Cross-seed robustness trajectories.** Left: individual seed trajectories (3 seeds, 30 cycles each) fluctuating around 0.90–0.95. Right: mean trajectory with ±1 SD band. Dashed lines show V11.0 baseline (−6.2%) and V11.2 heterogeneous chemistry (−3.8%) for comparison. V13 content coupling improves mean robustness but does not break the 1.0 threshold reliably.

Population size vs integration robustness showing near-zero correlation — **Population size vs integration robustness (r = −0.061).** Each dot is one cycle from one seed. The flat trend confirms that integration robustness is a per-pattern property, not a collective emergent effect. Small populations (bottleneck survivors) occasionally show robustness above 1.0, but population size itself has no predictive power.

V13 cross-seed summary table — **Cross-seed summary.** All 3 seeds survive 30 cycles. Mean robustness 0.923, with ~30% of cycles showing Φ increase under stress.

Source code

v13_substrate.py — Content-coupling substrate
v13_evolution.py — Evolution loop with curriculum
v13_gpu_run.py — GPU runner (Lambda Labs)
v13_aggregate.py — Cross-seed aggregation

V14: Chemotactic Lenia

Addition: Motor channels enabling directed foraging. Velocity field from resource gradients gated by the last two of $C{=}16$ channels.

Result: Patterns move 3.5-5.6 pixels/cycle toward resources. Motor sensitivity evolves. Robustness comparable to V13 (~0.90-0.95).

Source code

v14_substrate.py — Chemotaxis implementation
v14_evolution.py — Evolution loop
v14_gpu_run.py — GPU runner

V15: Temporal Memory

Addition: Two exponential-moving-average memory channels storing slow statistics of the pattern's history. Oscillating resource patches reward anticipation.

Result: Evolution selected for longer memory in 2/3 seeds — memory decay constants decreased 6x. Under bottleneck pressure, $\intinfo$ stress response doubled (0.231 to 0.434). Peak robustness 1.070.

Temporal integration is fitness-relevant. This was the only substrate addition evolution consistently selected for. Memory channels help prediction (~12x vs V13) but don't break the sensory-motor wall.

Source code

v15_substrate.py — EMA memory channels
v15_evolution.py — Evolution with memory tracking
v15_gpu_run.py — GPU runner
v15_experiments.py — Measurement re-runs on V15

V16: Hebbian Plasticity

Negative result. Mean robustness dropped to 0.892 — lowest of all substrates. Zero cycles exceeded 1.0.

Addition: Local Hebbian learning rules allowing each spatial location to modify its coupling structure in response to experience.

Lesson: Simple learning rules are too blunt. The extra degrees of freedom overwhelm the selection signal. Plasticity added noise faster than selection could filter it.

V13-V16 substrate comparison: robustness trajectories and aggregate comparison — **V13–V16 substrate evolution comparison.** Top-left: per-cycle robustness trajectories across all seeds (V13 green, V15 black, V16 red). V16 (Hebbian plasticity) consistently tracks lowest. Top-right: V16 learning rate evolution — highly variable, not converging. Bottom-left: V16 coupling spatial variance collapses to zero (homogenization, not differentiation). Bottom-right: aggregate comparison confirms V13 content coupling (0.923) > V15 temporal memory (0.907) > V16 plasticity (0.892).

Source code

v16_substrate.py — Hebbian plasticity implementation
v16_evolution.py — Evolution loop
v16_gpu_run.py — GPU runner

V17: Quorum Signaling

Addition: Two diffusible signal fields mediating inter-pattern coordination (bacterial quorum sensing analog).

Result: Produced the highest-ever single-cycle robustness (1.125) at population of 2. But 2/3 seeds evolved to suppress signaling entirely.

Lesson: Signaling is costly in large populations, beneficial only at extreme bottlenecks.

Source code

v17_substrate.py — Quorum sensing fields
v17_evolution.py — Evolution loop
v17_gpu_run.py — GPU runner

V18: Boundary-Dependent Lenia

Addition: Insulation field via iterated erosion + sigmoid creating genuine boundary/interior distinction. External FFT signals gated by $(1 - \text{insulation})$ , internal short-range recurrence gated by $\text{insulation}$ .

Three seeds, 30 cycles. Mean robustness 0.969 — highest of any substrate. Peak 1.651 (seed 42). 33% of cycles show $\intinfo$ increase under stress.

Surprise: internal_gain evolved down in all three seeds (1.0 to ~0.6). Evolution preferred permeable membranes over insulated cores. External sensing was more valuable than internal rumination.

Verdict: Best engineering result (highest robustness) but not the theoretical goal (breaking the coupling wall).

V18 internal gain, boundary width, and insulation field evolution — **V18 parameter evolution.** Left: internal gain evolves DOWN in all 3 seeds (starting ~1.0–2.5, converging below 1.0). Center: boundary width evolves UP (thicker membranes). Right: mean insulation field fluctuates. The convergent decrease in internal gain is the surprise — evolution consistently prefers permeable membranes over insulated cores. External sensing more valuable than internal rumination.

V18 membrane evolution: early vs late cycle comparison for seed 42 — **Membrane evolution, seed 42.** Top row: cycle 5 (early). Bottom row: cycle 20 (late). Left: pattern activity. Center: membrane field — at cycle 5 the membrane is tight (gain=1.09, bw=1.31); by cycle 20 it has loosened (gain=0.52, bw=0.12). Right: signal dominance — blue = external, red = internal. The shift toward red in specific regions shows that evolved patterns route information through the membrane rather than sealing it off.

V18 boundary-dependent Lenia four-panel snapshot — **V18 snapshot (seed 42, cycle 20).** Top-left: pattern activity across 16 channels. Top-right: insulation field — the evolved membrane with interior (orange, 46.4%) and boundary (pink, 17.5%) regions. Bottom-left: signal dominance showing where internal (red) vs external (blue) signals dominate processing. Bottom-right: resource field with pattern boundaries overlaid. The membrane creates genuine spatial compartmentalization without fully insulating the interior.

Source code

v18_substrate.py — Boundary-dependent dynamics
v18_evolution.py — Evolution loop
v18_gpu_run.py — GPU runner
v18_experiments.py — Measurement re-runs on V18

Cross-Substrate Summary

The Substrate Ladder: mean robustness across V11-V16 — **The Substrate Ladder.** Mean robustness (Φ_stress / Φ_base) across substrate versions V11.0–V16. Stars mark conditions where robustness exceeded 1.0. More mechanisms ≠ better results: V15 (memory + movement) outperforms V16 (+ plasticity). V16 is the lowest — Hebbian plasticity adds noise faster than selection can filter it.

Version	Mean Robustness	Max Robustness	> 1.0 Cycles	Verdict
V13 (content coupling)	0.923	1.052	3/90	Foundation substrate
V14 (+ chemotaxis)	~0.91	~0.95	~1/90	Motion evolves
V15 (+ memory)	0.907	1.070	3/90	Best dynamics
V16 (+ plasticity)	0.892	0.974	0/90	Negative
V17 (+ signaling)	0.892	1.125	1/90	Suppressed
V18 (boundary)	0.969	1.651	~10/90	Best robustness