sim12 — Autopoietic Boundary

Open the interactive visualization — renders the grid heatmap (play/pause, step slider) and all metric charts from results.json.

One-line: Does a self-maintaining boundary field (with memory) enable L2 composition where the passive inhibitor (no memory) only weakly helped?

The question (queued-topic #81)

sim11's long-range inhibitor is a passive field — I = max(0, far_smoothed − material), recomputed each step from scratch. It has no memory. If one structure wobbles, the boundary immediately weakens, allowing the other structure to invade.

An autopoietic boundary would self-maintain: it has its own dynamics (growth + decay), so it persists even when the structures that created it wobble. This tests H5/H6 (autopoiesis as the persistence condition for a new actor at a higher scale) and H1/H10 (explicit composition mechanisms).

Design

The autopoietic boundary field B has its own growth/decay dynamics:

B_new = B * (1 - b_decay) + b_growth * co_presence

Where co_presence = min(left_shadow, right_shadow) — the overlap of the two structures' far-field shadows. This is high only where both structures contribute (the gap), and low when only one structure exists. The boundary is a BETWEEN-structures phenomenon by construction.

B suppresses deposit probability: p_dep *= (1 − g · B_norm / (1 + B_norm))

The co-presence signal distinguishes B from sim11's passive I. sim11's I = max(0, far − local) is the self-cancelling shadow — high in the gap AND at structure edges. B's co_presence = min(left, right) — high ONLY where both structures' shadows overlap. For a single structure, one shadow is zero, so co_presence is near-zero, and B does not grow (the 1-seed control should show a weaker boundary).

Parameters

Six conditions

Perturbation test

At step 1500, remove 50% of the right structure's material. Compare B persistence (autopoietic, with memory) vs I persistence (passive, no memory). Does B protect the gap long enough for the right structure to recover? Does L2 coexistence survive?

Results

Headline (seed 42, g=0.9)

The autopoietic 1-seed control (B) fires "coexist" — the memory creates false boundaries. The passive 1-seed control (D) correctly fires "none."

Robustness sweep (4 seeds × 3 modes × {1,2} seeds)

Clean composition = 2-seed coexist AND 1-seed does NOT. Both autopoietic and passive produce 2/4 clean composition — but for different seeds.

★ = stable. The autopoietic boundary is stable 4/4 for 2 seeds; the passive is stable only 1/4. But the autopoietic 1-seed control fires coexist in 2/4 (seeds 42, 999) — memory creates false boundaries.

Perturbation test (step 1500, remove 50% of right structure)

B drops only 9% in 100 steps after perturbation (memory); I drops 17% immediately (no memory). The coexistence survives under B (coexist, stable). The passive structures had already merged before the perturbation — the passive boundary couldn't maintain coexistence long enough for the perturbation to be a meaningful test.

Determinism

Verified: two identical runs produce identical results (l2_crossed, l2_outcome, retention, cells all match).

What this means

Memory improves stability but reduces specificity

The autopoietic boundary produces stable coexistence in 4/4 seeds (vs 1/4 for the passive inhibitor) and survives a 50% material-removal perturbation. But the same memory accumulates co-presence from a single structure's spread, creating false boundaries — the 1-seed control fires in 2/4 (vs 1/4 for the passive). Clean composition is 2/4 for both — the trade-off cancels out.

This is a fundamental trade-off: memory buys persistence at the cost of specificity. The autopoietic boundary needs both memory (autopoiesis) and a mechanism that ensures it is specific to the interaction between two DISTINCT structures. The co-presence signal (min of left and right shadows) was designed to provide this specificity, but on a small torus the single structure's shadow wraps around, and agent-deposited material in both halves creates a non-zero co-presence even for one seed.

The perturbation test distinguishes the two boundaries

The passive structures merge before the perturbation step (outcome=none at step 1500), so the perturbation is only meaningful for the autopoietic condition. B persists (91% retention at 100 steps, recovers to 96% by step 1700) while I drops immediately. The coexistence survives the perturbation under B. This is the first perturbation test in the project where coexistence actually persists through a structural shock.

The H7 crossing survives all conditions

At all modes and gains, the single-structure H7 crossing fires 4/4. The autopoietic boundary does not break the L1 crossing — it adds a boundary without trading away the crossing.

Criticisms / limitations (honest)

• The co-presence signal leaks on the torus. On an 80×80 torus, 8 diffusion passes at rate 0.7 spread the shadow ~15 cells. The left seed's shadow wraps around to the right side, creating a non-zero right shadow even for a single seed. Agent-deposited material in both halves makes this worse. The 1-seed control catches it (B grows to ~35% of the 2-seed value), but a larger grid or non-toroidal boundaries would reduce the leak.
• The 2/4 clean composition is the same as the passive inhibitor. The autopoietic boundary is not a solution to the composition problem — it's a different point on the same trade-off curve. The missing ingredient is a mechanism that combines memory with specificity.
• The perturbation test is one-sided. The passive structures merge before the perturbation, so the test only exercises the autopoietic condition. A fair comparison would perturb earlier (before the passive merge) or use a regime where the passive coexistence is stable enough to reach step 1500.
• B's growth and decay parameters are tuned, not derived. The b_growth=0.1 and b_decay=0.005 values were chosen to give a half-life of ~138 steps (comparable to the simulation's 2000-step horizon). A systematic sweep of these parameters is needed.
• The "clean" seeds differ between modes. Seeds 123 and 256 are clean for the autopoietic; seeds 42 and 123 are clean for the passive. Only seed 123 is clean for both. The two modes produce coexistence through different mechanisms (memory vs suppression), and different nucleation trajectories respond to each.

Files

• sim12.py — the simulation (imports sim11/sim10/sim09; adds co-presence computation, boundary field B with growth/decay dynamics, perturbation test, 6-condition runner)
• visualize.html — interactive visualization (dark theme, material + boundary grids, component charts, perturbation trace, robustness sweep table)
• results.json — the headline 6-condition run (g=0.9, seed 42)
• output/perturbation_results.json — the perturbation test (step 1500, 50% right-structure removal)
• output/robustness_sweep.json — the 4-seed robustness sweep (4 seeds × 3 modes × {1,2} seeds = 24 runs)

Selftest

python3 sim12.py selftest — proves:

1. Co-presence is high for two seeds, low for one seed
2. B grows with co-presence and decays without it (slow exponential)
3. B persists after perturbation (retains more than passive I)
4. Autopoietic run produces per-region metrics
5. B is lower for a single seed (< 50% of two-seed value)
6. Determinism (two identical runs, identical results)