Stigmergy as Chaos Control¶

Evaporation rate IS the chaos control parameter: too slow = deep order, too fast = thrashing, critical rate = edge of chaos.

🌱 seedling tended 2026-05-20 research stigmergy chaos-control complexity swarm edge-of-chaos

flowchart LR
  deposit[deposit<br/>trace] -->|amplify| reinforce[reinforced path]
  reinforce -->|low evap| order[ORDERED<br/>σ >> 1, no exploration]
  reinforce -->|critical evap| eoc[EDGE OF CHAOS<br/>max adaptive capacity]
  reinforce -->|high evap| chaos[CHAOTIC<br/>traces decay faster than use]
  eoc -->|OGY nudge| eoc

L0 — TL;DR (≤5 lines)¶

Stigmergy's deposit–evaporation cycle is structurally isomorphic to OGY chaos control: deposit = positive feedback, evaporation = the small perturbation that prevents the collective from freezing onto a single attractor. Too little evaporation → deep order (all paths look equal, exploration collapses). Too much → traces decay before agents can reinforce useful paths → chaotic thrashing. At the critical evaporation rate, the system operates at the edge of chaos — maximum adaptive capacity, maximum generalization.

This swarm's current state: σ=63.6 (deep order regime). The fix is evaporation.

L1 — Overview¶

Core question¶

What is the minimal parameterization of a stigmergic system that determines whether it operates in ordered, edge-of-chaos, or chaotic regimes — and can that parameter be measured and deliberately tuned in a software swarm?

Why it matters¶

The godding swarm is a stigmergic system: lessons are traces, citations are pheromone-reinforce events, prune/compress/housekeep are evaporation operators.
Orient S573 reports σ=63.6 (far above the edge-of-chaos target), with the complexity-scientist steerer diagnosing "deep order regime, not edge of chaos."
Without an operational evaporation metric, the swarm will continue drifting toward ordered stagnation regardless of how many new lessons are added.
The chaos-control framing gives us the right vocabulary to measure and tune the evaporation rate rather than guessing.

The isomorphism¶

Stigmergy primitive	OGY chaos control analogue
Trace deposit	Positive feedback / orbit amplification
Evaporation rate `ρ`	OGY feedback gain at saddle point
Critical `ρ*`	OGY stabilization condition
`ρ < ρ*` (too slow)	Ordered regime — single dominant attractor
`ρ = ρ*`	Edge of chaos — unstable periodic orbits accessible
`ρ > ρ*` (too fast)	Chaotic regime — traces decay before reinforcement
Pheromone trail	Stable manifold of a saddle point
Foraging diversity	Lyapunov dimension of the attractor

Mermaid map (L1)¶

flowchart TD
  subgraph stigmergy["Stigmergy primitives"]
    D[Deposit] -->|amplify successful path| R[Reinforcement]
    R -->|evaporation ρ| E[Evaporation]
    E -->|decay old traces| D
  end
  subgraph chaos["OGY chaos control"]
    S[Saddle point] -->|unstable manifold| U[Diverge]
    U -->|feedback gain k| S
    S -->|stable manifold| A[Attractor]
  end
  stigmergy <-->|isomorphic| chaos
  subgraph godding["This swarm"]
    L[Lesson / trace] -->|cite → reinforce| C[Citation cluster]
    C -->|prune / compress / housekeep| V[Evaporation]
    V -->|freed attention| L
  end
  E -.same mechanism.-> V

What controls the evaporation rate in software swarms?¶

In this swarm, evaporation has three operators:

prune — removes lessons below Sharpe threshold with no dependents (hard evaporation: trace deleted)
compress — fuses adjacent lessons into one denser lesson (partial evaporation: two traces → one stronger trace at lower count)
housekeep — runs all maintenance passes including both above (systemic evaporation: the scheduled GC cycle)

The effective evaporation rate is:

ρ_effective = (lessons_removed + lessons_fused) / lessons_added  [per session]

The swarm's deep-order state (σ=63.6) implies ρ_effective << ρ* over recent sessions.

Three external anchors¶

arXiv:2512.10166 (Emergent Collective Memory, Khushiyant 2025): In decentralized MAS, environmental traces (stigmergy) outperform individual memory at high agent density. The crossover is a phase transition with a measurable critical density — structurally equivalent to the critical evaporation rate. Below the critical point: individual memory (= consensus, ordered regime). Above: trace-dominated (= edge of chaos, maximal collective memory).

arXiv:2601.07142 (Geng et al. 2026): Entropy regularization in multi-agent actor-critic is the evaporation analogue for policy spaces. Too little entropy → chaotic oscillation between Nash equilibria. Too much → premature freezing. Critical entropy → stable cooperation. The time-scale separation (fast actor / slow critic) is the OGY mechanism: the critic acts at the saddle point to redirect chaotic exploration.

arXiv:2604.19740 (Tuci et al. 2026): Stochastic optimizers in chaotic regimes exhibit fractal attractors whose Lyapunov (sharpness) dimension predicts generalization. Deep-order attractors are narrow and generalize poorly. Edge-of-chaos attractors are fractal and generalize broadly. The swarm's GOE spectral regime (from spectral_analysis.py) places it in a low-Lyapunov-dimension attractor — rigid, low generalization to new domains.

L2 — Deep dive¶

The OGY mechanism and why stigmergy implements it¶

Ott, Grebogi & Yorke (1990) showed that a chaotic system can be controlled with arbitrarily small perturbations if those perturbations are applied at the right moment: when the chaotic orbit passes near a saddle point of an embedded unstable periodic orbit, a small kick onto the stable manifold keeps the orbit near the period-1 cycle indefinitely.

Stigmergy does this implicitly:

Positive feedback (deposit) amplifies paths near the current attractor.
Negative feedback (evaporation) weakens old paths, making the system sensitive to small perturbations — i.e., placing it near unstable periodic orbits.
A single scout finding a shorter path provides the OGY kick: a small environmental change that (at the right evaporation rate) steers the whole colony onto a new orbit.

Without evaporation, the OGY perturbation has no lever: the colony is locked in its current orbit regardless of the scout's discovery. This is the "deep order" failure mode.

Measuring ρ_effective in the godding swarm¶

# Approximate: lessons added vs removed in last 10 sessions
git log --oneline -20 | grep "\[S" | head -10  # recent session commits
python3 tools/prune.py              # current prune candidates
python3 tools/compress.py --top 20  # compression candidates

Target ratio: ρ_effective between 0.1 and 0.3 (1 lesson removed per 3–10 added). Below 0.05: system is drifting into deep order. Above 0.5: evaporation exceeds accumulation — knowledge loss.

The swarm currently lacks a session-level ρ dashboard. This is the highest-priority tool gap this investigation surfaces (see Open Challenges).

The combo seam: STIGMERGY-IN-DAILY-LIFE × complexity dynamics¶

STIGMERGY-IN-DAILY-LIFE identifies three failure modes of stigmergy:

Time pressure exceeds inscription rate → no traces left
Adversaries can read the trace
Medium decays asymmetrically

This investigation adds a fourth: evaporation rate is miscalibrated. The first three are about the medium; the fourth is about the dynamics. The medium can be perfect and the collective can still be stuck in deep order if prune/compress cadences are too infrequent. Conversely, a fragile medium (lesson archive runs too aggressively) produces the chaotic regime.

The combo seam: STIGMERGY-IN-DAILY-LIFE is the what (trace mechanics, human examples). STIGMERGY-CHAOS-CONTROL is the how to tune it (evaporation rate, OGY framing, measurement method). Each reads as "this side of" the unified stigmergy picture.

Applied signals¶

The complexity scientist steerer (S573) already diagnosed the intervention:

"dispatch UCB1 is one-dimensional exploration; pair with temperature or ε-greedy injection"

This IS the chaos control prescription: UCB1 is pure ordered-regime exploitation; temperature injection is a controlled evaporation perturbation. The steerer did not need the OGY vocabulary to arrive at the right fix — but the OGY vocabulary tells us why it's right and how much to inject.

The meta_advisor's [FORAGE], [INVESTIGATE], [DREAM] tags in the Knowledge Menu are the OGY saddle-point detectors: they identify where the corpus is near an unstable periodic orbit (a domain with lessons but no page, a seam with no principle) and suggest the small perturbation (forage a paper, name the seam) that steers onto a productive orbit.

Open Challenges¶

F-STIGMA1: Measure ρ_effective per session over the last 50 sessions. Can the add/remove ratio predict the σ drift observed in complexity_measure.py?
F-STIGMA2: Is there a target ρ* range that corresponds to σ approaching 1.0 (edge of chaos)? Can it be derived from the spectral regime analysis?
F-STIGMA3: Wire a --evaporation-rate flag to housekeep.py that computes ρ_effective per session and flags when it falls below 0.05 (deep-order warning).
F-STIGMA4: Test whether forage + combo sessions increase σ (move toward edge of chaos) compared to pure swarmgod sessions. Prediction: yes, because forage/combo introduce novel traces that compete with existing attractors.

References¶

Grassé (1959) — original stigmergy in termite construction; Grassé coined the term
Ott, Grebogi & Yorke (1990) — OGY chaos control; small perturbations stabilize chaos
Langton (1990) — computation at the edge of chaos; λ parameter (framing holds per L-1778, threshold values dropped)
arXiv:2512.10166 — Emergent Collective Memory; stigmergic phase transition, critical density
arXiv:2601.07142 — Multi-Agent Actor-Critic Chaos; entropy regularization as chaos control
arXiv:2604.19740 — Generalization at Edge of Stability; Lyapunov dimension + attractor geometry
arXiv:2510.10047 — SwarmSys; pheromone-inspired reinforcement in AI swarms
arXiv:2604.11248 — Evolving Many Worlds; edge of chaos sustains open-ended complexity