PHY 351 — Independent Summer Research | UNCG
A computational study of force-based flocking agents on a periodic 2D domain, extended with predator-prey dynamics. Based on Charbonneau (2017), Ch. 10.
94 findings (F1–F94), all written up in findings.md and the report. Last updated 2026-06-16.
Threads, and whether they're closed:
| Thread | Findings | State |
|---|---|---|
| Baseline & validation | F1–F4 | ✅ closed |
| Phase transition (is the solid→fluid a true transition?) | F2, F8, F12, F17, F38–F40, F50 | ✅ closed — it's a crossover; no base_r^n potential crystallizes |
| Predator strategy (2D + 3D) | F5–F35, F43–F45, F49, F53, F65 | ✅ closed — only encirclement disrupts, and only in 2D |
| Predator–prey arms race (predictive encirclement vs collective escape) | F66–F71 | ✅ closed |
| Contagion / vaccination / kinematic mixing | F10–F37, F47–F48, F52, F54–F64 | ✅ closed — slow-recoverer targeting is the one strategy that beats random |
| Leadership / collective decision-making (incl. many-wrongs) | F72–F86 | ✅ closed (paused) |
| Co-adaptation / evolution (heritable traits under selection) | F87–F94 | ✅ complete arc (newest work) |
Most recent work — the co-adaptation thread (F87–F94): prey evolve a heritable escape weight under capture/removal predation. The F70 "dangerous valley" is a strong evolutionary brake (F87): escape is stable once present but can't evolve from scratch — it's a barrier to origination, not invasion (F88), and the resulting escape equilibrium is a robust mixed strategy (F89). With a co-evolving predator the arms race is asymmetric (F90), a self-test corrected an over-reading of it (F91), and under an energy-budget fitness model the brake proves model-independent while escape's persistence does not (F92). A second heritable trait, the alignment strength α, is also bistable — high alignment is a protective ESS that can't evolve from low (F93) — but unlike escape it does not invade from a seeded minority either (F94), because alignment is a mutual coupling rather than a free-rideable shared signal. All of it runs on a validated, fast harness (vectorized_predator.py, vectorized_predator_prey.py).
Where to pick up next: see the end of findings.md (Open Questions / Next Directions). The natural next experiments — a third fitness model (proximity-survival) or a two-trait predator (lead + aggression) — each rest on the same harness.
A new topic (Charbonneau Ch. 5), distinct from the flocking work below. Code in
sandpile/, findings in findings_sandpile.md
(S-series). The arc: validated 1-D core → rigorous critical exponents → the
chapter's 2-D "Grand Challenge" → a universality comparison against the canonical
abelian (Bak–Tang–Wiesenfeld) sandpile.
Headline result: the phenomenon of self-organized criticality (scale-free avalanches as a dynamical attractor, no parameter tuning) is robust, but the critical exponents are not — they depend on both dimension and toppling rule:
| model | avalanche exponent | same class? |
|---|---|---|
| 1-D slope sandpile | τ_E ≈ 1.03 (D_E ≈ 2.0) | — |
| 2-D slope sandpile | τ_E ≈ 0.87 | ✗ differs from 1-D (purely dimensional; local rule identical) |
| 2-D canonical BTW | τ_S ≈ 1.14 (lit. ~1.2) | ✗ differs from 2-D slope (τ_S ≈ 0.89) |
The 2-D slope-vs-BTW split is now confirmed by a second, convention-free measure: the avalanche duration exponent, τ_T ≈ 0.56 (slope) vs ≈ 1.22 (BTW), stable across lattices up to 512 a side (S10). That measurement needed an active-list, numba-compiled engine (Exercise 5, S9) that reproduces the original engines bit-for-bit and runs ~600× faster in 2-D.
And the criticality is exact only because the bulk is conservative: breaking conservation (destroying a fraction of toppled sand) collapses the cutoff scaling from N² to sub-N¹ and truncates the avalanche distribution at a dissipation-set size — singling out conservation among the four SOC ingredients (the OFC earthquake-model sensitivity, in the simplest sandpile).
Validated against the chapter: mass conservation to 3×10⁻¹¹, N-independent power-law avalanche PDFs, initial-condition independence (the SOC attractor), and a clarification of the angle-of-repose claim (the mean slope sits ~16% below Z_c independent of grain size; only the peak pre-avalanche slope approaches Z_c as grains shrink).
sandpile/
sandpile1d.py 1-D slope model (eqs 5.1–5.10), avalanche measurement
validate1d.py conservation, SOC signatures, IC-independence, eps-sweep
fss1d.py 1-D finite-size scaling: τ_E, D_E, D_T + data collapse
repose_peak.py angle-of-repose mean-vs-peak slope reconciliation
sandpile2d.py 2-D bond-slope generalization (Grand Challenge)
fss2d.py 2-D finite-size scaling + 1-D-vs-2-D comparison
btw_compare.py canonical 2-D abelian BTW, same pipeline (universality)
dissipation.py break bulk conservation -> is conservation necessary for SOC?
dissipation2d.py 2-D version of the conservation test (transfers from 1-D)
duration_compare.py duration-exponent universality cross-check (self-test, S6)
falloff.py boundary-evacuation avalanches vs bulk avalanches (Exercise 2)
sandpile_fast.py active-list, numba-compiled 1-D+2-D engine (Exercise 5, S9)
duration_fss2d.py large-L duration FSS; resolves S6 (S10)
moments.py moment-scaling machinery + FSS self-test (S11)
moment_slope.py slope-model moment spectrum: filamentary area (S12)
conditional.py conditional avalanche exponents; ballistic front (S13)
geometry2d.py per-avalanche footprint geometry: the filament (S14)
stochastic_split.py tunable split toward Manna; the causal test (S15)
geometry1d.py 1-D footprint geometry = the dimensional anchor (S16)
equilibrate2d.py reusable warmup to a verified-stationary L>256 (S16)
duration_closure.py single-scale exact in space, residual in time (S17)
area_multifractality.py area multifractality is asymptotic, not a corona (S18)
Exercises addressed: 2 (falloff avalanches, S8), 3 (initial-condition independence, S1), 4 (eps-dependence of the angle of repose, S2), 5 (fast active-list engine, S9), 6 (the 2-D Grand Challenge, S4) — plus the conservation study (S5/S7) and a self-test that was inconclusive (S6) then resolved (S10).
The scaling-theory arc (S11–S18). Beyond the exercises, the chapter builds one
extended argument about what a 2-D slope avalanche actually is. Moment-spectrum
analysis (S11–S12) finds the avalanche footprint is filamentary — its area grows only
linearly with system size (D_area ≈ 1), against the compact D ≈ 2 of canonical BTW through
the same pipeline — while the total toppling activity is space-filling (≈ L²): a thin front
that sweeps its own bonds ≈ L times. Conditional exponents (S13) and a direct footprint
recording (S14) confirm it geometrically — a constant-width, one-bond-wide, ballistic
filament (topple time ≈ distance from the seed), thinner than the exactly-solvable directed
sandpile (D = 3/2). A tunable stochastic split toward the Manna class (S15) shows the
filament is caused by the deterministic rule (its dimension climbs 1 → 1.87 as randomness
is switched on), yet the model never collapses onto simple Manna scaling. A 1-D dimensional
anchor (S16) proves D ≈ 1 is intrinsic to a slope avalanche, not a 2-D artifact, and ships
an equilibration tool that reaches a verified-stationary L = 512. With it, the last two
findings pin down how single-scale the model is: the spatial relations become
exactly single-scale as L → ∞ (size ∝ area², area ∝ duration), but duration stays a
permanently loose proxy for spatial extent (S17), and the avalanche area distribution
stays multifractal asymptotically rather than healing to simple scaling (S18) — the
model is single-scale in its means (the typical avalanche) and multifractal in its tails
(the largest avalanches). It sits in its own place in the SOC landscape: more filamentary
than the directed sandpile, outside the stochastic Manna class, a distinct anomalous class
from BTW. Full detail (S-series) in findings_sandpile.md.
A new topic (Charbonneau Ch. 8), the direct continuation of the sandpile
conservation thread. Code in earthquake/, findings in
findings_earthquake.md (E-series). The OFC model is a 2-D
lattice of "force" values driven uniformly until a node hits threshold and topples,
passing a fraction α to each neighbor (0 ≤ α ≤ 0.25). At α = 0.25 redistribution is
conservative; for α < 0.25 the bulk dissipates (1−4α) per topple — so α is a
continuous knob on the exact ingredient (bulk conservation) that finding S5 singled
out for SOC.
Headline result: OFC reproduces the Gutenberg–Richter law, and conservation tunes criticality. The avalanche-size cutoff grows with system size when (near‑)conservative and saturates to a dissipation‑set scale when not — the S5 result made quantitative on the canonical earthquake model. And unlike the sandpile, the nonconservative model is deterministic and develops synchronized domains that drive quasi‑periodic recurrent avalanching — temporal structure the sandpile entirely lacks.
| α (conservation) | PDF slope (book) | cutoff vs L | regime |
|---|---|---|---|
| 0.25 (conservative) | −1.19 (−1.19) | grows steeply (D ≈ 3.2) | critical |
| 0.20 | −1.87 (−1.92) | ≈ L² (D ≈ 1.95) | critical‑like |
| 0.10 (60% dissipated) | −3.52 (−3.34) | flat (D ≈ −0.15) | subcritical |
Validated against the chapter: the fig.-8.7 PDF slopes (all three match), the fig.-8.6 synchronization domains forming from a random start, the fig.-8.4 recurrent avalanching (raw period ~10,600 at α=0.15, matching the book's ~10,960; forcing-corrected ~3,982 vs the book's 4,002; vanishing at the conservative α=0.25). The size–duration relation steepens with conservation (E ~ T^γ, γ = 1.47 → 1.89 as α: 0.15 → 0.25). A self-test (Exercise 4) confirms the quasi‑periodicity is fragile: a ±0.01 per‑topple jitter in α halves the recurrence peak, because synchronization needs the redistribution to preserve equality exactly.
Grand Challenge (earthquake prediction): a forecaster that phase-locks to the recurrence rhythm beats chance only modestly (1.5–1.7×) and misses the largest events (top‑decile recall 0.09) — reproducing, in a fully-known noise-free model, the book's point that large events sit in an unpredictable tail.
earthquake/
ofc.py core OFC model + 6 validation self-tests (open/periodic BC,
per-topple stochastic α, Exercise-3 skip-forcing, bit-identical)
ofc_gr.py E1: Gutenberg–Richter validation (fig. 8.7)
ofc_fss.py E2: finite-size scaling / conservation test (cf. S5/S7)
ofc_quasiperiodic.py E3: recurrence period + synchronization domains (figs. 8.4/8.6)
ofc_et.py E4: avalanche size–duration relation (Exercise 5)
ofc_speedup.py E5: forcing skip-ahead speedup (Exercise 3)
ofc_stochastic_alpha.py E6: self-test — does stochastic α break periodicity? (Ex. 4)
ofc_predict.py E7: Grand Challenge — earthquake prediction (Exercise 6)
Exercises addressed: 2 (finite-size scaling, E2), 3 (skip-forcing, E5), 4 (stochastic-α self-test, E6), 5 (size–duration relation, E4), 6 (the Grand Challenge prediction, E7) — plus the validation (E1) and the recurrence/synchronization study (E3).
N agents move on a periodic unit square under four forces each timestep:
| Force | Description |
|---|---|
| Repulsion | Short-range — keeps agents from overlapping (range 2r₀) |
| Alignment | Drives velocity toward mean of neighbors within r_f |
| Self-propulsion | Corrects speed toward target v₀ |
| Noise | Uniform random perturbation in [−η, η] |
Key analytical result: equilibrium cruise speed is v_eq = v₀ + α/μ — not v₀. Derived from force balance in an aligned flock; verified experimentally to within 0.002 across four α values.
Default parameters: N=350, r₀=0.005, ε=0.1, r_f=0.1, α=1.0, v₀=1.0, μ=10.0, η=0.5, dt=0.01
The codebase has two layers.
Core layer (model.py) — object-oriented foundation for all current and future experiments.
Flock — holds prey positions, velocities, and all physics parameters
flock.evolve(predators=[...]) advances one timestep
Predator — configurable predator agent; strategy='naive'|'encircle',
coord_alpha for predator-predator repulsion, enc_radius for encirclement
simulate() — runs a full experiment, returns Phi and distance timeseries
New experiments import from model.py. To add a new experiment: import Flock, Predator, and simulate from model.py, set parameters, call simulate().
Legacy layer (flocking.py) — procedural implementation that predates the OOP refactor. The earlier experiment scripts (predator.py, multi_predator.py, encirclement.py, etc.) import from here. They are retained intact for reproducibility and are not broken by the model.py refactor.
root/
model.py ← current API. New experiments import from here.
geometry.py ← shared helpers (Rg, AR) — used by both old and new scripts.
flocking.py ← legacy: procedural baseline. [keep for reproducibility]
analysis.py ← legacy: validation sweeps. [keep for reproducibility]
predator.py ← legacy: single-predator API. [keep for reproducibility]
multi_predator.py ← legacy: multi-predator helpers. [keep for reproducibility]
encirclement.py ← legacy: encirclement scaffolding. [keep for reproducibility]
predator/ predator strategy experiments
contagion/ panic, epidemic, and vaccination experiments
phase/ phase-transition and statistical-mechanics experiments
3d/ three-dimensional extension experiments
figures/ output PNG figures
outputs/ captured text/log output from runs
The five legacy scripts at root are intentionally retained: every numbered finding F5
through F16 was generated by them, and rerunning them must produce identical figures.
New experiments should not import from them — they have no if __name__ == "__main__"
guard and will side-effect on import. Use model.py instead.
Experiment scripts in subfolders automatically add the project root to sys.path so they can import the core library files above.
The experiments follow a logical arc, each motivated by the result before it:
| Stage | Question | Scripts |
|---|---|---|
| 1. Baseline | Does the model reproduce expected flocking behavior? | flocking.py, analysis.py |
| 2. Phase transition | Is the solid-to-fluid transition a true phase transition? | phase/phase_transition.py, phase/compactness_phase.py, phase/compactness_search.py |
| 3. Geometry | What shape does the flock take? | geometry.py |
| 4. Single predator | Does flocking help prey survive? | predator.py |
| 5. Predator strategy hierarchy | How many and how coordinated do predators need to be to break the flock? | multi_predator.py → predator/evasion_analysis.py → predator/coordinated_predators.py → encirclement.py → predator/encirclement_scaling.py → predator/fragmentation.py |
| 6. Encirclement limits | Does the encirclement floor scale with N? Is it stable long-term? Does a gap help the flock? | predator/large_N_encirclement.py → predator/renc_scaling.py → predator/long_encirclement.py → predator/encirclement_gap.py |
| 7. Minimum viable size | Below what N does collective evasion fail? | predator/min_flock_size.py |
| 8. Reversibility | Does encirclement damage reverse after predator removal? | predator/reunion.py |
| 9. Realistic predator | What changes with limited sensing range? | predator/predator_sensing.py |
| 10. Internal panic | Does panic from within disrupt the flock? | contagion/panic.py |
| 11. Contagion | What if panic spreads by contact? (SI and SIS models) | contagion/panic_contagion.py → contagion/contagion_sis.py |
| 12. Hybrid stressors | How do predation and contagion interact? | contagion/hybrid_stressors.py → contagion/hybrid_sis.py → contagion/critical_shift.py → contagion/outbreak_removal.py |
| 13. Herd immunity | How many immune agents are needed to quench an outbreak? | contagion/herd_immunity.py → contagion/targeted_immunity.py |
| 14. Segregation | Does a mixed-speed population spatially separate? | contagion/segregation.py → contagion/segregation_alpha.py |
| 15. Adaptive predators | Do predators that track flock geometry outperform fixed strategy? | predator/adaptive_encirclement.py |
| 16. Vaccination strategies | Can targeting high-degree or spatially-distributed agents reduce herd-immunity threshold? | contagion/targeted_immunity.py → contagion/spatial_vaccination.py |
| 17. Phase transition mechanism | Why does the model lack a true phase transition? Is it the soft repulsion, or something else? | phase/hard_repulsion.py → phase/langevin_repulsion.py → phase/langevin_hexatic.py |
| 18. 3D extension | Does flocking and the v_eq result hold in three dimensions? Extended noise sweep | 3d/flocking3d.py → 3d/flocking3d_noise.py |
| 19. 3D predators | Does encirclement transfer to 3D? Radius, count, adaptive, sphere/planar arrangement | 3d/flocking3d_predator.py → 3d/flocking3d_predator_scaling.py → 3d/flocking3d_adaptive.py → 3d/flocking3d_strategy.py |
| 20. 3D contagion & segregation | Do vaccination nulls and α-contrast segregation transfer to 3D? Does 3D mix faster than 2D? | 3d/flocking3d_vaccination.py → 3d/flocking3d_segregation.py → contagion/mixing_dimension.py |
| 21. Section 5 self-tests | Does topological alignment slow mixing? Does freezing contacts rescue targeting? | contagion/topological_mixing.py → contagion/contact_freezing.py |
| 22. Phase-transition closure | Does hard repulsion crystallize? | phase/langevin_hexatic_hard.py |
| 23. Agent memory | Does fatigue make encirclement damage irreversible? Do heterogeneous recovery rates shift the SIS threshold? | predator/fatigue.py → contagion/recovery_heterogeneity.py |
| 24. Heterogeneity & targeted vaccination | Does infectiousness spread shift the threshold? Can vaccinating slow recoverers preferentially beat random — in 2D, 3D, under continuous γ, with noisy estimates, and for rare reservoirs? | contagion/infectiousness_heterogeneity.py → contagion/slow_recoverer_vaccination.py → contagion/het_recovery_spatial.py → 3d/flocking3d_slow_vaccination.py → contagion/continuous_gamma_vaccination.py → contagion/noisy_gamma_vaccination.py → contagion/rare_reservoir_vaccination.py |
Flock forms reliably above α ≈ 0.1. With all forces active, the order parameter Φ stays above 0.97 up to noise η ≈ 10, then collapses near η ≈ 20. The alignment force makes the system dramatically more noise-resistant than the repulsion-only case.
Finite-size scaling across N = 25–200 (with compactness fixed via r₀ = √(C/πN)) shows KE/N curves are N-independent and susceptibility χ = N·Var(KE/N) increases monotonically at every tested compactness value (C = 0.10–0.78). No diverging peak appears anywhere. The solid-to-fluid transition is a smooth crossover throughout — a consequence of the soft repulsion potential used in this model. A true phase transition would require hard-core exclusion.
Flocking prey maintain Φ ≈ 1.0 under sustained predator pressure; non-flocking prey scatter to Φ ≈ 0.1 almost immediately. A minimum evasion buffer distance (~0.10) persists regardless of predator aggression.
With multiple predators, flock coherence remains high (Φ > 0.97) because all predators independently target the same center of mass and co-localize (measured separation ~0.001). This self-undermining behavior was confirmed in evasion_analysis.py.
Adding predator-predator repulsion (coordinated predators) successfully spreads predators out — separation rises to 0.29 — but Φ never drops below 0.92. The flock absorbs distributed pressure from multiple directions without breaking.
Encirclement (each predator assigned a fixed compass angle, targeting CoM offset by R_enc in that direction) is the first strategy to substantially disrupt the flock. At n_pred = 6, Φ drops to 0.77. The minimum predator-prey distance falls to 0.050 vs 0.105 for naive predators.
This Φ = 0.77 does not represent dissolution. fragmentation.py shows that encirclement divides the flock: predators compress agents spatially (60 clusters → 24 larger clusters) while splitting them directionally — each sub-flock escapes through a gap between predators and remains internally coherent (sub-flock Φ = 0.997). This is analogous to wolf-pack herding.
92 findings documented — full evidence and figures: findings.md
Selected highlights:
| # | Finding |
|---|---|
| 1 | Cruise speed is v_eq = v₀ + α/μ (exact analytical result, not just v₀) |
| 8 | Solid-to-fluid transition is a smooth crossover at all compactness values — no true phase transition |
| 5 | Flocking prey maintain Φ ≈ 1.0 under predator pressure; non-flocking scatter to Φ ≈ 0.1 |
| 11 | Multiple naive predators co-localize at CoM, self-undermining — paradoxically helps flock |
| 14 | Encirclement (fixed-angle targets) is the only strategy to substantially disrupt the flock: Φ = 0.77 at n=6 |
| 16 | Encirclement causes flock DIVISION (coherent sub-flocks heading in different directions), not dissolution |
| 22 | Encirclement damage is fully reversible: sub-flocks reunite within ~10 time units of predator removal |
| 25 | SIS contagion has a clean epidemic threshold at β/γ ≈ 1; flock coherence tracks it |
| 30 | Herd-immunity threshold in the flock is ~2× mean-field prediction due to spatial clustering |
| 31 | Encirclement scaling collapses on R_enc/Rg; optimal at R_enc/Rg ≈ 0.5 — strategy is size-invariant |
| 32 | Long-time encirclement is intermittent: Φ oscillates 0.4–0.95 in a sustained merge/split cycle |
| 33 | Incomplete encirclement (1 gap) is more disruptive than full ring; no global escape-route detection |
| 34 | Predator removal after encirclement+SIS: kinematic damage reverses in ~10 tu, epidemic persists ~100+ tu |
| 35 | Adaptive R_enc = 0.5×Rg outperforms fixed radius: Φ 0.778→0.713, high-coherence dwell time −34% |
| 36 | Targeted vaccination null: hub-targeting fails; kinematic reorganization restores hub positions |
| 37 | Spatial vaccination null: farthest-point spatial sampling fails; kinematic mixing scrambles positions |
| 38 | Repulsion exponent null: sweeping n=1.5→12 gives identical crossover; non-equilibrium driving is cause |
| 39 | Langevin thermalizes correctly (KE/N=kT to 1%), but chi_KE cannot detect KTHNY structural melting |
| 40 | Hexatic |ψ₆| confirms n=1.5 cannot crystallize: flat at ~0.4 across all kT; soft repulsion prevents lattice formation |
| 41 | 3D flocking validates: v_eq = v₀ + α/μ exact in 3D; Φ = 0.841 at η=10; 3D less noise-robust than 2D |
| 43 | 3D encirclement fails entirely: Φ ≈ 1.0 at every R_enc, every n_pred — encirclement is strictly 2D-specific (point predators cannot seal a closed surface) |
| 46 | 3D vaccination null transfers: random / spatial / degree-targeted vaccination all identical in 3D |
| 47 | Section 5 self-test #1 FALSIFIED: k-NN alignment does NOT slow kinematic mixing (Jaccard 0.036 vs 0.037) |
| 48 | Section 5 self-test #2: Freezing contacts does NOT rescue degree-targeting → the null is structural (no hubs), not kinematic |
| 50 | Hard repulsion null (F40 falsified): exponent n=12, 24 also flat |ψ₆| — base_r^n cannot crystallize at ANY exponent; raising n shrinks the core, doesn't harden it |
| 52 | "3D mixes faster" theme FALSIFIED: at matched contact degree, 3D rewires at ~0.56× the 2D rate — 3D mixes ~1.8× SLOWER |
| 53 | Prey fatigue null: encirclement damage stays reversible even with per-agent fatigue Q; align-mode fatigue deepens during-attack disruption (F27 echo), speed-mode doesn't (F24 echo) |
| 54 | Heterogeneous SIS recovery: spread in per-agent γ at fixed mean lowers β_c by ~2.5× (0.385 → 0.155); slow recoverers are reservoirs (1.5–2× more panic than fast); reframes vaccination toward slow recoverers |
| 55 | Heterogeneous infectiousness does NOT shift the threshold: super-spreaders source 74–97% of transmissions but γ stays homogeneous, so no stock asymmetry — the vaccination target is γ_i, not β_i |
| 56 | Slow-recoverer vaccination beats random by 2–3× — the first targeting strategy in this study (of ~15) to beat random. At p=0.40 slow-targeting eradicates (0.000) vs random 0.095. The hub label lives in per-agent γ_i, which kinematic mixing cannot scramble |
| 58 | Slow-targeting transfers to 3D unchanged: at p=0.50 slow eradicates (0.000) vs random 0.282; the per-agent-rate mechanism is dimension-independent |
| 59 | Slow-targeting survives continuous (lognormal) γ — no bimodal class structure needed; "vaccinate the bottom X% by γ_i" works for any plausible distribution |
| 60 | Slow-targeting tolerates noisy γ estimates: identical to perfect knowledge up to σ_obs ≈ 0.8, still beats random at σ_obs = 2.0 |
| 61 | Slow-targeting works for rare reservoirs: even a 5% slow class sustains the epidemic under random vaccination; targeting it at a matched budget eradicates |
| 62 | Slow-targeting needs a durable recovery-rate label: if γ_i drifts (state, not trait), mild drift erodes the advantage and fast drift eradicates the epidemic outright by self-averaging γ to its mean (undoing F54's threshold cut). The policy is valid exactly as long as the slow class persists on the epidemic timescale (~1/γ_slow) |
| 63 | Combined β_i + γ_i heterogeneity: targeting slow recoverers (the reservoir) is the robust vaccine across all correlations; targeting super-spreaders (the transmission engine) is equally good only when they aren't anti-correlated with slow recovery — when supers are fast recoverers, only slow-targeting eradicates. β-targeting is effective for removal, refining F55's "target γ not β" to a robustness statement |
| 64 | Reservoir-targeting reverses the predator+contagion damage asymmetry: F34's "contagion is the worst stressor" (epidemic outlasts predator removal) holds only while the reservoir survives. Vaccinating the slow class at a budget matching the reservoir fraction (p≥f_slow) eradicates the epidemic and lets the flock reunite to Φ≈1.0 — fully reversible combined damage. Below that budget the epidemic persists for every strategy |
| 65 | 3D flocks are robust to all point-predator strategies, not only sealing: a fast transecting predator that punches through the core gives Φ=1.000 at every count and speed up to 40× prey speed — same as encirclement (F43). The 3D flock fills the box near-uniformly (Rg=0.43 of ~0.5 max), so it has no perimeter to seal AND no interior to transect; finite-range predators perturb a vanishing fraction while the alignment graph heals the wake. Refines F43's mechanism: it's "no spatial localization," not "no surface to seal." Disrupting 3D needs a per-agent alignment attack (contagion does this) |
| 66 | Predictive encirclement (predators target CoM + lead_time · v̄) is the first predator-side adaptation in this study to substantially beat F14: Φ drops to 0.530 at lead=2 tu (vs F14's 0.77 and F35-adaptive's 0.713), non-monotonic with optimum near lead ~ R_enc/v̄ where the lead distance matches the encirclement radius. Inverts the F33 asymmetry — the flock can't detect global escape directions, but predators can detect v̄. Adapting position (F66) is independent of adapting radius (F35) |
| 67 | Predictive + adaptive predators do NOT compose: combined predictive-adaptive Φ=0.535, within noise of predictive-fixed (0.530). Under encirclement the flock compresses to Rg~0.05–0.10, so adaptive R_enc=0.5·Rg shrinks the ring to ~0.03 while predictive shifts it 0.24 ahead — predators degenerate into a near-point block in the heading direction, yet are as effective as a proper ring. Placement is the dominant lever; angular spread becomes secondary once the heading is blocked |
| 68 | Predictive encirclement is less noise-tolerant than slow-targeting: noisy v̄ estimates degrade Φ monotonically and gracefully — but graded from σ=0, no plateau (0.530→0.629→0.709→0.804 as σ_obs goes 0→25%→100%→400% of |v̄|). Unlike F60's slow-targeting, which is identical to perfect knowledge up to σ ≈ half the signal separation. Statistical reason: per-agent rankings are buoyed by N-sample averaging; global summary statistics (one vector per step) have no averaging buffer |
| 69 | Predictive encirclement is far more sensitive to delay than noise: acting on a stale v̄ destroys the advantage fast — a 0.25 tu lag loses ~83%, by 1 tu it's gone (Φ≥F14). Delay is a systematic directional bias on a forward-projected quantity (vs noise's zero-mean error), and v̄ decorrelates sub-tu under disruption. Dual of F60: a per-agent invariant is both noise-robust and delay-free; a global heading is both noise- and delay-sensitive. Closes the predator-learning thread (F66–F69) |
| 70 | The arms-race step: collective escape intelligence beats predictive encirclement — if committed. Giving prey the dual global signal (flee the predator centroid, weight w) is non-monotonic: weak escape (w=0.25) is worse than none (Φ=0.275, competes with alignment), but strong escape (w≥2) fully restores Φ=1.000 — a unified flee reinforces alignment and outruns the trap. Threshold ≈ alignment strength. Elegantly, the counter works only because predictive predators mass ahead (defining the escape direction) — the predator's own intelligence creates the prey's opening; predictive encirclement is self-defeating vs committed escape-intelligent prey |
| 71 | But the F70 escape needs a globally shared direction, not just escape info: with realistic local per-prey sensing (flee predators within r_sense), escape only partially works — Φ peaks at ~0.83 near the ring scale, never the full 1.000, even at global range. Per-prey escape vectors point different ways and compete with alignment instead of reinforcing it; too-large r_sense sees the symmetric ring and cancels (F33 echo). Honest caveat on F70: full escape is partly an artifact of a shared signal; the flock acts collectively only on already-shared signals |
| 72 | A tiny informed minority steers the whole flock — and it works for the same reason F70 did. Couzin-style leadership: a fraction ρ of agents carry a preferred direction g, the rest are naive followers. Just ρ=0.05 (18 of 350) already drives accuracy 0.63–0.83; ρ=0.10 reaches 0.87–0.96; saturates at ρ≈0.20. Stronger leaders reach a given accuracy at smaller ρ and with lower seed variance. Cohesion is never lost (Φ≥0.995 throughout) — the opposite of the predator case, where steering costs coherence. The minority's power is agreement, not numbers: all leaders share one common vector g, which alignment amplifies — the constructive half of the F70/F71 shared-signal rule (F70 escape, leadership, and flocking itself are one phenomenon: a globally shared direction is amplified, a locally heterogeneous one is not) |
| 73 | Conflicting leaders: the flock compromises, then votes — reproducing Couzin's decision dynamics. Two informed subgroups pull in different directions. At small angular conflict (θ≤90°) the flock compromises, traveling almost exactly the midpoint (θ=90°→ heading 45°), tight across seeds. Past a critical angle (~90–120°) it switches to consensus: cross-seed heading spread explodes (22°→74°) as different seeds commit to one goal or the other — averaging two near-opposed directions isn't a viable heading, so symmetry breaks. It picks one, it does not split (Φ≥0.96, split fraction ≤0.16 even at 180°). And the majority wins: at direct opposition a 21:14 informed-agent margin already biases the flock +0.42 toward the majority goal, rising to +0.93 — group direction is an effective majority vote among the informed. Alignment doesn't just propagate one shared direction, it arbitrates among several (average-when-compatible, vote-when-not) |
| 74 | Numbers vs conviction: the decision is set by total pull (count × strength), not headcount. At equal numbers (18 vs 18), the more strongly committed subgroup wins, more so with the conviction ratio (+0.20 tie → +0.71 at 5×). And a small strong minority beats a large weak majority: 10 strongly-committed agents tie then overtake 26 weak ones as the minority's total pull crosses the majority's — accuracy crosses zero near pull balance (−0.27 at pull 10 → ≈0 at 26 → +0.07 at 50). The zero-crossing sits slightly above equal pull, a mild residual numbers bonus (more agents nucleate the direction in more places). The flock is a weighted majority integrator: each vote scaled by commitment, decided by summed directed force — the quantitative form of the F72/F73 alignment-arbitration rule, echoing F70's force-vs-alignment escape threshold |
| 75 | Time-resolved decisions: leadership is fast & noise-robust, and the flock shows critical slowing at the decision boundary. Recording the full heading time series (not just the steady state): strong leadership is both faster and more accurate — settle time collapses from ~4.5 tu at ρ=0.20 to 0.46 tu at ρ=0.50, accuracy →1.0; no real speed-accuracy tradeoff (the "fast but wrong" ρ=0.02 case is just under-led). Noise barely matters — across a 20× noise range accuracy stays ≥0.99 and commitment slows only 8.9→11.3 tu (cf. F4). Headline: commitment time peaks at θ=90° (12 tu), falling off on both sides — the dynamical signature of a bistable system slowing near its bifurcation, sitting exactly at the F73 compromise→consensus boundary. The transition is a genuine bifurcation, and the flock takes longest to decide precisely when the decision is hardest |
| 76 | Leadership is a signal, not an identity: rotating which agents are informed never hurts — and faster rotation helps. Keep the goal fixed but re-draw the informed set every τ: accuracy equals or beats the fixed-leader baseline at every τ, and fast rotation raises accuracy (0.86→0.94 at ρ=0.05) while collapsing seed variance (std 0.14→0.07; at ρ=0.10, 0.04→0.007). The same total pull smeared uniformly over all agents steers more reliably than a fixed subset that must propagate its bias. The exact opposite of F62, where drifting the per-agent label destroyed the advantage: contagion targeting needs a durable per-agent identity, leadership needs only a durable shared direction. Closes the "what makes a target exploitable" arc — fragile if it rests on a persistent label, robust (even helped) by turnover if it rests on a shared global quantity |
| 77 | The flock has a steering bandwidth: leaders can drive a turn only below a critical rate. With a goal rotating at ω, tracking is near-perfect at ω=0 but degrades (54° lag at ω=0.05) and fails by ω=0.10 at ρ=0.10 (the goal laps the heading). The bandwidth scales with the informed fraction as 1/(F75 response time) — ≈0.11 rad/tu at ρ=0.10, ≈0.22 at ρ=0.20 (doubling leaders ≈ doubles ω_crit); F75 and F77 are the time- and frequency-domain views of one timescale. Below it the flock is a low-pass steering filter (lags, then attenuates). And over-steering costs cohesion: a turn faster than the flock can follow drops Φ to 0.78 — unlike cohesion-free fixed steering. Steerability and coherence are the same resource, mediated by the alignment response time — the same tension as predation |
| 78 | Leadership counters encirclement — the two biggest threads meet. Encirclement (F14) is the one predator strategy that breaks 2D coherence (Φ→0.79). Give a fraction ρ of prey a shared goal direction (not fleeing — just a heading) while 6 predators encircle: leaders both restore the coherence the predators destroyed (Φ 0.79→0.94 at ρ=0.40) and steer the flock through the ring (accuracy 0→0.98). Encirclement raises the leadership threshold (ρ=0.05 steers freely with no predators but needs ρ≈0.2–0.4 under the ring) — the quantitative cost. Generalizes F70: it's not the content of the shared signal (flee vs goal) that counters the predator but the presence of any strong shared heading. Encirclement wins by erasing the common direction; leadership (even predator-oblivious) is its antidote. Predation and leadership pull on opposite ends of one lever — shared alignment |
| 79 | Spreading panic severs the rudder, not the hull — the complement of encirclement. SIS panic makes agents erratic and a panicked leader can't lead. As β rises, steerability collapses (accuracy 0.94→~0 by β/γ≈2) but coherence is untouched (Φ stays ≥0.98 even at 98% panic — noise below the F4 melting point). The flock stays a tight flock flying a random, leaderless heading. Mechanism = the F74 pull law taxed by panic: panic saturates immediately (spatial R0≫1, cf. F18–F25), so what matters is the depth — at any instant a fraction f of leaders is silenced, giving effective ρ=(1−f)·ρ; steering tracks it exactly. Encirclement attacks coherence (leadership fixes it); panic attacks steerability (leadership can't fix it — the disease disables the leaders). Explains why contagion is the study's most durable stressor: the shared heading can't repair itself once its carriers are panicking |
| 80 | Adversarial leadership: denial is cheaper than capture. A saboteur minority pushes toward a "trap" against true leaders (ρ_true=0.10 toward goal). Denial (deadlock the flock, deny its goal) needs only parity — at ρ_sab=ρ_true goal-accuracy collapses 0.92→0.11, and half-parity already halves it. Capture (drive the flock to the trap) needs a majority — accuracy crosses zero only past parity and decisive capture (acc<−0.5) takes ρ_sab≈2× the true leaders. Between sits a deadlock band. The zero-crossing at pull parity is exactly the F74 product law; the new content is the threshold gap (denial ≈1×, capture ≈2×). Security asymmetry: an adversary can paralyze a led flock at parity but must dominate to hijack it — disrupting the shared heading is easier than commandeering it. Φ only dips to 0.88 (the fight is over heading, not integrity) |
| 81 | (self-test) Steering is set by the informed fraction, not the absolute number — correcting F72's offhand Couzin attribution. F72 cited Couzin (2005)'s "informed number needed drops as the group grows" but only ever swept ρ at one N. Varying N at fixed leader count n_lead, accuracy falls with N at every fixed n_lead (n_lead=20 → 0.96/0.76/0.48 at N=100/250/500); re-indexed by fraction the data collapses with no residual N trend. Steering delivers exactly the F74 product law per capita — total injected force n_lead·w divided by all N — so growing N at fixed n_lead dilutes the per-capita pull. The literature's number-suffices scaling comes from a many-wrongs preferred-direction-averaging amplification that linear velocity alignment does not have; this model delivers per-capita pull with no amplification. The fraction-based frame (F72/F78/F79/F80) is correct; the one number-based intuition is the exception removed here. A many-wrongs follower rule would be needed to recover the literature scaling — an open direction. Fourth self-test (cf. F47/F48/F52) |
| 82 | Many-wrongs navigation: noisy private goal estimates average to a 1/√N wisdom of crowds — recovering exactly the amplification F81 predicted but found absent for exact-shared vectors. Give every agent its own goal estimate at per-agent angular error σ_pref and bias it toward its own: the flock's RMS heading error falls 16°→2° as N grows 30→250 (log-log slope −0.52, predict −0.5) and accuracy rises with N (0.96→0.999) — the clean inverse of F81. Each agent alone would err ~57°, but a flock of 250 navigates to within 2°. No contradiction with F81: alignment averages whatever signal the agents carry — an exact shared vector has no error to average (per-capita pull, F81), heterogeneous noise averages down as 1/√N (F82). Two limits: a ~2° floor (size-independent dynamical jitter) and a noise ceiling — past σ_pref≈1.3 rad the pooled estimate magnitude (~exp(−σ²/2)) collapses below the spontaneous-heading threshold and accuracy falls 0.99→0.58 with exploding seed scatter while Φ stays ~0.90 (the many-wrongs form of the F72/F74 pull threshold). Alignment is a directional averager: per-capita for shared signals, √N-amplifying for noisy ones |
| 83 | Correlated estimates: F81 and F82 are the two ends of one axis (error correlation ρ_c), and shared sensing error caps the wisdom of crowds. Build each agent's goal error as √ρ_c·(shared) + √(1−ρ_c)·(private): at ρ_c=0 error falls 1/√N (F82), at ρ_c=1 it's exactly N-independent (68° at every N, Φ=1.0 — the F81 limit, all agents confidently agree on the same wrong heading). Any ρ_c>0 imposes an N-independent floor ≈σ√ρ_c that no flock size can beat: a mere 10% correlation pins accuracy at ~0.92 whether N=30 or 500. Bonus: correlation buys coherence (Φ 0.88→1.0) at the cost of accuracy (0.99→0.44) — a perfectly coherent flock can be unanimously wrong (consensus ≠ correctness, cf. F73). Ties to F80: an attacker who can't out-number the leaders can instead inject a single shared false cue and cap the collective's accuracy regardless of size — common-mode deception is cheaper than majority capture. Closes the many-wrongs sub-thread (F81–F83) |
| 84 | The noisy minority: informed-minority steering and the wisdom of crowds are distinct mechanisms that don't combine in a minority. A fixed number of noisy-informed agents (rest naive) still fails as N grows — exactly F81, not F82: at n_lead=20 accuracy falls 0.86→0.43 as N=100→500, and noisy sits ≤ exact everywhere (the pooled-direction penalty σ/√n_lead — leaders agree on a heading ~18° off, which followers can't fix). Only growing n_lead recovers accuracy (0.22→0.91 at N=250). The 1/√N many-wrongs amplification (F82) needs the informed fraction to grow; confined to a fixed cadre it gives per-capita-diluted steering toward a fixed-accuracy pooled target — strictly worse than an exact minority. Separates Couzin (informed-minority) from Simons/Codling (many-wrongs) within one model. Completes the leadership mechanistic map (F72–F84): alignment is a directional averager whose accuracy = per-capita pull (fraction×strength) toward a target set by the estimates' correlation (F83) and sample size (F82/F84) |
| 85 | Misinformation: a crowd averages out noise but flips to a coordinated falsehood of the same size. A fraction f of agents are misinformed — either lost (uniform-random) or adversarial (coordinated toward a false goal). Lost is near-harmless: accuracy stays 0.998 even at f=0.5, only 0.983 at f=0.7 (random unit-votes cancel). Adversarial is decisive: accuracy crosses zero at parity f=0.5 (0.62→0.11→−0.62 across f=0.4–0.6), Φ bottoming at 0.78 at the deadlock point (F80 product law + F73/F75 critical-slowing dip). Same number of equally-wrong agents — only the correlation of their error differs (ties F83). Lost-robustness is scale-free (N-independent at fixed f). The lesson across F80/F83/F85: what threatens a collective's heading is never the amount of error but its correlation — alignment averages out everything independent and is moved only by what's shared. Caps the many-wrongs arc (F81–F85) |
| 86 | (self-test) A noisy crowd tracks a moving goal at the same bandwidth as a sharp leader — spatial (many-wrongs) and temporal (F77 bandwidth) averaging are independent. With a goal rotating at ω and every agent carrying a fixed private offset, the tracking-vs-ω curves for σ_pref=0/0.5/1.0 overlay (bandwidth flat at ~0.20 rad/tu) even as the averaged-bias magnitude falls to 0.61. My pre-registered prediction (bandwidth ∝ exp(−σ²/2)) is falsified: the static offsets rotate with the goal and add no lag, and the reduced magnitude stays above the steering threshold. Noise is free below the F82 ceiling and catastrophic above it (σ=1.5 collapses, not a graceful bandwidth drop) — binary, not graded. Shows the directional average is recomputed each timestep, not integrated. 5th self-test (cf. F47/F48/F52/F81); closes the many-wrongs arc (F81–F86) |
| 87 | Evolution: the F70 escape-weight "dangerous valley" is a strong evolutionary brake, not a barrier (opens the co-adaptation thread). Making the collective-escape weight a heritable per-agent trait under capture/removal selection against the predictive predator (F66): escape (w≥α) is evolutionarily stable and near-cost-free once present — seeded at w₀=2 it stays at 2.0 with ~6 captures, Φ=1.0 — but does not evolve from the no-escape state. Selection on w is directional-upward from every start, yet the valley throttles the climb so hard that w₀=0 crawls to only w~0.5 in 400 tu (never reaching w=1) while taking the heaviest predation (captures peak in the valley: ~1800–1900 at w₀=0–0.25 vs ~6 at w₀=2). Strong evolutionary hysteresis / first-mover problem: escape is easy to keep, hard to evolve de novo, because the path runs through a region where partial commitment is selected against (the F16/F24/F70 domination-not-blending theme, read at the evolutionary level). Fitness model = capture/removal (a deliberate scientific choice). Predator side still fixed — next: co-evolve it |
| 88 | The F87 brake is a barrier to origination, not invasion — escape spreads once present. Seeding a 5% escaper founder group (w=2) into a no-escape flock carries the mean weight into the escape regime (w_end 1.18, escaper fraction 0.05→0.55, captures halved); larger seeds settle the same. Escape establishes at a mixed ~60% equilibrium, not fixation — a free-rider / herd-protection effect of the shared escape signal (once enough flee, the predator is outrun and low-w agents ride along protected; the public-good face of the F70/F72 shared-direction rule). From a uniform w=0 start, the F87 mutation step (σ=0.10) never reaches w=1, but σ=0.30–0.60 cross in 100% of seeds (σ=1.0 noisier, 50% — an intermediate sweet spot). So whether escape evolves is mutation-/standing-variation-limited, not selection-limited: selection favours escape once the valley is cleared, but variation must deliver an agent past it in one step or a pre-adapted founder group must arrive |
| 89 | The escape free-rider equilibrium is robust — escape never fixes. Mapping the F88 mixed equilibrium against predation pressure: sweeping the capture hazard across an 8× range moves the steady escaper fraction only 0.56 → 0.66, and escape never approaches fixation — even under the heaviest predation ~⅓ of the flock rides the shared escape as protected free-riders (mean w stays in the escape regime; runs from different starting fractions settle into the same band). Intensifying predation erodes free-riding only weakly, confirming the public-good reading: a shared, non-excludable escape direction supports a persistent non-contributing fraction, so escape stabilises as a durable mixed strategy rather than sweeping to fixation — the population-level face of the F70/F72 shared-direction rule. Carries the F87/F88 hysteresis signature (mild start-dependence) |
| 90 | Two-sided arms race is asymmetric (closes the co-adaptation thread). The predator co-evolves a heritable predictive lead time, selected on capture success (replace-worst-with-mutated-best). The predator climbs to its optimum from any start, but the prey counter is origination-limited (F87/F88), so de-novo co-evolution favours the predator (prey stall at w |
| 91 | (self-test) The capture optimum coincides with the disruption optimum — correcting F90. Measuring capture rate and coherence directly against a fixed predator lead (frozen prey, no evolution): the capture rate peaks at lead~2 (9.6/tu) — exactly where coherence is lowest (Φ=0.584) — and collapses by lead 4 (predators overshoot). So the lead that catches the most prey is the lead that most disrupts the flock; the F90 evolved lead |
| 92 | Robustness: the origination brake is model-independent, the persistence of escape is not. Re-running the thread under an energy-budget fitness model (an explicit metabolic death hazard ∝ w, paid even when safe) splits the earlier results. The brake survives — escape still can't evolve from no-escape (w₀=0 → 0.05), so the F70-valley barrier is general, not an artifact of capture/removal. But F87's "escape is free & stable once present" fails: at cost c=0.5 every start collapses to w~0.05 (even a w₀=2 seed), and the ESS falls sharply with cost (c=0 → w=1.28, but c=0.25 → 0.11) — nearly all-or-nothing, no interior optimum. Mechanism: the cost is paid by every escaper continuously while predation threatens only the few near a predator at any instant, so a modest per-capita cost outweighs the diffuse benefit. Collective escape is viable only where it's essentially free — even more evolutionarily fragile than F90/F91 implied |
| 93 | A different heritable trait — alignment strength α — is also bistable: an origination brake mirroring F87. Evolving the flocking force itself (heritable per-agent α, no escape force) under the same capture/removal predation: the outcome is history-dependent. A high-alignment flock is a strong protective ESS — α₀=2 stays at 2.00, Φ=1.0, just 6 captures (a tight flock evades the predictive encircler) — but alignment does not climb from below: α₀=0.2 → 0.19, α₀=0.5 → 0.39, and α₀=1.0 drifts down to 0.85 (Φ≈0.55, ~1400 captures, |
| 94 | But unlike escape (F88), a seeded high-alignment minority does not invade — alignment is a mutual coupling, not a free-rideable signal. Seeding f=0.05–0.50 of high-α agents (α=2) into a low-α flock: the minority is diluted at every fraction (f=0.05/0.10 → |
Full documentation, evidence, and figures for each finding: findings.md
| File | Description |
|---|---|
model.py |
OOP foundation — Flock, Predator classes; flock.evolve(); simulate() helper. Import this for new experiments. |
flocking.py |
Procedural core — buffer zone, vectorized forces, run loop, order parameter. Used by legacy experiment scripts. |
vectorized_predator.py |
Vectorized predator→prey repulsion force; reproduces model.Predator.force_on_prey exactly (self-test asserts 1e-17 agreement) at ~250× the speed. Additive helper. |
vectorized_predator_prey.py |
Fast predictive-encirclement (F66) + collective-escape (F70) episode runner, run_episode(). Verified bit-identical to the legacy predator scripts; supports a per-agent escape weight and returns final state for downstream analysis. |
Experiments live in four theme subfolders. Each script is self-contained, has an if __name__ == "__main__" guard, and imports the root-level core library (flocking.py, model.py, geometry.py) via a sys.path insert at the top of the file.
| Folder | Theme | Representative scripts |
|---|---|---|
predator/ |
predator strategies, encirclement, fragmentation, reunion, sensing, adaptive radius, prey fatigue, predictive encirclement, collective/local escape (F5–F16, F19, F21–F22, F28, F31–F35, F53, F66–F71) | encirclement_scaling.py, adaptive_encirclement.py, fragmentation.py, long_encirclement.py, fatigue.py |
contagion/ |
panic, SI/SIS contagion, vaccination, segregation, mixing, heterogeneous recovery, slow-recoverer targeting (F18–F37, F47–F48, F52, F54–F64) | contagion_sis.py, targeted_immunity.py, spatial_vaccination.py, recovery_heterogeneity.py, slow_recoverer_vaccination.py |
phase/ |
finite-size scaling, hard repulsion, Langevin, hexatic order parameter (F2, F8, F12, F17, F38–F40, F50) | phase_transition.py, langevin_repulsion.py, langevin_hexatic.py, langevin_hexatic_hard.py |
3d/ |
three-dimensional flocking, predators, vaccination, segregation, slow-recoverer targeting, transect-predator robustness (F41–F46, F49, F51, F58, F65) | flocking3d.py, flocking3d_predator.py, flocking3d_vaccination.py, flocking3d_slow_vaccination.py |
collective/ |
collective decision-making — informed-minority leadership, conflicting leaders, compromise vs consensus, numbers-vs-conviction product law, time-resolved decisions & critical slowing, signal-vs-identity rotation, steering bandwidth, leadership-vs-encirclement, leadership-under-panic, adversarial leadership, fraction-not-number scaling self-test, many-wrongs wisdom-of-crowds navigation, correlated-estimate ceiling, noisy-minority mechanism split, misinformation robustness, moving-goal crowd tracking (F72–F86; leadership.py lives at root) |
conflicting_leaders.py, conviction.py, decision_time.py, rotate_leaders.py, moving_goal.py, led_encirclement.py, panic_leadership.py, adversarial_leaders.py, leader_scaling.py, many_wrongs.py, correlated_estimates.py, noisy_minority.py, misinformation.py, moving_goal_crowd.py |
evolution/ |
co-adaptation — heritable per-agent escape weight under capture/removal selection vs the predictive predator; the F70 valley as an evolutionary brake (F87) that blocks origination but not invasion (F88); robust free-rider equilibrium (F89); two-sided arms race with a co-evolving predator (F90); direct capture-vs-lead diagnostic (F91 self-test, correcting F90); energy-budget robustness check (F92). Builds on the validated vectorized_predator.py + vectorized_predator_prey.py harness. |
escape_evolution.py, escape_invasion.py, escape_freerider.py, escape_coevolution.py, escape_capture_curve.py, escape_energy.py |
A complete file-by-file index lives in the per-finding evidence sections of findings.md. A predator-force sign bug in the 3D scripts was found and fixed in May 2026 (commit 30ead1c); F43/F44/F45/F49 were rerun with the corrected sign and write-ups updated.
| File | Description |
|---|---|
make_demo.py |
Generates figures/demo.gif for this README |
build_report.py |
Generates report_draft.pdf from report_draft.md using reportlab |
sim_demo.html |
Interactive browser simulation (open locally or via htmlpreview link above) |
logs.html |
Time log and research log — open in browser |
findings.md |
Running notes on all 92 findings with figures |
report_draft.md |
Full research report in Markdown |
All experiment scripts are invoked from the repository root and write figures into figures/ and logs into outputs/.
# Validation, phase transition, baseline (root-level legacy scripts)
python analysis.py
# Phase transition (subfolder)
python phase/phase_transition.py
python phase/compactness_search.py
python phase/langevin_hexatic_hard.py
# Predator strategy (legacy roots + new subfolder)
python predator.py
python multi_predator.py
python encirclement.py
python predator/encirclement_scaling.py
python predator/adaptive_encirclement.py
python predator/long_encirclement.py
python predator/fatigue.py
python predator/predictive_encirclement.py
python predator/predictive_adaptive_encirclement.py
python predator/predictive_noisy_encirclement.py
python predator/predictive_delayed_encirclement.py
python predator/collective_escape.py
python predator/local_escape.py
# Contagion, vaccination, mixing
python contagion/contagion_sis.py
python contagion/targeted_immunity.py
python contagion/spatial_vaccination.py
python contagion/topological_mixing.py
python contagion/contact_freezing.py
python contagion/mixing_dimension.py
python contagion/recovery_heterogeneity.py
# Heterogeneity and slow-recoverer vaccination (F55-F61)
python contagion/infectiousness_heterogeneity.py
python contagion/slow_recoverer_vaccination.py
python contagion/het_recovery_spatial.py
python contagion/continuous_gamma_vaccination.py
python contagion/noisy_gamma_vaccination.py
python contagion/rare_reservoir_vaccination.py
python contagion/drifting_gamma_vaccination.py
python contagion/het_beta_gamma_vaccination.py
python contagion/predator_slow_vaccination.py
# 3D extension
python 3d/flocking3d.py
python 3d/flocking3d_predator.py
python 3d/flocking3d_vaccination.py
python 3d/flocking3d_segregation.py
python 3d/flocking3d_slow_vaccination.py
python 3d/flocking3d_transect.py
# Collective decision-making / leadership (F72-F86)
python leadership.py
python collective/conflicting_leaders.py
python collective/conviction.py
python collective/decision_time.py
python collective/rotate_leaders.py
python collective/moving_goal.py
python collective/led_encirclement.py
python collective/panic_leadership.py
python collective/adversarial_leaders.py
python collective/leader_scaling.py
python collective/many_wrongs.py
python collective/correlated_estimates.py
python collective/noisy_minority.py
python collective/misinformation.py
python collective/moving_goal_crowd.pyFor the full set of scripts and what each tests, see the per-finding sections of findings.md.
Open sim_demo.html in a browser for a real-time interactive simulation with adjustable parameters.
- Language: Python 3 — numpy, matplotlib, reportlab
- AI assistance: Claude (Anthropic) — code generation, debugging, research guidance. All AI use documented in research log.
Charbonneau, P. (2017). Natural Complexity: A Modeling Handbook. Princeton University Press.
Silverberg et al. (2013). Collective motion of humans in mosh and circle pits. Physical Review Letters, 110, 228701.