SwarmWorld: Stigmergic technological evolution in societies of language-model agents

Subhadeep Pal; Fiona Y. Wang; Markus J. Buehler

Figure 1: Conceptual lineages leading to SwarmWorld; connectors indicate conceptual convergence rather than direct descent between every adjacent item. (A) Biological collectives and swarm-computing methods contribute decentralized coordination, feedback, and stigmergy. (B) Local-rule models and artificial societies contribute persistent worlds in which local actions alter shared state and generate population-level organization. (C) Distributed-agent and LLM systems contribute explicit agent state, memory-guided planning, embodiment, communication, and reusable executable skills. (D) SwarmWorld combines these elements in a materially constrained multi-agent world where agents build persistent artifacts and inherit or modify their programs. The resulting technological ecology can be evaluated after the agents are removed. Image credits. Ant photograph by Kiran Vati K, CC BY 4.0 , cropped and color-adjusted. Boids still from a video by Andrew Magill, CC BY 2.0 , with a frame extracted, cropped, and color-adjusted. Game of Life glider-gun diagram by Bryan.burgers, public domain , placed on a grid background. Micropolis screenshot based on the original software by Will Wright and Maxis Software/Electronic Arts, the Unix port by Don Hopkins and DUX Software, screenshot by Tomhannen, and edit by bayo; GPLv3 or later with Section 7 additional terms , cropped and color-adjusted. The Sugarscape view, method schematics, and SwarmWorld rendering were created by the authors.

Figure 2: Simulated world and agent-environment algorithm. (A) Authoritative state at tick 600 from a representative

N=200

society. Numbered callouts identify language-model agents, persistent agent-built artifacts, fixed processing stations, resource biomes, an active disturbance field, and tidal resources. The map is the state on which actions are resolved, not a decorative visualization. Agents can move through the terrain, gather and transform matter, inspect or operate artifacts, and encounter local environmental changes produced by both disturbances and other agents. (B) One staggered macroturn begins with a local observation and retrieved private memory, continues through language-model deliberation and a strict structured plan, and ends with transactional validation of actions, targets, permissions, and material preconditions. The deterministic world tick then advances motion, metabolism, resources, fields, disturbances, and every installed artifact program. Resulting events enter agent memory and the shared substrate before the next scheduled observation. The agents decide what to try, but the world decides what actually happens; durable artifacts let one agent’s successful work become part of another agent’s future environment.

Figure 3: Mechanism-resolved conditions and the agent-free held-out resilience assay. (A) Rows define the four interventions and columns identify the mechanisms available in each. A filled circle means the mechanism is present. Full culture combines a shared physical world, explicit cultural actions, cross-agent program inheritance, and artifact stigmergy. No communication removes nearby messages, public records, teaching, trading, task claims, and publication-dependent composition while preserving the shared world and executable inheritance. No explicit culture also removes cross-agent program forking and measured skill inheritance, leaving agents able to coordinate only through persistent artifacts and environmental changes. Independent search consists of

N

isolated one-agent worlds and therefore has none of the three collective mechanisms. (B) At a discovery checkpoint, the complete state is frozen into eight exact clones. Each clone receives a paired unseen schedule of contamination, drought, and storm, with new centers, timings, and orderings. Agents take no actions during evaluation, but the world physics and installed artifact programs continue. Balanced service coverage

Q_{s}(t)

is integrated over assay time and averaged across schedules to produce held-out resilience. The assay asks whether the technology left behind can protect the habitat under new stresses after its inventors have gone.

Figure 4: Population scaling and mechanism-resolved collective effects over 800 discovery ticks. Points and heavy lines in panels A-D are means across four matched world seeds; error bars are paired seed-bootstrap 95% intervals. (A) Discovery-frontier AUC integrates the running best measured artifact performance, rewarding discoveries that occur early and remain on the frontier. (B) Held-out resilience AUC measures agent-free service coverage under eight unseen disturbance schedules. (C) Portfolio resilience quantifies the breadth and redundancy of functional service across the final artifact collection. (D) Validated inventions count technologies that pass the simulator’s objective validation criteria. (E) Each cell is a shared-world condition minus the paired endpoint-wise independent-search envelope. Printed values are raw paired effects, asterisks mark intervals excluding zero, and color is normalized within each outcome row because the four outcomes have different units. The shared world yields the most consistent gains in held-out and portfolio resilience and in invention count, whereas discovery AUC depends on condition and scale. Societies become better at building useful collections of technologies, but more communication does not automatically make them better at finding the single fastest early winner.

Figure 5: Data-driven behavioral phenotypes discovered in the 800-tick scaling study. Each point represents one complete agent trajectory, and the two-group k-means classification is learned from 15 robust-scaled behavioral features without access to condition, population, seed, identity, or an assigned role. (A) PCA gives an auditable linear projection. The numbered arrows are the six largest loading vectors and point toward increasing social interaction, cultural coordination, technology work, artifact proximity, construction/control, and net displacement. Clustering is performed in the full feature space rather than in this two-dimensional display. (B) Cluster-average standardized signatures identify C1 as artifact-centered work and C2 as mobile exploration; red indicates above-corpus values and blue indicates below-corpus values. (C) Stacked bars show the mean

N=200

composition, with four seed fractions overlaid. (D) The artifact-centered fraction is followed across

N=50

, 100, and 200 for each shared-world condition. Initially identical agents divide into a smaller group that stays near and works on technology and a larger group that continues exploring, and explicit culture shifts more agents toward the technology-centered mode.

Figure 6: Executable technological culture. Seed means and 95% seed-bootstrap intervals are shown across population size. (A) Fraction of constructed artifacts with recorded contributions from multiple agents. Full culture produces the largest collaborative fraction at every population, while appreciable collaboration without explicit culture demonstrates that agents can still meet around and modify persistent objects. (B) Fraction of eligible program forks whose child author differs from the parent author. Cross-agent descent grows with population under full culture and remains possible without direct communication because executable inheritance is still available in that intervention; it is zero by construction when explicit culture and cross-agent inheritance are disabled. (C) Focused content-addressed program lineage centered on Adaptive Chitin Maintenance . Gray boxes are ancestor programs, the green box is the focal program, and purple boxes are descendants. Each node records first tick, number of authors, and installations; each arrow records fork tick, author, and instruction-level edit count. Agents did not merely discuss ideas: they reused, edited, installed, and propagated one another’s executable environmental controllers, producing attributable technological descent.

Figure 7: Sixteen ranked, deduplicated agent-invented technologies from the 800-tick study. The colored rule above each panel identifies its experimental condition and the number at upper right is lifetime-peak simulator performance. Panels A-D show the Three Layer Connected Chitin Exchange Lattice, Mycelial Mineral Spring Veil, Fermented Tidal Chitin Panel, and Breathing Cuticle Veil. Panels E-H show the Myco Repair Exchange Panel, Replicated Tri-Phase Healing Exchange Lattice, Chitin Healing Vein Partition, and Myco Mend Lattice. Panels I-L show the Myco Porous Buffer Sheet, Catalyst Springveil Reactive Lattice, Catalyst Venation Habitat Membrane, and Cellulose Nutrient-Moisture Exchange Trellis. Panels M-P show the Stonecap Mycelial Vent Panel, Basalt Mycelium Lattice, Hyphae Pulse Interface, and Kelp Shell Tideveil Panel. Each portrait combines a complete form, partial cutaway, and dominant component specimens inferred from the recorded architecture, geometry, composition, process sequence, and controller. Text below each image reports the input-process-output flow, agent-authored functional claim, sensor-to-actuator control signature, and leading material fractions. The society explored multiple technological families rather than converging on one prewritten object; the images communicate the proposed mechanisms, while the quantitative score comes only from the simulator. See Section S2.13 for details on how these representative technologies were selected.

Figure 8: Representative

N=200

movement trajectories from matched seed-3202 societies. For readability, 24 deterministically selected complete paths are shown in each panel over the identical terrain. White circles mark trajectory starts, colored circles mark endpoints, and gold diamonds mark artifacts active at tick 800. (A) Full culture produces paths that repeatedly intersect the central artifact ecology; all-agent summaries report mean path length 36.0 cells, 3.3 regions visited, and artifact-contact AUC 0.31. (B) Without explicit culture, mean path length remains 36.0 cells, but region coverage falls to 2.7 and artifact-contact AUC to 0.14. (C) Without communication, mean path length is 37.0 cells, region coverage is 2.6, and artifact-contact AUC is 0.11. The inset values use all 200 agents, not only the displayed paths. The agents travel similar total distances, but full culture makes their movement more likely to intersect the shared technological infrastructure.

Figure 9: Movement linked to scientific work and interaction in representative

N=200

societies. Eighteen focal agents per condition are selected by round-robin ranking on distance, artifact work, social interaction, and successful actions so that the display spans the observed behavioral repertoire. Segment color gives instantaneous path speed in cells per tick. Blue circles mark observations or tests, gold diamonds mark artifact construction, purple triangles mark program installation, coral stars mark explicit interaction, and black squares mark active artifacts; square area increases with the number of distinct participants. (A) Full culture combines broad observation with dense construction, installation, and explicit social events around shared artifacts. (B) No explicit culture retains observation and physical artifact work but lacks the direct cultural channel. (C) No communication shows the corresponding spatially mediated activity when messages are unavailable. These are not simply tracks of where agents wandered: they show when travel became measurement, building, code deployment, or coordination, and where repeated work turned artifacts into local activity hubs.

Figure 10: Within-run evolution of a representative no-explicit-culture society with

N=200

and seed 3202. (A-C) Authoritative world states nearest ticks 0, 400, and 800; the stored snapshots occur at ticks 0, 408, and 800. Agents are black circles, artifacts are gold diamonds, and processing laboratories are open squares. The artifact count increases from 0 to 25 to 61 as the disturbance field and local activity pattern change. (D) Stepwise accumulation of persistent artifacts across the episode. (E) Running best artifact performance and portfolio resilience. The best-object curve rises rapidly after the first construction wave, whereas portfolio resilience grows more slowly as the society adds complementary technologies. (F) Normalized spatial entropy of agent occupancy on a fixed

10\times 10

grid declines from roughly 0.86 to 0.76, indicating moderate concentration rather than complete aggregation. Agents progressively convert an initially empty landscape into a persistent technological habitat; the first strong object appears quickly, but a useful portfolio and stable spatial organization take longer to assemble.

Figure 11: Recorded knowledge lineage from evidence to technology. (A) Society-scale directed ancestry of eight high-performing active artifacts. Circles denote agents, squares denote evidence, small gold nodes denote insights, purple hexagons denote executable programs, and green diamonds denote artifacts. Typed arrows encode authorship or observation, recorded parent references, construction, installation, and program forking; node area increases with betweenness centrality. Labels are selectively placed to preserve readability. (B) Focused ancestry around AdaptiveChitinExchangeScaffold . Multiple agents, evidence records, precursor artifacts, and inherited programs converge on the target artifact; arrow direction is from recorded precursor to downstream record, program, or artifact. (C) Evidence, insight, and program nodes ranked by the number of distinct downstream artifacts they reach. The passive material system has the largest reach, followed by several maintenance and exchange records. Technologies are not isolated model responses: recorded observations and executable ideas become reusable building blocks that pass through several agents and contribute to multiple later artifacts.

Figure 12: Construction and operational matter pathways for the 16 technologies in Figure 7 , retained in the same A-P order. The left matrix reports construction feedstocks. Filled circles identify named recipe inputs and circle area increases with input mass; gray open circles mean that the material is absent. The center matrix reports fabrication sequence. Connected numbered circles provide the exact processing order, distinguishing, for example, wash-grind-ferment routes from mineralize-align-weave routes. The right matrix reports realized operational matter flow per 100 active ticks in the authoritative final snapshot. Filled colored circles and printed values encode the realized rate; colored open circles indicate that a controller pathway exists but had zero realized flux; gray open circles indicate that the pathway is unavailable. Water capture transfers local moisture into artifact storage, contamination removal reduces the environmental field, and embodied reserve supports repair, growth, and nutrient release. Construction feedstocks are consumed once at build time and are not automatically replenished during operation. The figure distinguishes what an artifact is made from, how it was fabricated, and what it actually did after construction; only the final columns are evidence of executed simulator function.

Figure 13: Outcome-dependent cultural crossover over 3,200 discovery ticks. Four matched

N=100

seeds are evaluated at five frozen checkpoints. Thin lines are individual world seeds, heavy lines are seed means, and shaded regions are 95% seed-bootstrap intervals. (A) Agent-free held-out resilience for full culture, no explicit culture, and the endpoint-wise best-of-100 independent-search envelope. Both shared worlds generally remain above the isolated envelope, but their ordering changes. (B) Paired full-minus-no-explicit-culture held-out effect; the mean changes sign and ends near zero. (C) Best active artifact performance crosses in favor of full culture by tick 800. (D) Portfolio resilience crosses near tick 1,600 and remains modestly higher under full culture. (E) Cumulative artifact production also crosses near tick 1,600 and ends at means of 277.5 versus 238.5 artifacts. (F) Validated inventions never cross; no explicit culture remains higher at every checkpoint and ends at 7.0 versus 5.75. Explicit culture helps some capabilities after enough time, but there is no single moment after which it improves everything.

Figure 14: Long-horizon endpoint tradeoffs at tick 3,200 for four matched

N=100

world seeds. Conditions are full culture, no explicit culture, and an endpoint-wise best-of-100 isolated envelope. Filled points are individual seed outcomes, gray lines preserve within-seed pairing, open diamonds are means, and error bars are 95% seed-bootstrap intervals. (A) Portfolio resilience favors both shared worlds; full culture averages 0.2474, no explicit culture 0.2365, and isolated search 0.1794. (B) Validated inventions likewise favor shared worlds, with means of 5.75, 7.00, and 2.75. (C) Held-out resilience is highest on average without explicit culture, 0.0446, compared with 0.0356 in the isolated envelope; full culture is similar to no explicit culture at the endpoint. (D) Best final artifact reverses the ordering: the isolated envelope averages 0.3488 versus 0.2380 for full culture. Societies win by maintaining several complementary technologies, while isolated agents can still win a contest defined only by the strongest single artifact.

Figure 15: Cultural self-organization couples spatial hubs to executable code descent. (A) Phase portrait of mean cumulative path length and local regional crowding for full culture and no explicit culture. Light trajectories are the four matched seeds, heavy trajectories are seed means, numbered checkpoints indicate ticks 400, 800, 1,600, 2,400, and 3,200, and arrows point forward in time. Full culture ends with shorter paths and greater crowding, consistent with localized technological hubs. (B) Full-minus-no-explicit-culture allocation of active actions in five time windows, in percentage points. Movement and observation decline relative to the ablation, while explicit cultural activity and construction/control increase. (C) Mean maximum executable-program fork depth rises from 3.75 at tick 400 to 9.75 at tick 3,200, while approximately half of eligible forks remain cross-agent. (D) Exact deepest content-addressed lineage from full culture, seed 3301. Green nodes form the 12-edge longest path, purple nodes are deterministic one-hop branches, coral arrows are cross-agent forks, gray arrows are same-author or starter forks, and node area increases with installation count. The society gradually stops roaming as widely, concentrates around shared infrastructure, and builds a many-generation inheritance system for executable technology.

Figure 16: Explicit culture reorganizes physical behavior around shared artifacts. Each point in panels A and B is a complete 3,200-tick trajectory from the eight

N=100

shared-world episodes. A two-group k-means model is fit in the original nine-dimensional robust-scaled physical feature space without condition, seed, identity, communication, cultural-action, or technology-work labels. (A) PCA gives an auditable linear display; numbered arrows point toward increasing values of the five strongest loading features. (B) UMAP shows nonlinear neighborhood structure, but its axes have no direct behavioral meaning. (C) Cluster means identify C1 as artifact-centered movement, characterized by greater artifact proximity and artifact-bound motion with shorter and less frequent travel, and C2 as mobile exploration. (D) Thin lines pair the four seeds, filled circles are seed fractions, and open diamonds are means. Full culture increases the C1 fraction from 31.0% to 52.8%, a paired gain of 21.8 percentage points; the 95% seed-bootstrap interval is 12.0 to 33.5 points and the clustering silhouette is 0.472. Explicit culture changes where agents physically spend their lives, not only what they say.

Figure 17: A technological society develops persistent temporal circuitry. (A, B) Complete recovered interaction histories for matched

N=100

, seed-3301 full-culture and no-explicit-culture societies over 3,200 ticks. Horizontal tracks in the upper band are agents and tracks in the lower band are artifacts; each artifact track starts at construction. Vertical strokes connect entities at the exact event tick. Blue encodes observation, gray-green recorded parent reference, gold construction, purple program installation or executable descent, and coral explicit messaging. Repeated observations and messages are display-binned with exact counts retained; construction and executable events remain at exact ticks. Tracks are ordered by final data-derived community, not assigned role. The full-culture example records 389 artifacts, 3,924 delivered-message recipient edges, and 358 cross-artifact program-descent events; the matched ablation records 248 artifacts and lacks the disabled event types. (C) Interaction modularity remains substantial, indicating local technological neighborhoods. (D) Adjusted mutual information between successive community assignments rises, showing that those neighborhoods acquire memory. (E) The percentage of artifacts touched by a noncreator approaches saturation in both conditions. A dense web of recurring relationships grows over time, and explicit culture adds message and code-inheritance pathways without replacing physical artifact-mediated coordination.

Figure 18: Network anatomy of the long-horizon technological society. (A, B) Deterministic visualization backbones of matched

N=100

, seed-3301 networks accumulated over 3,200 ticks. The underlying graph links agents to artifacts through observation, recorded parent reference, construction, contribution, programming, repair, and dismantling. The display retains each node’s two strongest physical ties and a maximum-weight spanning tree for each component, then adds the strongest local social-exchange and executable-lineage ties. This is a reproducible readability filter, not a significance threshold; complete graphs are retained in GraphML. Full culture produces 489 displayed nodes and 1,156 edges, versus 293 nodes and 514 edges without explicit culture. Circles are agents, diamonds are artifacts, edge color denotes interaction layer, and node area increases with interaction count. Node color denotes community within a panel; colors do not identify matched communities across conditions. Labels beginning with A are stable agent identifiers. (C, D) Degree-conditioned agent coordination projections. An agent pair is validated only when it shares at least two artifacts and its overlap exceeds a hypergeometric null conditioned on both agents’ artifact degrees, after Benjamini–Hochberg correction at

q\leq 0.05

. Full culture yields 1,100 validated pairs among 92 agents, compared with 261 pairs among 45 agents without explicit culture. The display keeps each agent’s four strongest local surprise links, while GraphML retains all validated pairs. (E) The analogous artifact co-use projection joins technologies used by unexpectedly overlapping agent populations, not technologies with merely similar names. Full culture contains 18,563 validated pairs among 385 artifacts; 710 strongest local links are displayed across 15 components. (F) Node-role cartography. Participation coefficient measures cross-community mixing, and within-module z-score measures local centrality. Reference lines at 0.62 and 2.5 are heuristic thresholds from prior work rather than universal classification boundaries. All nodes have participation below 0.26, and only four full-culture artifacts exceed the hub reference line. (G) Replicated temporal comparison across four matched seeds and five checkpoints. Thin lines are seeds and heavy lines are means; solid curves show binary NODF nestedness divided by 100 and dashed curves show mean agent participation. At tick 3,200, mean nestedness is 0.094 under full culture and 0.096 without explicit culture, while mean participation is 0.0016 and 0.0044. Explicit culture creates a larger and more statistically connected technological network, but it does not merge the society into one centralized hierarchy. Both conditions form specialized local neighborhoods, with explicit culture adding more pathways among them.

Figure 19: Technological interaction networks assemble, differentiate, and retain relationship memory. (A, B) Temporal allocation of eight event classes across 32 nonoverlapping 100-tick intervals under full culture and no explicit culture. Each row is normalized to sum to 100%, so color locates when that event type occurs rather than comparing absolute counts between rows. (C, D) Alluvial maps follow all 100 agents in matched seed 3301 among Louvain communities at ticks 400, 800, 1,600, 2,400, and 3,200. Community identities are propagated by maximum-overlap matching, and ribbon width is the exact number of transitioning agents. (E) Cumulative unique agent-artifact ties plotted against agents plus constructed artifacts on log-log axes. Thin lines are seeds, heavy lines are means, and the fitted descriptive exponents are

\alpha=3.47

for full culture and

\alpha=3.48

without explicit culture. The exponent describes densification with network size, not growth per unit time. (F) Fraction of interval ties reused in the next interval, rising to means of 0.650 and 0.588. Both societies develop stable neighborhoods, but full culture produces roughly twice as many distinct agent-technology relationships by tick 3,200 and retains more of them from one period to the next.

Figure 20: Technology diffusion through the shared world. (A) Temporal motif tested under full culture. A creator messages, teaches, or trades with the eventual first adopter at

t_{1}

, and that agent first reuses the artifact at

t_{2}

. The double-headed bracket denotes the elapsed lag

\Delta t=t_{2}-t_{1}

; it is not an additional interaction edge. (B) Observed motif frequency divided by a 200-replicate timestamp-shuffled null that preserves directed dyads and the global activity schedule. The dashed line is parity. The mean ratio is 1.175 at a 25-tick lag but remains below one at 50 to 400 ticks, so direct transmission is not consistently enriched. (C) Kaplan–Meier fraction of artifacts not yet reused, with unreused artifacts right-censored at tick 3,200 34 . (D) Complementary cumulative distribution of distinct noncreator adopters. The full-culture intervention produces earlier and broader reuse. (E) First-reuse channels; approximately 95% of adoption begins with physical observation in both conditions, while recorded parent reference and programming are much rarer immediate channels. (F) Maximum executable lineage depth grows to a mean 9.75 under full culture and remains zero where cross-agent program descent is disabled. The explicit-culture intervention is associated with faster and broader reuse, but most agents encounter technology through the shared world rather than receiving a direct handoff from the inventor.

Figure 21: Zoomed-in view of a representative SwarmWorld AshenRealm environment. The rendering shows the

72\times 54

-cell world for seed 1703, highlighting the spatial substrate through which agents explore, gather resources, fabricate materials, and construct persistent technologies. Distinct environmental regions include magma sea and resource biomes such as the iron mountain, lava channel, sulfur marsh, and obsidian waste. Cross-world transfer of collective technological behavior from BioFoundry to AshenRealm. Twelve endpoints summarize societies operating in the original BioFoundry and the independently specified volcanic AshenRealm environment: (A) best-artifact performance, (B) discovery-frontier AUC, (C) behavioral novelty, (D) validated inventions, (E) collaborative-artifact fraction, (F) cross-agent program-fork fraction, (G) number of program forks, (H) held-out resilience AUC, (I) portfolio resilience, (J) program-lineage depth, (K) mean distance traveled, and (L) mean number of cells visited. AshenRealm occupies a different functional regime, with lower performance and resilience measures, but retains multi-agent construction, executable inheritance, lineage formation, and broad spatial exploration.

Figure 22: Representative agent-invented technologies in AshenRealm with full communication between agents (N=50). Eight performance-ranked technologies drawn across AshenRealm world seeds illustrate the material and functional design space generated by the agents. (A–D) The Cinderveil Thermal Segment, Ashbound Obsidian Threshold Baffle, Emberfracture Segment Shield, and Emberglass Load Shield are predominantly obsidian-based thermal and structural systems with lifetime-peak simulator performances of 0.248, 0.214, 0.207, and 0.156, respectively. (E–H) The Embervein Provenance Loadshield, Ashgate Vent Loadshield, Ashbound Meridian Baffle, and Cindervein Interlock Shield are iron-rich load-bearing and heat-management systems with performances of 0.148, 0.135, 0.133, and 0.116. Each panel reports the recorded material-processing pathway, agent-authored functional description, installed controller program, dominant composition, world seed, and construction tick. The renderings visualize the recorded architecture and proposed operating mechanism; they are not literal simulator meshes or experimentally manufactured structures. All quantitative performance values are obtained from the deterministic simulator.

Figure 23: Production state of the Protein Realms no-communication society at tick 800 (

72\times 54

traced cells,

N=50

, seed 3801). The four-sided isometric plane is the complete traced rectangular terrain, containing a solvent sea, amino-acid basin, membrane lagoon, chaperone forest, cysteine marsh, cellulose plains, metal-and-salt peaks, ribosome enclave, and stress proving ground. Patterned glyphs mark a deterministic spatial sample of the trace’s molecular-feedstock cells for legibility. Numbered markers identify the ribosome array, purification column, matrix loom, folding chamber, stress assay, and sequence archive; white circles are final agent positions. The green marker is the persistent collagen–cellulose installation constructed at tick 741. Separating feedstocks, processing facilities, and the proving ground forces designs to move through an executable spatial workflow rather than being scored directly from language.

Figure 24: Trace-grounded designs and outcomes from the single-seed, 800-tick Protein Realms pilot. (A) Stage counts from proposals through microbatches, tests, and persistent installations across all four conditions; endpoint labels give mean resilience AUC across eight frozen, agent-free disturbance schedules. Independent member 15 is the selected member of the predeclared best-of-50 isolated-search envelope and represents one 16-call world, not another shared

N=50

society. (B) The three realized installations. Colored sequence strips reproduce the exact retained catalog sequences by residue class; the adjacent protein-in-cellulose drawings are explanatory architecture schematics, not molecular-structure predictions. (C) Recorded recipe inputs and executed fabrication pathways. Bar widths give input mass fractions, numbered nodes preserve operation order, and node color encodes recorded intensity. (D) Realized consequences: normalized tested utility and heat, protease, and flood/shear resistance, followed by health and current performance at tick 800. These are simulator outputs from fixed catalog priors and executed recipes, not biochemical measurements. Only no communication and the selected independent member completed the hidden spatial assay gate; full culture and no explicit culture therefore remain visible in panel A but have no invented design rows. The pilot demonstrates an executable sequence-to-persistent-material workflow but does not support inferential comparison among conditions.

Term	Technical definition	Plain-language meaning	Broad example
World tick	One discrete deterministic state transition, $S_{t+1}=F(S_{t},A_{t})$ , where $S_{t}$ is the complete world state and $A_{t}$ is the set of accepted agent actions at tick $t$ . Given the state, actions, and seeded disturbance schedule, $F$ advances movement, metabolism, resources, fields, artifacts, and installed programs.	The basic clock step of the simulated world. The world keeps changing even when no agent is currently asking the language model what to do.	A video game advances one frame at a time; machines, weather, and moving characters continue between a player’s major decisions.
Macroturn or decision opportunity	A scheduled occasion on which one agent receives a local observation and memory context, calls the language model, and proposes a structured multi-action plan. Macroturn phases are staggered and matched across paired conditions.	One chance for an agent to stop, look around, think, and choose its next actions.	A field scientist periodically checks instruments and updates the day’s plan while the experiment continues running between checks.
Persistent artifact	An agent-constructed world object with recorded creator, contributors, materials, geometry, services, provenance, state, and optionally an executable controller. It remains in the world until modified, retired, dismantled, or otherwise changed by simulator rules.	A technology that stays behind and can later be found, tested, operated, or modified by someone else.	A device left on a shared laboratory bench can influence the next researcher even if its builder is absent.
Artifact program	A validated instruction sequence installed on an artifact and executed by the deterministic simulator every tick. Conceptually, $u_{a,t}=\pi_{a}(o_{a,t})$ : program $\pi_{a}$ reads the artifact’s permitted local sensors $o_{a,t}$ and emits permitted control operations $u_{a,t}$ .	Code that lets a built object sense local conditions and act without another language-model call.	A thermostat repeatedly reads temperature and turns heating on or off after the installer leaves.
Full culture	The intervention containing one shared physical world, explicit cultural actions, cross-agent executable-program inheritance, and artifact stigmergy. Explicit actions include messages, public records, teaching, trading, task claims, and publication-dependent composition.	Agents can communicate directly, inherit one another’s code, and also coordinate indirectly through the things they build.	A research group shares a laboratory, talks, writes notebooks, and modifies common software and equipment.
Artifact stigmergy	Indirect coordination produced when an agent changes persistent artifacts or the environment and another agent later observes or acts on that changed state. It remains available in the no-explicit-culture condition even when direct cultural channels and cross-agent program inheritance are disabled.	Agents coordinate through traces in the world rather than through direct conversation.	Ants coordinate through modified trails; people can likewise coordinate by adding parts or annotations to a shared workbench.

Table S1: Glossary of technical terms, implementation-aligned definitions, plain-language interpretations, and broadly accessible examples.

Condition	Available interaction substrate
Full culture	One shared world with physical stigmergy, messages, publications, teaching, trade, task claims, shared records, program reuse, and program forking.
No communication	One shared world with physical stigmergy. Messaging, publication, teaching, trade, task claims, and publication-dependent composition are removed; physically observable program reuse and forking remain available.
No explicit culture	One shared world with physical stigmergy. Communication, program forking, cross-agent sequence inheritance, the skill library, authored artifact text, and mutation-parent access are removed from the treatment interface.
Independent search	$N$ isolated one-agent copies of the seeded world. Member $i$ matches shared agent $i$ in initial position and macroturn phase. Each endpoint is the maximum over all $N$ members.

Table S2: Mechanism-resolved experimental conditions.

Figure S1: Semantic selection of representative agent-invented technologies. (A) UMAP visualization of 1,718 technologies extracted from 48 condition–population–seed episodes across the four experimental conditions. Each small point represents one complete trace-derived technology and is colored by its originating condition. Technology descriptions were encoded locally as normalized 768-dimensional vectors using google/embeddinggemma-300m . Large outlined points numbered 1–16 identify the technologies retained for the representative gallery in the main text. Nearby points have similar recorded architectures, functions, materials, fabrication processes, biological inspirations, and controller operations. UMAP used cosine distance, 30 neighbors, a minimum distance of 0.12, and random seed 42. Its axes have no direct physical meaning, and selection was performed in the original embedding space rather than in this two-dimensional projection. (B) Recorded lifetime-peak simulator performance of the 16 retained technologies, ranked from highest to lowest and colored by experimental condition. Candidates were considered in descending performance order. Exact textual duplicates were removed, no selected pair was permitted to have cosine similarity greater than 0.82, and no more than four technologies could be drawn from any of the 11 data-derived semantic clusters. Consequently, the featured set includes global performance ranks 1, 2, 3, 14, 16, 17, 22, 24, 26, 35, 54, 154, 232, 275, 300, and 366. the procedure selected strong inventions while preventing the gallery from being dominated by many nearly identical versions of the same design. Neither the UMAP coordinates nor the generated technology illustrations entered simulator scoring or statistical inference. The detailed procedure is given in Algorithm 2 .

Figure S2: Structural robustness of evolved agent-artifact networks. Rows compare full culture (A-C) and no explicit culture (D-F). At each checkpoint and seed, agents are removed randomly over 64 deterministic permutations, from highest degree downward, or from highest exact betweenness downward; the graph is not rewired. (A, D) Largest connected component retained relative to the intact network at tick 3,200 as 0 to 50% of agents are removed. Random loss is gradual, while targeted high-degree and broker removal causes greater fragmentation. (B, E) Fraction of artifacts retaining at least one surviving agent connection. After random 50% removal, access remains 0.983 under full culture and 0.952 without explicit culture; high-degree removal lowers these values to 0.596 and 0.739, and broker removal to 0.629 and 0.684. (C, F) Largest-component robustness AUC across the full removal curve at five checkpoints. Thin lines are seeds and heavy lines are means. The societies have enough overlapping participation to survive indiscriminate dropout, but a small set of highly connected or bridging agents remains disproportionately important. The assay measures graph structure only, not functional performance or adaptive recovery after knockout.

Figure S3: Zoomed-in view of a representative SwarmWorld BioFoundry environment. The rendering shows the

72\times 54

-cell world for seed 3202, highlighting the spatial substrate through which agents explore, gather resources, fabricate materials, and construct persistent technologies. Distinct environmental regions include deep water and resource biomes such as the fungal grove, cellulose field, mineral spring, and chitin field. Individual LLM agents move through these regions and interact locally with resources and infrastructure, while fixed foundries provide processing locations and agent-created artifacts persist in the environment after construction. The spatial separation of resources, processing sites, agents, and durable artifacts creates localized constraints on discovery and enables indirect coordination through repeated encounters with the modified world.

Figure S4: Behavioral specialization appears as recurring states and changes over the lifetime of the society. The analysis uses nonoverlapping 200-tick windows from 20 shared-world episodes, giving 22,400 agent-windows, with an episode-balanced sample of 16,000 used for fitting. Thirteen movement, spatial-context, task-action, and cultural-interaction features enter the model; condition, study, population, seed, identity, and time do not. (A) Silhouette audit of candidate broad mode counts. All 13 features select two broad modes with score 0.467, while an anti-circularity fit using only 11 physical/task features selects three modes with score 0.551. The adjacent bars are the accepted two-way conditional split scores inside the artifact-centered and mobile parents, 0.379 and 0.259, with a minimum 5% child occupancy. (B) PCA display of a deterministic 6,000-window sample colored by final role. PC1 and PC2 explain 44.6% and 16.1% of variance; clustering occurs in the original 13-dimensional space. (C) Mean robust-scaled feature signatures. R1 is constructor/operator, combining artifact proximity with construction and control; R2 is artifact-local caretaker, marked by artifact-local motion, processing, and maintenance-context activity; R3 is cultural coordinator, enriched in cultural and social activity; and R4 is mobile surveyor, characterized by movement and observation/testing away from persistent artifacts. (D) Mean state fractions across four N=200 seeds in the 800-tick study. (E) Mean state fractions across four N=100 seeds in the 3,200-tick study. Full-culture societies in both panels reallocate activity toward construction as they mature, and the longer run shows a pronounced coordinator-to-constructor succession. (F) Window-to-window state switching. Open circles are seed means and diamonds are condition means; full culture switches more often in both studies. Leave-replicate-out adjusted Rand indices are 0.999 for the broad modes and 0.921 and 0.980 for their conditional subdivisions. Agents do not acquire fixed assigned professions; they repeatedly enter a small, stable vocabulary of activities as the society changes. The R3 comparison is partly intervention-defined because cultural features are disabled in the ablations, whereas the three-mode physical/task-only sensitivity provides the noncircular evidence for finer differentiation. Agent windows are descriptive, seed is the inferential unit, and the two studies are not a controlled comparison of horizon alone.

Figure S5: Interactive SwarmWorld interface for visualizing collective technological discovery and knowledge evolution. The central panel provides a three-dimensional view of the shared simulation environment, in which LLM agents move through a spatially heterogeneous world, encounter resources and processing stations, and construct persistent technological artifacts. The interface reports the evolving simulation state, including the current world tick and active agent population, while selecting an agent or artifact exposes its local state, observations, and associated actions in the side panel. Persistent artifacts remain accessible to subsequent agents, allowing earlier discoveries, constructions, and executable controllers to modify the environment encountered by later agents and thereby support stigmergic coordination. Society-level trajectories displayed along the lower panel track the temporal development of collective activity and technological accumulation. The interface additionally exposes the knowledge-lineage graph, which reconstructs how scientific information propagates through the society by linking agent observations and evidence to authored insights, executable programs, precursor artifacts, and downstream technologies. Typed lineage edges record grounded events including authorship or observation, causal dependence, construction, program installation, and cross-agent program forking, allowing complex inventions to be traced back to the agents, evidence, and reusable technological components from which they emerged. In this way, the interface visualizes not only where agents act, but also how discoveries are accumulated, inherited, recombined, and transformed into persistent technologies over time. All functional outcomes are determined by the underlying deterministic simulator rather than by the visualization or agents’ textual claims.

Figure S6: Data-driven behavioral phenotypes in AshenRealm with full communication and N=50. (A) PCA projection of complete agent trajectories represented by 15 robust-scaled behavioral features. PC1 and PC2 explain 33.1% and 20.2% of the variance, respectively; numbered vectors indicate the six strongest displayed loading directions, including path length, artifact proximity, net displacement, artifact-bound movement, mobile activity, and technology work. Clustering is performed in the full behavioral feature space rather than in the two-dimensional projection. Each (B) Cluster-average standardized signatures identify C1 as artifact-centered work, C2 as mobile exploration, and C3 as stationary/low activity. (C) Behavioral composition across AshenRealm seeds 1702–1705 shows that all three modes recur across independent worlds. (D) Comparison of the artifact-centered fraction between BioFoundry and AshenRealm. The recurrence of artifact-centered and exploratory behavior under a distinct geography and materials task indicates that behavioral differentiation is not restricted to the original BioFoundry environment.

Figure S7: Within-run technological accumulation in a representative AshenRealm society with full communication with N=50 (seed 1703). (A–C) Authoritative world states at ticks 0, 400, and 800 show the progressive modification of the volcanic landscape by persistent technologies. Agents are black circles, artifacts are gold diamonds, and processing laboratories are open squares. The number of constructed artifacts increases from 0 to 2 to 20 as the world changes. (D) Persistent-artifact count through the 800-tick episode. (E) Running best-artifact performance and portfolio resilience. Best-object performance rises through discrete discovery events, whereas portfolio resilience develops as additional technologies accumulate. (F) Normalized spatial entropy of agent occupancy on a fixed

10\times 10

grid declines over the episode, indicating increasing localization of activity as persistent technological sites emerge. This single trajectory is illustrative rather than inferential, but shows how agents progressively transform a materially distinct volcanic environment into a persistent technological landscape.

Figure S8: Material inputs, fabrication pathways, and realized functions of representative AshenRealm technologies. Rows A–H correspond to the eight performance-ranked technologies shown in Figure 22 . Left: construction feedstocks recorded when each artifact was built. Filled circles identify recipe inputs and circle area scales with consumed mass; gray open circles indicate absent or unavailable feedstocks. The four highest-ranked designs (A–D) are predominantly obsidian-based, whereas E–H use iron ore. Center: ordered fabrication pathways. Filled numbered nodes identify executed processing operations and connecting lines show their sequence; open circles mark operations not used. Obsidian technologies generally employ longer multistep routes involving washing, smelting, refining, casting, forging, quenching, or annealing, while the iron-based designs use shorter wash–crush pathways. Right: realized lifetime-peak functional service recorded by the simulator. Circle area and printed values encode the realized service magnitude; open circles indicate no realized service in that dimension. Obsidian designs are dominated by thermal regulation, reaching 0.34 for the Cinderveil Thermal Segment, whereas the iron-based technologies primarily provide structural support, with several designs also contributing thermal regulation. The figure separates what matter agents actually consumed, how it was processed, and what functions the resulting artifacts actually realized, preventing agent-authored design claims from being conflated with executed simulator behavior.

SwarmWorld: Stigmergic technological evolution in societies of language-model agents

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