Simulation Speed

What you're seeing

Each tank runs an independent Bayesian agentAn agent that updates its beliefs using Bayes' theorem — combining prior beliefs with new evidence to form a posterior probability. The more evidence, the more confident the belief. simulation. Agents (nodes) run experiments to determine which of two treatments is better, share results with their network neighbors, and update beliefs accordingly.

Green particles carry honest evidence between agents. Red particles are false testimony from the agnotologistA "manufacturer of ignorance" — an agent who never updates their beliefs and always reports misleading evidence to their neighbors, attempting to prevent the network from discovering the truth. (the red node). Compare hub-biased tanks against peripheral ones — the hub agent poisons beliefs far more effectively.

Node size reflects degree centralityA measure of how many connections a node has relative to the maximum possible. High centrality = hub position = more influence over the network's collective beliefs.. Color shifts from blue (misled) through neutral to green (approaching truth).

Real-world parallels

Tobacco industry (1950s–90s): Industry-funded scientists at hub positions in citation networks published doubt about the link between smoking and cancer, delaying public consensus by decades.

Pharmaceutical lobbying: Key opinion leaders paid by companies to endorse drugs occupy central positions in medical information networks, shaping prescribing behavior across entire communities.

Build your own epistemic network. Tune every parameter and watch effects unfold in real time.
Parameters
Topology iWho talks to whom. Stars concentrate influence; cycles spread it evenly.
What Is Going On? A single hub connects to all other nodes. Extremely vulnerable to a biased hub.
Agents iNumber of scientists (nodes) trying to discover the truth. 12
Adversary Settings
Bias placement iWhere the adversary sits. Hub = many connections, Peripheral = few.
Number of Agnotologists iHow many adversaries to place in the network. More agnotologists = harder for truth to survive. 1
Bias strength i1.0 = maximal deception (always lies). 0.5 = honest half the time. 1.00
Environment
Task difficulty (δ) iGap between treatments. Smaller = harder to tell truth from noise. 0.10
Evidence per round iExperiments per tick. More = faster convergence toward or away from truth. 20
Guide: Color = belief (green truth, blue misled, red adversary). Size = centrality. Drag nodes or draw a box to group-select.
Simulation Speed

Emergence on non-standard grids

Traditional cellular automata run on a rigid 2D grid where every cell has exactly 8 neighbors. Here, we've mapped these simple rules (like Conway's Game of LifeA node is born if exactly 3 neighbors are alive, survives if 2 or 3 are alive, and dies otherwise.) onto complex network topologies.

By using Fractional Rules (e.g., a node comes to life if 25%–40% of its neighbors are alive), we reveal something profound about structures: on scale-free networks, massive hubs frequently die of "overpopulation" because they have too many alive neighbors, while peripheral chains die of "underpopulation".

Explore how fractional “birth/survival” thresholds behave on different network topologies by adjusting density, population size, and rule bounds.
Fractional Automata
Topology iThe underlying graph structure. Grids sustain life well; scale-free networks are chaotic.
Agents iNumber of nodes (cells) in the network. 64
Initial Density iFraction of nodes that start alive. Higher = more initial life. 0.35
Rule Parameters
Nodes calculate the percentage of their alive neighbors. They are "Born" or "Survive" if that percentage falls within these bounds.
Birth Threshold Min iDead nodes come alive if the fraction of alive neighbors is at least this value. 0.25
Birth Threshold Max iDead nodes come alive only if the fraction of alive neighbors is at most this value. 0.40
Survival Threshold Min iAlive nodes die if the fraction of alive neighbors drops below this value (underpopulation). 0.10
Survival Threshold Max iAlive nodes die if the fraction of alive neighbors exceeds this value (overpopulation). 0.50
Alive
Dead
Simulation Speed

Evolutionary Game Theory

These agents don't update beliefs — they choose strategiesA complete plan of action: Cooperate (always help), Defect (always exploit), Tit-for-Tat (copy your opponent's last move), or Pavlov (win-stay, lose-switch). Strategies compete for survival.. Each round, every agent plays a game with each neighbor. After all games are played, agents imitate the most successful neighbor's strategy — a process of evolutionary selectionStrategies that earn higher payoffs spread through the population, while unsuccessful strategies die out. This mirrors natural selection but for behavioral rules rather than genes..

In the Prisoner's DilemmaTwo players simultaneously choose to Cooperate or Defect. Mutual cooperation pays 3 each. Mutual defection pays 1 each. But if one defects while the other cooperates, the defector gets 5 and the cooperator gets 0. The temptation to defect is the core tension., cooperation is fragile but can survive in spatial networks where cooperators form clusters. Network topology determines whether cooperation or defection dominates — a finding with implications for institutional design.

Why topology matters

Grid/lattice: Cooperators survive by forming protective clusters. Defectors dominate edges but can't penetrate dense cooperative cores.

Scale-free networks: Hubs amplify whatever strategy they adopt. A cooperative hub can sustain cooperation network-wide; a defecting hub can collapse it.

Well-mixed (complete): No spatial structure means no shelter for cooperators. Defection typically dominates — the classic "tragedy of the commons."

Run evolutionary games on different topologies: pick the payoff structure, set population size and mutation noise, then watch strategies spread or collapse.
Game Parameters
Payoff Matrices Explained
Prisoner's Dilemma: Mutual Coop=3, Mutual Defect=1. Defecting against a Cooperator yields the Temptation payoff (T=5), leaving the Cooperator with 0.
Stag Hunt: Mutual Coop=4, Mutual Defect=2. Defecting against Coop yields 3.
Hawk-Dove: Mutual Coop=3, Mutual Defect=0. Defecting against Coop yields 4, Cooperator gets 1.
Game Type iThe payoff structure that governs agent interactions. Each game creates different strategic tensions.
Topology iThe network structure. Spatial structure can protect cooperators from exploitation.
Agents iNumber of strategic agents in the network. 36
Noise (ε) iProbability of random mutation each round. Prevents the system from getting stuck in a fixed state. 0.02
Initial Strategy Mix
Cooperators % 25
Defectors % 25
Tit-for-Tat % 25
Pavlov % 25
Advanced
Temptation payoff (T) iThe reward for defecting against a cooperator. Higher = more temptation to cheat. 5
Cooperate
Defect
Tit-for-Tat
Pavlov

Global Consensus Nodes in Epistemic Networks

What happens when we introduce an aggregator nodeA global signal that observes the average belief of the community and broadcasts it back. Agents periodically consult this signal and adjust their own beliefs toward it. Can function as a prediction market, polling aggregator, or any consensus mechanism. into a vulnerable network? The Purple Diamond represents a global consensus signal — it could act as a prediction market, a polling aggregator, or any mechanism that distills collective belief into a single reference point.

Agents intermittently check this signal and pull their beliefs toward it. The core tension: Does the aggregator protect honest agents from isolated bad actors by providing a solid global baseline, or does it accidentally amplify the bad actor's influence by broadcasting a corrupted consensus to agents who were otherwise safe?

Experiment with how aggregator nodes interact with epistemic networks under adversarial conditions.

Topology iThe underlying network structure that agents communicate through. The aggregator node sits above this structure.
Aggregator Mechanisms
Consult Frequency (f) iHow often agents check the aggregator's consensus signal. 0 = never, 1 = every round. 0.5
Aggregator Weight (w) iHow heavily agents anchor their beliefs on the aggregator signal when they consult it. Higher = stronger pull toward consensus. 0.10
Adversary Tactics
Bias Placement iWhere the adversary sits. Hub = many connections, Peripheral = few. None = no adversary.

About

Explore interactive simulations of computational agents on networks. Watch, configure, and experiment with four types of agent dynamics: Bayesian agents that update beliefs via evidence sharing, network automata that demonstrate emergent complexity from simple rules on graphs, strategic agents that model evolutionary game theory (cooperation and defection), and aggregator markets that explore how prediction-market-style consensus mechanisms interact with epistemic networks.

Research Context

These simulations grew out of research into agnotology — the study of manufactured ignorance. That work examines how a biased agent's network position amplifies its ability to suppress truth. The toolkit expanded from there into a broader set of experiments for exploring agent-based dynamics across multiple paradigms — each new simulation type offering a different lens on emergent behavior in networks.

Further reading

About the author

Created by Rouzbeh Rezaei Sanjabi as part of ongoing research in epistemic network dynamics. For full papers, more on these simulations, or to get in touch, visit rouzbehrezaei.com.

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