# Complex system A complex system comprises many interacting elements whose collective behavior exhibits nonlinearity, [[Feedback|feedback]], adaptation, spontaneous order, and [[Emergence|emergence]] that cannot be predicted from the parts alone. Open, far-from-equilibrium networks—an [[Ecosystem|ecosystem]], a brain, a city, a market—display critical transitions, nested hierarchies, small-world topologies, and edge-of-chaos dynamics. <!-- LEGACYSIM:BEGIN v1.5 — generated by g03_mint_wave.py; three.js first; do not hand-edit inside --> ## Microsims (promoted from legacy — three.js first) ### MicroSim spec ### Parameters (tunable controls) - `Agent count` · 10–500 · number of locally-interacting units - `Coupling strength` · 0–1 · how strongly neighbours influence each other - `Noise` · 0–1 · random perturbation injected each step ### What animates Many agents interact locally; a global pattern (clusters/waves) emerges on the canvas. ### Learning objective Show how local interactions among many agents produce emergent global patterns. ### MicroSim spec - **Recommended sim type:** particle/agent simulation - **Microsimmability score:** 100/100 - **Layout:** agent field (canvas) on top with an order-parameter readout; sliders below. ### Parameters (tunable controls) - `Number of agents N` - `Interaction radius` - `Coupling strength` ### What animates Many simple agents follow local rules; a global pattern emerges and shifts as the rule parameters change. ### Learning objective Show how local agent rules produce emergent global order. ### MicroSim spec - **Recommended sim type:** [[Agent-based_model|agent-based model]] - **Microsimmability score:** 78/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Number of parts` - `Coupling strength` - `Noise` ### What animates Many coupled parts interact and the whole shows behavior absent from any single part. ### Learning objective Show how interactions among many parts give a [[System|system]] its collective behavior. ### MicroSim spec - **Recommended sim type:** agent-based - **Microsimmability score:** 80/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Number of components` - `Coupling strength` - `Noise` ### What animates Many coupled components interact and a [[System|system]]-level pattern emerges as [[Coupling|coupling]] changes. ### Learning objective Show how interacting parts produce hard-to-predict collective behavior. <!-- LEGACYSIM:END --> <!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside --> ## Microsims — three.js ### Complex system (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Complex_system.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Complex system — three.js microsim"></iframe> </div> **Open it full-screen:** [Complex_system.html](https://wikitube-3d-microsims.netlify.app/Complex_system.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree: - [[Agent-based_model]] *(in tree)* - [[Emergence]] *(in tree)* - [[Feedback]] *(in tree)* - [[Network_theory]] *(in tree)* - [[Phase_space]] *(in tree)* - [[Self-organization]] *(in tree)* *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.* <!-- MICROSIMGEN:END --> ## Reveal %%REVEAL:p5%% %%REVEAL:d3%% %%REVEAL:three%% --- *Concept aligned with [Wikipedia](https://en.wikipedia.org/wiki/Complex_system); adapted text, where present, is licensed [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/).* ## Overview Formally, complexity lives where the [[Dynamical_system|dynamical system]] meets the [[Nonlinear_system|nonlinear system]]: trajectories in [[Phase_space|phase space]], [[Chaos_theory|chaos]], [[Phase_transition|phase transitions]], and [[Self-organization|self-organization]] far from equilibrium in the tradition of [[Ilya_Prigogine|Ilya Prigogine]]. Structure is read through [[Graph_theory|graph theory]] and [[Information_theory|information theory]]; strategy among adaptive agents through [[Game_theory|game theory]], [[Bounded_rationality|bounded rationality]], and the [[Prisoner's_dilemma|prisoner's dilemma]]. Executable complexity runs on the [[Agent-based_model|agent-based model]], the [[Cellular_automaton|cellular automaton]], the [[Multi-agent_system|multi-agent system]], and the [[Genetic_algorithm|genetic algorithm]], with [[Neural_network_(machine_learning)|neural networks]] carrying the theme into [[Artificial_intelligence|artificial intelligence]]. The lineage threads [[Cybernetics|cybernetics]] and [[Systems_theory|systems theory]] through [[Jay_Wright_Forrester|Forrester]]'s [[System_dynamics|system dynamics]] into today's [[Systems_biology|systems biology]] and [[Systems_science|systems science]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Complex_system) : [Wikitube](https://en.wikitube.io/wiki/Complex_system) ## Previous hub tags Hubs: `Systems`. Portals: [[PORTAL_Systems]], [[PORTAL_Complex_system]].