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Complex Systems

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Awesome Complexity Awesome

A curated list of resources related to complex systems, the scientific field studying systems with multiple interacting parts and emergent properties.

Concepts

Attractor

A trajectory in the state space of a system in which it tends to evolve towards.

Autopoiesis

The ability of a system to create and maintain itself.

Chaos

Theory of chaotic systems.

Complexity

The subject of complex systems science.

Developmental Systems Theory

Theoretical perspective on biological development, heredity, and evolution.

Dissipative System

A thermodynamically open system far from thermodynamic equilibrium.

Distributed Control

A control system without a central supervisor.

Edge of Chaos

The transition zone between order and disorder.

Emergence

The whole is greater than the sum of the parts.

Fractal

Self-similar structure.

Hysteresis

Dependence of the state of a system on its history.

Network/Graph

Network with non-trivial topological features.

Phase Transition

Transition between states of matter.

Robustness

Ability to tolerate perturbations.

Self-Organization

The process where form arises from local interactions between parts of an initially disordered system.

Simulation

Imitation of the operation of a real-world process or system.

  • Holon - System that is both a whole and a part.

Scientific Journals

Complexity

Cross-disciplinary journal about complex adaptive systems (open access).

Blogs/Journals

The Systems Thinker

Articles with a systems perspective on various topics.

Complexity Digest

News feed on complexity.

Fractal forums

Forum and discussion community about fractals.

Societies/Communities

Complex Systems Society

Scientific society for the study of complex systems.

Complexity research

Informal slack community for keeping up to date with new findings in complex systems research.

Complexity Adventures

Complexity community of practice (formerly known as Complexity Weekend).

Organizations

New England Complex Systems Institute (NECSI)

Independent academic research and educational institution.

The Vermont Complex Systems Center

Research and educational center (University of Vermont).

Santa Fe Institute

Independent research and education center.

Institut rhônalpin des systèmes complexes - IXXI

Research center (ENS Lyon).

Waterloo Institute for Complexity & Innovation (WICI)

Research center (University of Waterloo).

Institut des Systèmes Complexes - Paris Ile-de-France (ISC-PIF)

An inter-institutional organization (CNRS unit) on complex systems research.

Models

Boids

Emergent flocking behavior.

Cellular automata

Discrete compuation model.

Elementary cellular automaton

One-dimensional cellular automata.

Game of Life

Two-dimensional cellular automaton with emergent life-like patterns.

Double pendulum

Chaotic motion.

Kuramoto model

Synchronization.

Barabási–Albert (BA) model

Algorithm for generating random graphs with preferential attachment.

Schelling's model

Agent-based model for segregation.

Ising model

Simple model that can show phase transitions.

Reaction-diffusion

Self-organization and pattern formation model.

Abelian sandpile model

Model showing self-organized criticality.

  • Craig Reynolds' Boids page - The creator's webpage with lots of links to multiple implementations.
    • ConwayLife - Community for game-of-life and similar simulations.
    • golly - State-of-the-art simulator.
    • Lenia - Continuous generalization of the game of life.

Software

Freely to use or open source

NetLogo

Multi-agent modeling environment based on the LOGO language. It comes with a very large library of toy models.

Simulus

ABM library in Python.

Swarm

A platform for agent-based models written in Objective-C, models are coded in Java or Objective-C.

Repast

Agent-based modeling and simulation platforms, models coded in C++ and Java.

MASON

Multiagent simulation library core in Java.

HASH

Graph and agent simulation platform.

Hybrid Automata Library

Java library for hybrid modeling combining agent-based and partial-differential equation components.

Proprietary

Stella

Modelling and interactive simulations.

Ventity/Vensim

Simulation software.

Cosmo Tech platform

Digital twins simulator software.

Other Resources

Complexity Explorer

Educational site with news/blog.

Map of Complex systems History

An impressive overview of the evolution of complex systems thinking.

Stanford Complexity Group

YouTube channel with videos from the group's events.

Awesome Network Analysis

Resources for analysis of network data.

Complexity Explained

Interactive educational website.

Books

Wiener, N. (2016). Cybernetics or control and communication in the animal and the machine.

The book introduced the term cybernetics to describe a self-regulation mechanism.

Scheffer, M. (2009). Critical transitions in nature and society. Princeton, N.J: Princeton University Press.

A nicely written and accessible description of the critical transition and related concepts.

Nicolis, G., Basios, V., & (Firm), W. S. (2015). Chaos, information processing and paradoxical games: the legacy of John S. Nicolis. Singapore; Hackensack, N.J.: World Scientific Pub. Co.

An edited volume of studies honoring the legacy of John Nicolis contribution to complex systems.

Newman, M. E. J. (2010). Networks: an introduction. Oxford; New York: Oxford University Press.

A comprehensive introduction to network science.

Mitchell, S. D. (2013). Unsimple truths: science, complexity, and policy. Chicago: Univ. of Chicago Press.

The book introduces the perspective of integrative puralism as a way of understanding and studying the world.

Maturana, H. R., & Varela, F. J. (2008). The tree of knowledge: the biological roots of human understanding. Boston: Shambhala.

The book is an exposition of the non-representational vew of knowledge.

Mandelbrot, B. (2006). The fractal geometry of nature. New York: W.H. Freeman and Company.

Beautiful introduction to the world of fractals.

Kauffman, S. (2014). At Home in the Universe The Search for the Laws of Self-Organization and Complexity. Cary: Oxford University Press, USA.

The book introduces in an accessible way the influence of concepts such as self-organization and the edge of chaos.

Gros, C. (2015). Complex and adaptive dynamical systems: a primer. Cham: Springer.

Technical and accessible introduction to a number of important concepts in complex systems science.

Downey, A. (2012). Think complexity. Needham, Massachusetts: Green Tea Press.

A hands-on approach exploring complex systems models with Python.

Boccara, N. (2014). Modeling complex systems. Springer-Verlag New York.

An overview of important mathematical models of complex systems.

Barrat, A., Barthelemy, M., & Vespignani, A. (2013). Dynamical processes on complex networks. Cambridge: Cambridge University Press

Dynamic models on complex networks.