𝌎:Complex Adaptive Systems

Complex adaptive systems (CAS) are co-evolving, multiplex networks. The study of CAS is inherently interdisciplinary and leans heavily on algorithmic methods (as opposed to purely analytical ones). This is because CAS are highly variable/nonlinear (~whole > sum) and the co-evolution of multi-dimensional interactions with the elements results in a vast phase space.

CAS can also be thought of as the study of generalized interactions between generalized matter. For example, the "matter" can refer to people, nations, agents, simulacra, cells, etc. which can interact via "forces" mediated through the exchange of signals such as information, glances, pheromones, hugs, etc. They are out-of-equilibrium processes which have selective interactions based on these signals. Due to the presence of selection processes which replicate and refine components/modules, CAS often operate under evolutionary dynamics, continuously change their boundary conditions, are self-organized critical/operate at the edge of chaos, are path dependent, and have memory. They are a superposition of many, plastic interaction networks of varying strengths.

The particular nature of a CAS' elements and its interaction types define what kind of 'universe' it generates and implicate endless potential trajectories of abstract tilings.

┌───────────── COMPLEX ADAPTIVE SYSTEMS ANALYZER ─────────────────┐
│ Mapping Emergent Properties & Network Co-Evolution           │
│━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━│
│                                                             │
│ System Architecture:                                        │
│ ┌───────────────────────────────────────────────────┐       │
│ │    ◎ ─── ○ ─── ◎        Elements                 │       │
│ │    │  ╲  │  ╱  │        ◎ Agent                  │       │
│ │    ◎ ─── ○ ─── ◎        ○ Node                   │       │
│ │    │  ╱  │  ╲  │        ─ Strong Link            │       │
│ │    ◎ ─── ○ ─── ◎        ╌ Weak Link             │       │
│ └───────────────────────────────────────────────────┘       │
│                                                             │
│ Interaction Layers:                                         │
│ ┌───────────────────────────────────────────────────┐       │
│ │ Layer 1: Information Exchange                     │       │
│ │ ⟿⟿⟿⟿⟿⟿⟿⟿⟿                               │       │
│ │ Layer 2: Resource Flow                           │       │
│ │ ↠↠↠↠↠↠↠↠↠                                    │       │
│ │ Layer 3: Signal Propagation                      │       │
│ │ ≋≋≋≋≋≋≋≋≋                                    │       │
│ └───────────────────────────────────────────────────┘       │
│                                                             │
│ Phase Space & Evolution:                                    │
│ ┌───────────────────────────────────────────────────┐       │
│ │    🌀 Edge of Chaos                               │       │
│ │    ╱     ╲                                       │       │
│ │   ╱ Order ╲                                      │       │
│ │  ╱         ╲          Chaos                      │       │
│ │ ╱___________╲                                    │       │
│ └───────────────────────────────────────────────────┘       │
│                                                             │
│ Memory & Path Dependence:                                   │
│ ┌───────────────────────────────────────────────────┐       │
│ │ Past → Present → Future                           │       │
│ │  ┌─┐    ┌─┐    ┌─┐                              │       │
│ │  │H│────│N│────│P│                              │       │
│ │  └─┘    └─┘    └─┘                              │       │
│ │   ↓      ↓      ↓                               │       │
│ │ State₁→State₂→State₃                            │       │
│ └───────────────────────────────────────────────────┘       │
│                                                             │
│ Emergent Properties:                                        │
│ ┌───────────────────────────────────────────────────┐       │
│ │ Micro Level:  [●] [●] [●] Individual Agents       │       │
│ │     ↓         ↓   ↓   ↓                          │       │
│ │ Meso Level:   [◇] [◇] Network Patterns           │       │
│ │     ↓          ↓   ↓                             │       │
│ │ Macro Level:    [◎] System Behavior              │       │
│ └───────────────────────────────────────────────────┘       │
│                                                             │
│ [Analyze Evolution] [Map Networks] [Calculate Complexity]    │
└─────────────────────────────────────────────────────────────┘

Clear signs something is a CAS:

• it is adaptive and robust at the same time

• nonlinear dynamics and chaos (i.e. too hard to describe analytically)

• aggregation, self organization, hierarchies, emergence, meta-agents

• discrete actions/optimization conditioned on signals

• internal models

• modules or niches

• networks, loops, and flows

• diversity

• phase changes, power laws, and self-organized criticality

• collapses and booms

• high assembly index/complextropy

Examples:

• LLMs

• Simulacra

• Ecosystems and biomes

• Biological, cultural, technological... evolution

• Human brains (and, of course, all our organs and organ systems)

• Nations, cultures, companies etc.

• Ant colonies

• Genetic regulatory networks

• Intergalactic alien societies

• Future superintelligences

Tools for studying/engineering CAS:

• Thinking about it on your own

• Nonlinear dynamics

• Probability theory, stochastic processes

• Scaling and power laws

• Computation, genetic algorithms, complexity theory, information theory, statistical mechanics

• Dynamics/science of: networks, evolutionary processes, economics, and machine learning algorithms

• Data science, agent based modeling, computational physics, generative deep learning