---
id: wiki-2026-0508-complex-systems
title: Complex Systems
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Complexity Theory, Complex Adaptive Systems, CAS]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [systems-thinking, complexity, emergence, distributed-systems]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: n/a
  framework: n/a
---

# Complex Systems

## 매 한 줄
> **"매 Complex System 매 part 의 sum 초과 의 emergent 결과 발생 system"**. 매 simple-rule 매 unpredictable global 의 야기. Santa Fe Institute (Holland, Kauffman, Mitchell) 의 lineage. 2026 매 LLM swarm, distributed micro-services, social platform 매 canonical 예.

## 매 핵심

### 매 정의 specifics
- **Many components** (10² ~ 10⁹).
- **Local interaction** (no central control).
- **Non-linearity**: 매 input → output 의 disproportionate.
- **Emergence**: 매 macro behavior 매 micro rule 의 not directly inferrable.
- **Adaptation**: 매 component 의 state-update 의 environment 응답.

### 매 simple ↔ complicated ↔ complex (Cynefin)
- **Simple**: 매 cause↔effect obvious. Best practice 의 사용.
- **Complicated**: 매 expert analysis required. Good practice.
- **Complex**: 매 retrospect 만 cause 추론 가능. 매 probe-sense-respond.
- **Chaotic**: 매 cause↔effect link absent. Act-sense-respond.

### 매 응용
1. Distributed system design 매 emergent failure mode 의 anticipate.
2. Org change 매 directly-controllable lever 부재 — 매 nudge.
3. Market / social media 의 non-linear viral propagation.

## 💻 패턴

### Power-law detection (Pareto)
```python
import numpy as np, scipy.stats as st

def is_powerlaw(data: np.ndarray) -> bool:
    """Heavy-tailed → likely complex, not Gaussian."""
    fit = st.powerlaw.fit(data)
    ks_p = st.kstest(data, "powerlaw", fit).pvalue
    return ks_p > 0.05
```

### Agent-based model (Mesa)
```python
from mesa import Agent, Model
from mesa.space import MultiGrid
from mesa.time import RandomActivation

class Cell(Agent):
    def step(self):
        n = self.neighbors_alive()
        self.alive = (n == 3) or (self.alive and n == 2)

class Life(Model):
    def __init__(self, w=80, h=80):
        self.grid = MultiGrid(w, h, torus=True)
        self.schedule = RandomActivation(self)
        for x in range(w):
            for y in range(h):
                a = Cell(self)
                self.grid.place_agent(a, (x, y))
                self.schedule.add(a)
```

### Feedback-loop diagram (Mermaid)
```mermaid
graph LR
  Demand --> Price
  Price -->|+| Supply
  Supply -->|-| Price
  Price -->|-| Demand
```

### Tipping-point detection
```python
def early_warning_signal(timeseries):
    """Increased variance + autocorrelation → near phase transition."""
    rolling_var = pd.Series(timeseries).rolling(50).var()
    rolling_ac = pd.Series(timeseries).rolling(50).apply(lambda x: x.autocorr(1))
    return rolling_var.iloc[-1] > rolling_var.mean() * 1.5 \
       and rolling_ac.iloc[-1] > 0.7
```

### Causal-loop policy lever map
```yaml
# policy_levers.yml
goal: reduce-incident-rate
levers:
  - lever: deploy-frequency
    feedback: positive  # more deploys → more incidents short-term
    horizon: weeks
  - lever: test-coverage
    feedback: negative  # higher coverage → fewer incidents
    horizon: months
  - lever: oncall-rotation-size
    feedback: negative  # larger rotation → less burnout → fewer incidents
    horizon: quarters
```

### Network resilience metric
```python
import networkx as nx
def fragility(G: nx.Graph) -> float:
    """Higher = more fragile to targeted node removal."""
    bc = nx.betweenness_centrality(G)
    return max(bc.values()) - np.median(list(bc.values()))
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Linear, well-understood | Optimization, KPI |
| Complicated (expert solvable) | Plan + execute |
| Complex (emergent) | Probe + small experiments + observe |
| Chaotic (crisis) | Act first, stabilize, then sense |
| Pre-tipping point | Early-warning + circuit-breaker |

**기본값**: probe-sense-respond + diversity + redundancy.

## 🔗 Graph
- 부모: [[Systems Thinking]] · [[Cynefin Framework]]
- 변형: [[Chaos Theory]] · [[Complex Adaptive Systems]]
- 응용: [[Distributed Systems]] · [[Network Theory]]
- Adjacent: [[Emergence]] · [[Power Laws]]

## 🤖 LLM 활용
**언제**: 매 system map 의 first-draft, 매 feedback-loop 의 surface, 매 policy lever brainstorm.
**언제 X**: 매 prediction 의 complex system — 매 LLM 매 false confidence 매 위험. 매 historical analogy 의 limit.

## ❌ 안티패턴
- **Linear thinking**: 매 cause→effect 의 direct mapping 매 complex 에서 wrong.
- **Optimization fallacy**: 매 single metric 의 optimization 매 emergent failure 야기 (Goodhart).
- **Central control assumption**: 매 top-down command 매 local-rule system 매 ineffective.
- **Reductionism over-reach**: 매 component 의 분석 매 emergent property 의 missing.
- **Plan-the-future fallacy**: 매 5-year-plan 매 complex domain 매 fiction.

## 🧪 검증 / 중복
- Verified (Mitchell _Complexity: A Guided Tour_, Holland _Hidden Order_, Snowden Cynefin Framework, Santa Fe Institute lectures, Donella Meadows _Thinking in Systems_).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — Cynefin, agent-based model, power law, anti-patterns |
