refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-understanding-complex-systems
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title: Understanding Complex Systems
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Complexity Science, Complex Adaptive Systems, CAS]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [complexity, systems-thinking, emergence, networks]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python
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framework: NetworkX / Mesa / SciPy
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---
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# Understanding Complex Systems
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## 매 한 줄
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> **"매 부분의 합 그 이상 — 매 emergence"**. Santa Fe Institute 1984 founding 이후 complexity science 는 economics, biology, AI safety 까지 확장됐고, 2026 현재 ABM + GNN + dynamical systems 의 hybrid analysis 가 standard toolkit이다.
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## 매 핵심
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### 매 정의 axes
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- **Many components**: 매 대량의 interacting agent.
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- **Nonlinearity**: small cause → large effect (butterfly).
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- **Emergence**: macro pattern not reducible to micro rules.
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- **Adaptation**: agent rule 의 evolution (CAS).
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- **Self-organization**: external designer 없이 ordered structure.
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### 매 phenomena
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- **Phase transitions** (percolation, Ising).
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- **Power laws / scale-free networks** (Barabási 1999).
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- **Chaos & strange attractors** (Lorenz 1963).
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- **Synchronization** (Kuramoto oscillators).
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- **Critical brain hypothesis** (Beggs & Plenz 2003).
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### 매 응용
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1. Epidemic modeling (COVID-19, agent-based + network).
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2. Financial market (heavy tails, flash crashes).
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3. AI safety: emergent behaviors in LLM scaling, multi-agent.
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4. Climate tipping points.
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5. Urban / supply chain resilience.
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## 💻 패턴
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### Game of Life — emergence demo
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```python
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import numpy as np
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def step(grid):
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n = sum(np.roll(np.roll(grid, i, 0), j, 1)
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for i in (-1, 0, 1) for j in (-1, 0, 1)
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if (i, j) != (0, 0))
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return ((n == 3) | ((grid == 1) & (n == 2))).astype(int)
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g = np.random.binomial(1, 0.3, (200, 200))
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for _ in range(500):
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g = step(g)
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```
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### Scale-free network (Barabási–Albert)
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```python
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import networkx as nx
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G = nx.barabasi_albert_graph(n=10_000, m=3, seed=42)
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degrees = [d for _, d in G.degree()]
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# verify power-law
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import powerlaw
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fit = powerlaw.Fit(degrees, discrete=True)
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print(fit.alpha, fit.xmin, fit.distribution_compare("power_law", "lognormal"))
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```
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### Kuramoto synchronization
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```python
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import numpy as np
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from scipy.integrate import odeint
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def kuramoto(theta, t, omega, K, N):
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dtheta = omega.copy()
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for i in range(N):
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dtheta[i] += (K/N) * np.sum(np.sin(theta - theta[i]))
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return dtheta
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N, K = 100, 1.5
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omega = np.random.normal(0, 1, N)
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theta0 = np.random.uniform(0, 2*np.pi, N)
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t = np.linspace(0, 50, 1000)
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sol = odeint(kuramoto, theta0, t, args=(omega, K, N))
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# order parameter r(t)
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r = np.abs(np.exp(1j * sol).mean(axis=1))
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```
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### SIR epidemic on network
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```python
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import networkx as nx, random
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def sir(G, beta=0.05, gamma=0.01, init=5, T=200):
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state = {n: "S" for n in G}
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for n in random.sample(list(G), init): state[n] = "I"
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history = []
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for _ in range(T):
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new = state.copy()
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for n, s in state.items():
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if s == "I":
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if random.random() < gamma: new[n] = "R"
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for nb in G.neighbors(n):
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if state[nb] == "S" and random.random() < beta:
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new[nb] = "I"
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state = new
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history.append((sum(v=="S" for v in state.values()),
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sum(v=="I" for v in state.values()),
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sum(v=="R" for v in state.values())))
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return history
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```
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### Lyapunov exponent (logistic map)
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```python
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import numpy as np
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def lyapunov(r, x0=0.5, n=10_000, burn=1000):
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x = x0
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for _ in range(burn): x = r*x*(1-x)
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s = 0.0
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for _ in range(n):
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x = r*x*(1-x)
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s += np.log(abs(r - 2*r*x) + 1e-12)
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return s / n
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for r in np.linspace(2.5, 4.0, 16):
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print(f"r={r:.2f} λ={lyapunov(r):+.4f}")
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```
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### Causal emergence via effective info (PyPhi-lite idea)
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```python
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# coarse-grain & measure mutual info gain — 매 Hoel 2017
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def effective_info(P_micro, grouping):
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# P_micro: (S, S) transition matrix
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# grouping: list of macro-state index per micro-state
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import numpy as np
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macro = max(grouping) + 1
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P_macro = np.zeros((macro, macro))
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for i, gi in enumerate(grouping):
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for j, gj in enumerate(grouping):
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P_macro[gi, gj] += P_micro[i, j]
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P_macro /= P_macro.sum(axis=1, keepdims=True) + 1e-12
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return P_macro
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Local rules, emergent macro | Agent-based (Mesa, NetLogo) |
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| Network structure matters | NetworkX / igraph + null models |
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| Continuous coupled oscillators | Kuramoto / ODE |
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| Discrete-time chaos | Iterated maps + Lyapunov |
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| Real data, latent dynamics | SINDy / Koopman / NeuralODE |
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**기본값**: NetworkX + Mesa for structure+dynamics, SciPy for ODE, powerlaw for tail fit.
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## 🔗 Graph
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- 부모: [[Systems Theory]] · [[Nonlinear Dynamics]]
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- 응용: [[Pedestrian-Modeling]]
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- Adjacent: [[Entropy in Information Theory|Information Theory]] · [[AI_Safety_and_Alignment|AI Safety]]
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## 🤖 LLM 활용
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**언제**: model scaffolding, parameter sweep, hypothesis enumeration, literature 정리.
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**언제 X**: long-horizon stability claim — 매 numerical proof / theorem 직접 검증.
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## ❌ 안티패턴
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- **Power-law claim 의 over-fit**: 매 lognormal vs power-law 비교 검증 필수 (Clauset 2009).
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- **Emergence as magic**: 매 정의 명확화 — weak (epistemic) vs strong (ontological).
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- **Single ABM run**: Monte Carlo ensemble 필수 (≥100 runs).
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- **Network metric without null**: 매 configuration model baseline 비교.
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## 🧪 검증 / 중복
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- Verified (Mitchell "Complexity: A Guided Tour", SFI lectures, Strogatz "Nonlinear Dynamics and Chaos", Newman "Networks" 2nd ed).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — emergence + networks + chaos pattern set |
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