Map of Complexity & Chaos
Why a few simple rules, repeated among countless individuals, give rise to order & complex behavior that no one controls.
self-organization · chaos · emergenceFlocking & Emergence Đàn chim & Trồi sụt
Each one follows just 3 rules (separate – align – cohere) with its neighbors, with NO leader — yet the whole flock swirls as one.
Chaos Hỗn loạn & Con lắc kép
The butterfly effect: a tiny initial error → completely diverging trajectories. The double pendulum & the Lorenz attractor.
Cellular Automata Game of Life
4 live/die rules on a square grid → producing gliders, guns, self-replicating structures.
Networks Mạng lưới & Lan truyền
Six degrees of separation, spreading epidemics/rumors, the tipping point — the power of connected hubs.
Game Theory Lý thuyết trò chơi
The prisoner’s dilemma, cooperation vs betrayal — when selfishness wins, when cooperation emerges.
L-Systems Tăng trưởng & Phân nhánh
Trees, blood vessels, river networks grow from one repeated branching rule — the fractal of life.
Epidemic · SIR Lan truyền dịch
The SIR model, a deliberately simplified one: an outbreak from patient zero, R₀ deciding the peak; vaccination & distancing flatten the curve.
Traffic Jam Kẹt xe tự phát
The Nagel–Schreckenberg model: ‘phantom’ jams emerge from density, stop–go waves traveling backward with no obstacle at all.
Sandpile · SOC Đống cát tới hạn
Self-organized criticality: adding one grain can trigger avalanches of every size — a power-law distribution like earthquakes.
Percolation Thấm
Fill cells at random and at the threshold p_c ≈ 0.59 a spanning cluster appears — a sudden phase transition, water seeping through.
Reaction–Diffusion Hoa văn Turing
Two chemicals diffusing + reacting self-form spots (leopard), stripes (zebra), mazes — just change 2 numbers. No one draws them, the patterns emerge.
Synchronization Đồng bộ tự phát
Fireflies, metronomes, heart cells self-sync to the SAME phase once weak coupling crosses a threshold — synchrony emerges with no conductor (Kuramoto).
Elementary CA Tự động tế bào 1D
One 8-bit rule + one black cell: Rule 30 gives chaos, Rule 90 draws Sierpinski, Rule 110 is Turing-complete. Complexity needs no complex rule.
Segregation Mô hình phân tách Schelling
Everyone wants only a few neighbours like themselves, and yet the neighbourhood splits into stark red and blue blocks. Segregation from a mild preference.
Ant Colony Optimization Kiến & Tối ưu bầy đàn
Ants leave pheromone; the shorter path builds scent faster so the colony converges on it — with no map or commander. The idea became the ACO algorithm.
Slime Mold Mốc nhầy giải mê cung
A single giant brainless cell self-weaves a tube network linking points, once matching the Tokyo rail map for efficiency and fault tolerance. Order from local rules, with no brain anywhere.
Forest-Fire Model Cháy rừng & Lan truyền
Trees grow, lightning strikes and fire spreads until the forest settles at the critical threshold where fires come in every size, a power law like earthquakes.
Bifurcation Điểm tới hạn & Rẽ nhánh
A one-line formula x’=r·x·(1−x): raise r and 1 point → 2 → 4 → chaos. Order & chaos nested in a fractal structure (Feigenbaum).
Opinion Dynamics Lan truyền ý kiến & Phân cực
People move closer if their views are close enough. Openness → society reaches consensus; listening only to the like-minded → polarization & echo chambers.
Genetic Algorithm Thuật toán tiến hóa
A population of candidate solutions evolves toward a goal through selection, crossover and mutation, borrowing Darwin for problems with no known answer.