A fractal structure in which circles are infinitely packed together. A fractal shape in which tiny circles increase infinitely. Fractals + Number Theory = Apollonian City デカルトの定理曲線都市 Galaxy cluster ↓ galaxy ↓ Star cluster ↓ fixed star ↓ planet Soddy–Gossett theorem 銀河分布・泡宇宙構造・重力レンズ構造 Mathematical Architecture spce

"The surface with the smallest area under the same boundary conditions" → soap film Dividing space infinitely periodically Smoothly continuous curved surface A maze-like structure full of holes The famous Schwarz surface Schwarz D surface Schwarz Psur Gyroid (Diamond surface) (Primitive surface) (A close relative discovered after Schwartz's discovery) 三次元迷路の曲面 The entire building is a single curved surface A gigantic sculpture of continuous curved surfaces 空間の骨格 Gyzo structu

Fractal shapes created from iterative calculations using complex numbers Dragon type, Seaweed type, Flame type, Coral type Simple mathematical formulas → infinitely complex forms = principles of nature フラクタル植物のような建築 The basics of chaos theory Mathematical Architecture space

Instead of using force directly, it uses kinetic energy T and potential energy V. L = T − V The most natural flow of space エネルギー差が形を決める建築 Kinetic energy T = flow of people Potential energy V = weight of space Energy Valley ラグランジュ文化ホール Mathematical Architecture space

Geometry where you can draw infinitely many parallel lines A curved surface that expands into space, like a saddle (horse saddle). 宇宙の形 一般相対性理論 カオス理論 フラクタル 無限空間 hyperbolic city Poincaré disc-shaped hyperbolic city Mathematical Architecture :

A small courtyard within a courtyard, and an even smaller courtyard within that... This is a theoretically infinitely continuing architectural structure. Typical models Sierpinski Courtyard Cantor Courtyard Peano City Courtyard Spatial experience: This is how it feels when people walk through it. Go out into the courtyard There is a small courtyard there. Turning the corner further down the corridor leads to another courtyard. No matter how far you go, it's a "nested courtyar