"A phenomenon in which the interface grows due to the 'field gradient'." A phenomenon in which shapes self-organize and grow in accordance with an "invisible flow." The easiest image to understand When you drop ink into water, In some places, it spreads quickly. Some places are slow The tip is more likely to grow Then, branching Lightning arborescent coral-like It takes on a complex shape. "Space expands autonomously." スライムモールド都市 1. Lightning 2. Crystal growth 3. DLA ( Diffus

“A mathematical fingerprint for distinguishing knots” "The way space is intertwined" Intersection of traffic flow Eye contact Penetration of the atrium Loop cycle Multilayer connection “Topological fingerprint” 1. Exterior Multiple loops penetrate Intersecting continuum "I don't know which is the front." 2. Introspection The flow of movement remains tangled. The seating area and the corridor are in phase connection. The feeling of upside down being reversed 3. Cross-section S

"A 'natural-looking randomness' where similar patterns are repeated even when the scale is changed." Natural shapes like mountains, clouds, smoke, and water surfaces 「設計しないのに、リアルになる空間」 Perlin noise generates smooth, pseudo-random patterns that are widely used in computer graphics and procedural generation. Simplex noise is a noise generation algorithm used in computer graphics and procedural generation. Mathematical Architecture space "If you like this architectural artwork,

"Line (knot)" → "Plane (impossible orient)" → "Bundle structure of space" 👆 "Three-dimensional space is made up of 'bundles of circles'." ① Base (foundation space) = the framework of the city ② Fiber = flow/circulation ③ Connection = Control Rules "Intertwining of lines" → "Structure of bundles" → "Space itself" 建築＝静止 → 建築＝流体 "Walking Architecture" It is an important fundamental concept in differential geometry, topology, and theoretical physics. Mathematical Architecture sp

"What kind of movement would make this world 'most natural'?" "The force that wants to move" - "The force that wants to stay still" "Architecture that arises spontaneously from the principles of motion," rather than "architecture that has been designed." fluid architecture Continuous surface City optimized for traffic flow Field-generated architecture Crowd flow analysis architecture “空間そのものが法則になる建築” More natural cities: underground cities and underwater cities ~ like ruins M

An equation that smooths out the "uniformity of curvature and shape" of space over time. Wrinkled surface → Uniform shape → Heat diffusion in space → Curvature is smoothed out The shape of space changes over time. Previously proposed architecture　“Chaos → Order” Thinking of it as a city Topology × Time × Curvature Consider it as a bridge (Tokyo to New York) 過去 → 遷移 → 均一 Consider it as an underground space 時間を持った建築 Surgery Architecture Mathematical Architecture space "If you l