"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

As I've mentioned before, this is a framework of mathematical physics that attempts to describe physics using light rays and causal structures as its fundamental objects , rather than spacetime itself . Roger Penrose proposed a profound theory that connects quantum gravity, scattering amplitude, and complex geometry. 「時空は本当に基本的な存在なのか」 Let's consider the bridge between Tokyo and Yokohama. The paths of light propagating at the speed of light and conformal symmetries are natural

トポロジーによる不安感 "Architecture that first gives you the feeling of unease with topology." 建築は、私たちの空間認識を挑戦します。特に、トポロジーの概念は、私たちの理解を超えた新しい形を生み出します。以下の要素がこの建築の特徴です。 連続した表面 動線の逆転 内外の消失 境界の消失 価値の再発見 "Lost, discovered, and cyclical" becomes valuable. このような建築は、私たちに新しい視点を提供します。私たちの周囲の世界を再発見する手助けをします。建築は、私たちの感覚を刺激し、思考を促進します。 Mathematical Architecture 未来的なメビウスストリップ建築 この建築は、単一の連続した非向きの建物であり、ねじれたループを形成します。外部、内部、断面が一つのイメージに融合しています。カットアウェイの視点から見ると、構造がどのように機能するかが明らかになります。 構造の特徴 屋根、壁、床の統合: すべてが一つの

"The smallest unit of finite symmetry that cannot be further decomposed." "Symmetry like that of 'elementary particles' in a finite world" → Finite simple group = "Prime number" in the world of groups Finite simple group = symmetric atom The concept of a room disappears. There is no hallway Structure and traffic flow are integrated. ① You get lost (but it's not broken) → The symmetry is so strong that you lose your sense of direction. ② No center → Everything feels like the c

Space itself is a "structure that possesses power." "Architecture that designs changes in space," rather than "architecture that creates form." The realm of designing "relationships themselves" → "Architecture that visualizes the distribution of invisible forces" 空間＝位置と運動のペア system Content Relationship with Symplectic Mandelbrot Shape generation ❌ Wrong Lehman Face multilayer space △ Related topology connection ◎ Core non-commutative interaction ◎ Deeply related Yang Mills pl

Mathematics that goes as far as "the relationship of the relationship of the relationship..." "Relationships are more important than material things." dimension Content 0 subject 1 Relationship of the subject 2 Relationship 3 Relationship of relationships n Infinite Layers The most abstract theory → A universe where structures are stacked hierarchically. 多層ネットワーク空間建築 Symplectic → “The geometry of motion” Mathematical Architecture space