A space that records "how different geometric shapes surfaces with the same topology can be transformed into." A map that collects all the "differences in shape". Long and slender shape, round shape, constricted shape, twisted shape Design parameter space where the proportions, distortions, curvatures, and opening positions of the space change while maintaining the same framework and connection relationships. Not "the form of architecture," but "the very possibility that arch

A theory that studies whether "motion over long periods of time" and "the statistics of the entire space" coincide. Can "local movements" represent the "overall structure"? "Architecture where the flow of people itself defines the space." 無数の回遊ループ Mathematical Architecture space

"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

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

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

(An energetic perspective) Energy (Hamiltonian) → Time evolution → Motion There is an "invisible topography (energy undulation)" in space, and particles flow through it. "Architecture that designs movement itself" 動いていないのに動いて見える "Dynamic Space Architecture" Mathematical Architecture space ■ Gumroad https://shomei.gumroad.com/l/apmao ■ Lemon Squeezy https://shomei.lemonsqueezy.com/ ■ Payhip https://payhip.com/MathematicalArchitectureS ■ BOOTH https://shomei-a.booth.pm

They may look different, but their relationship structure is the same. Two spaces exist: A: Physical space (visible architecture) wall floor volume light B: Relational space (invisible architecture) Traffic flow network Eye contact Sound propagation Function links Space becomes "doubled" 「空間ではなく、空間同士の関係を設計し、それが別の幾何として現れる建築」 "Visible architecture" and "invisible architecture" Mathematical Architecture space

"A geometry that describes space and time through the relationship of light." Creating a world from "lines of light" rather than "points" → "Architecture made of flowing light" "Designing spaces with light at the center." 光の動線 ① Ray structure ② Twisted space ③ "Core of light" in the center Rotation in complex space Mathematical Architecture space

"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

"Geometry that deals with the relationships between motion and energy" Geometry that governs the motion of the universe Geometry of movement paths → Human movement × Space 流れが凍結した建築 If topology is about "preserving shape," then symplectic architecture is about "preserving motion." Mathematical Architecture :

"A structure in which distant places or spaces are directly connected within a building." The "instantaneous" connection of space → "architecture that eliminates distance" The internal space is topologically broken. Visual perception and movement patterns do not align. "Time" also becomes a design subject. Opening the sliding door of a Showa-era house reveals a futuristic city—this is a "disconnecting jump." "Architecture that breaks down and reconnects distance, continuity,

"Architectural design generated using probability and randomness" Buildings = Topography of probability distributions → Topographication Order × Randomness = Statistical Order 臨界状態（壊れる一歩手前） (Space becomes distorted) A space where a continuous function appears discontinuous → The architectural representation of phenomena Mathematical Architecture space

"Geometric spaces with completely different shapes actually contain the same information." Space A Space B Geometry: Counting Curves Geometry for studying hole structure Space A Space B (Complex curve) ←→ (Complex hole) 鏡宇宙を移動する体験 Twin buildings with different shapes Architecture A Architecture B Organic forms full of curves linear Flowing Corridor Courtyard type Movement distance, line of sight, and spatial volume are in perfect agreement. Mathematical Architecture space

Mathematics that deals with "shape (topology)" and "logic/programs" in the same language. Space = Transformable proof → Architecture that allows you to walk through a proof → Architecture that is a maze yet leads you to the same place ∞次元トポロジー Mathematics = multidimensional space → Loops, twists, non-Euclidean wires Mathematical Architecture space

"The study of mathematically dealing with patterns of randomly (accidentally) placed points, lines, and surfaces." Mathematical modeling of random spatial structures 建築と都市の中間 "Cities are architecture that grow like living organisms." "Architecture that has come into existence" rather than "architecture that has been designed" Mathematical Architecture space