A mathematical design method for securely transmitting information. How to find and fix errors with minimal additional information 1. Identify errors in the error detection process. 2. Correct errors: Fix the parts that are incorrect. 3. Streamline the process by sending accurate data in the shortest possible format. A theory of spatial configuration that is robust against noise, congestion, confusion, and omissions. Hamming Distance Cultural Hall 意味を復元するための劇場空間 周囲の回遊空間が誤り訂正の

"A theory that mathematically deals with how much information is contained, how accurately it can be transmitted, and how much it can be compressed." 1. Amount of information The rarer something is, the more information it contains. 2. Entropy How uncertain is it? How difficult is it to predict? 3. Compression Information theory is about how much data can be shortened. 4. Communications How accurately can information be transmitted even with noise? How well can we organize an

A theory that considers "how short a program can be used to represent a given piece of information." For example, let's compare the following two: A 111111111111111111111111111111 this is, "Repeat 1 30 times" It can be explained briefly as follows: In other words, the amount of information is small. B 101001110100101101011000111010 The rules are not very clear, so we have no choice but to write it almost exactly as it is. In other words, there is a lot of information. The mor

A curved surface that has a singularity where a smooth surface abruptly tapers towards a point or line and then folds back. Even though the surfaces are continuous, they suddenly converge at a certain point, creating a singularity such as a sharp ridge, valley, or mouth. 空間が破綻する直前の美しい尖り A place where countless streams converge to a single singularity. 数学的建築定義 Mathematical Architecture space

"A movement in which the next move is determined entirely by probability." "A series of coincidences creates the landscape." "Random with order" 設計しない、確率で生成する Features of the space The floor, walls, and ceiling shake continuously. Perfect horizontal and vertical lines disappear. Depending on your perspective, the space can appear completely different. Countless random movements come together to create "height" and "density." Not smooth (rough) The structure remains similar e

"A network that spreads information to almost the highest level with very few connections." "Despite the small number of connections, the entire system connects surprisingly well." "It's practically impossible to create a more efficient network than this." ① Minimal connections yet a huge cycle ② No central point ③ "Local" and "whole" coincide Actual applications Communication network semiconductor quantum computing data center Cryptography AI Network Distributed computing 最適

"A movement that flows over time in the 'most natural way' within space." 「空間の形そのものが、運動の運命を決める現象」 “都市の流れの増幅器” Navier-Stokes equations Navier-Stokes equations [\rho\left(\frac{\partial \mathbf{u}}{\partial t}+\mathbf{u}\cdot\nabla\mathbf{u}\right) -\nabla p+\mu\nabla^2\mathbf{u}+\mathbf{f}] (\rho)：Fluid density (\mathbf{u}): Velocity field (p): pressure (μ): viscosity coefficient (\mathbf{f}): External force This equation is, water flow air vortex turbulence Thermal convection

"No other point can be found within the circumcircle of any triangle." "The most beautiful triangular network" "A structure that resembles the natural world" Not Designed. Generated. "Architecture born from relationships" 「生活の点配置から住空間が生成される」 Computational Geometry Delaunay House If it's a cultural hall, it becomes "architecture of connection" = "large-scale spatial network". ひとつの箱ではなく、結ばれた公共空間 Mathematical Architecture space

Architecture is becoming "biological." Architecture changes based on its "state" rather than its "purpose." Growing due to congestion Extinction due to depopulation Mutation through activity Evolves through connection “進化する建築” How do vacation homes multiply? How it multiplies internally 時間的可変性 Now, let's create a desert island using this math game. Autonomous Grid Architecture Mathematical Architecture space

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

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

A structure in which countless circles within a 3-dimensional sphere correspond neatly to a 2-dimensional sphere. "A space created by the intertwining of infinite circular corridors." ”思考スタイル”として再構成した比較想像図 ① Flowing curved surface type ② Silent minimalist type ③ Structural logic exposed type Fluid / Continuous / Dynamic Geometry 迷路ではなく流体空間 Mathematical Architecture space

A collection of exceptional symmetries that do not belong to any large pattern (an infinitely continuing family). Monster group Mathieu Group Conway Group Fisher group, etc. Sporadic group: "An unknown creature that suddenly appears (only one exists)." "A structure that deviates from theory, yet somehow works perfectly." 全体ルールが存在しないのに、崩壊しない構造 "Experiences are continuous, but space is not." "A cross-section where a different building emerges no matter where you cut it." Mathem