Geometry that "the space itself is in a state of collapse." "Self-intersecting architecture of space" 1. Central singularity 2. Self-penetrating traffic flow 3. The collapse of the front and back. "Space that collapses due to projection" Mathematics → Structure → Space → Experience "Space as a limit of perception" 自己交差型代数曲面 Mathematical Architecture space

"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

"An invisible spatial structure generated by zero point placement" 1. Aperiodic resonance city 2. The Architecture of the "Invisible Order" 3. Become an architectural masterpiece of light. "The deep frequencies of the universe" 夜になると金色の光点群が浮遊する A hall that seems to have become a building in itself, a "space of resonance." Architecture that doesn't focus on form, but rather on conveying an invisible order . "Architecture like a constellation": The interior space of a gigantic

A quantity that measures how much the "true probability distribution" differs from the "approximated probability distribution". "The amount of extra information needed due to using the wrong model." "The discrepancy between the spatial use envisioned by the designer and the actual usage patterns." The difference between "predicted cities" and "actual cities" Architecture that optimizes probability distributions, rather than architecture that designs form. "An information syst

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

Architecture can be viewed not merely as a physical "thing," but as a "continuous space" where boundaries blend together, surfaces transform, and space flows without interruption. This perspective transcends conventional architectural concepts and invites us into the world of mathematical architecture, incorporating mathematical structures and topology. This time, we will introduce a new perspective on architecture centered on continuity and topology, along with specific meth

"The phenomenon in which the boundary grows according to the gradient of the field." 1. Dendritic crystals (snow crystals) 2. Electric discharge (lightning) 3. The boundary between oil and water "The most unstable, yet the most natural" 「空間が自己生成する」 拡散律速凝集 CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=641439 サフマン・テイラー不安定性 By Claire Trease, Kingston University - Own work, CC BY-SA 4.0,https://commons.wikimedia.org/w/index.php?curid=45344174 Now let's consider sk

As an ebook nears completion, anticipation grows, along with thoughts about its content and how it can be used. In particular, ebooks dealing with themes gaining attention in contemporary design fields, such as #Parametric Design, #Generative Art, and #Algorithmic Architecture, become valuable learning resources for students and creators. This article will introduce the appeal of an ebook nearing completion and offer practical ways to utilize it. What is the appeal of ebooks?

Architecture is not merely the design of space; by applying mathematical principles and theories, it creates unprecedented and innovative forms and structures. In particular, translating abstract mathematical concepts such as chaos theory, topology, and higher-dimensional geometry into spatial ideas and visual forms has made it possible to create architectural designs that defy gravity and possess a sense of weightlessness. This article explores in detail the influence of mat

"A method for dividing the region closest to a certain point." "Space is distributed autonomously." plant leaf vein cell bark geology Cracked dry land living thing Giraffe feather pattern structure universe galaxy distribution Instead of "designing the form," we "arrange the relationships." “空間が自ら育ったような建築” Voronoi ↔ Delaunay: "Mathematics that generates spatial order solely through the relationships between points" Object Design　→　Field Design Mathematical Architecture space

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

What is Lorenz Attractor Architecture? How Chaos Theory Is Reshaping the Future of Spatial Design Architecture has always borrowed from nature — from the golden ratio of the Parthenon to the organic curves of Zaha Hadid. But what happens when architecture borrows not from nature's forms, but from nature's behavior? Lorenz Attractor Architecture is a design methodology that derives spatial structure directly from chaos theory — specifically from the mathematical system known a

"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

"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

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