"The symmetry of natural laws gives rise to conservation laws." Symmetry is not about visual beauty, but a principle that determines what the world preserves. 対称性によって空間の安定が保存される The golden axis extending from the circular void at the top to the stage and the center of the audience seating is "the amount to be preserved". The surrounding balconies and radial acoustic ribs unfold symmetrically, and the movements, sounds, and lights of the audience all converge towards an unchan

The amount of "flow" that is created and disappears within a given space is equal to the total amount of flow that enters and leaves the surface of that space. "What happens internally is reflected at the interface." 内部の「発散」が建築の外皮に現れる With the central stage as the "source" of emission, golden light and movement lines radiate from the floor to the audience, walls, and ceiling, finally exiting through vertical slits in the ceiling. The relationship where "the total amount produ

If you move a disc or sphere continuously without cutting or flying it, at least one point will always remain in its original position. There is at least one point where the "actual floor position" and the "position depicted on the map" perfectly coincide. Architecture where everything appears to be in motion, yet there is always one unmoving center. 黒い曲面屋根：連続的に変形する空間 A thin, golden light at the center of the stage is the "fixed point." Even though the entire surrounding spac

The Japanese architectural world possesses a unique culture where tradition and innovation merge. In particular, in the field of modern architecture, architects who incorporate mathematical concepts into spatial design, creating buildings with a sense of weightlessness that transcends gravity, are attracting attention. They translate abstract theories such as chaos theory, topology, and higher-dimensional geometry into visual and spatial forms, opening up new possibilities fo

The world of architecture is constantly evolving. In particular, new perspectives on architectural design that transcend gravity are creating innovative designs that go beyond the conventional framework of architecture by translating mathematical theories and abstract concepts into spatial ideas and visual forms. This article explores the forefront of architectural design using mathematical approaches such as chaos theory, topology, and higher-dimensional geometry, and explai

A mathematical and scientific way of thinking that interprets the overall structure and flow from the relationship between "points" and "lines". Point = person, station, building, room, information, urban hub Line = connection, road, communication, relationship, movement, influence A structure in which people naturally gather, move, meet, and engage in a chain reaction of activities. 複数の広場や屋上テラスが、網目状の動線で接続された文化施設 A giant living room in the city An urban hub where people, acti

Self-intersecting surfaces that appear when a projective plane is pushed into three-dimensional space.one "A surface that has no distinction between front and back, but is forced to appear as such in three-dimensional space." exterior: A cultural hall where three large curved shells overlap in the center, making it impossible to tell which is the front and which is the back . Introspection: The walls, ceiling, and floor continuously reverse, creating a space where the sense o

The world of architecture is creating unprecedented and innovative spaces through the fusion of mathematical concepts and cutting-edge technology. In particular, attempts to apply abstract mathematical ideas such as chaos theory, topology, and higher-dimensional geometry to architecture to achieve gravity-defying, floating designs are attracting attention. This article will provide a detailed explanation of the applications and future prospects of these innovative architectur

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

"A three-dimensional object in which there is no distinction between inside and outside." 1️⃣ There is no front or back. 2️⃣ There are no boundaries. 3️⃣ In 4th dimension, they do not self-intersect. The sequence is: city → building → city → building. 「内外の連続」＋「有機的な膨張」 Landscape architecture Looking at the cross-sectional diagram makes the mechanism of a Klein bottle instantly clear. 建物に入った瞬間が存在しない 「街の中に“外”と“内”が存在しない都市」 　 "The city itself is inverting into space." The boundar

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?

The shape changes depending on the viewpoint, and perspective, vanishing points, and depth themselves constitute the structure. Perspective / Vanishing Point / Infinite Horizon Architecture Projective Variety Architecture Parallel lines intersect at infinity. 射影多様体建築の原理 Mathematical Architecture space

"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

xn + yn + zn + wn = 0 "An entity where pure mathematical formulas themselves have become space." "The Topological Universe Created by Mathematical Formulas" ① Algebraic geometry We construct spaces from polynomials. ② Complex Geometry The shape of the complex number space. ③ Hodge Theory Analysis of the "information layer" within a space. ④ Mirror symmetry Connection to superstring theory. ⑤ Arithmetic geometry The fusion of integers and space. Spatial characteristics 1. Perf

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

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

"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

"Rules that preserve structure even after transformation" "Operation of symmetry" Finite simple group classification theorem (Classification of Finite Simple Groups) sporadic = sporadic, isolated 「説明不能な秩序」 Mathematical Architecture space "If you like this architectural artwork, you can purchase the high-resolution digital file [here on Payhip (https://payhip.com/MathematicalArchitectureS)] or [here on Gumroad (https://shomei.gumroad.com/l/apmao)]."

(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