Fractal shapes are always uniquely determined as a "combination of reduced copies". "By repeatedly shrinking, moving, and rotating a single architectural unit, the whole converges into a stable, self-similar form." The fundamental principle that makes all self-similar architecture possible 中央へ向かって形が無限に収束して見える部分が、定理における「唯一のフラクタル・アトラクター」を表現 The stage itself becomes the "attractor" in Hutchinson's theorem. Hutchinson's repetition principle is an architectural principle that inte

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

Architecture is not merely the construction of space, but a fusion of art and science. Mathematics, in particular, plays a crucial role in architectural design. By translating abstract mathematical concepts into spatial ideas and visual forms, innovative architecture that transcends conventional concepts of gravity and structure can be created. This article explores how mathematical theories such as chaos theory, topology, and higher-dimensional geometry are applied to archit

Algebraic spaces that operate using multiplication It's not a "point," but a space created by ratios, magnifications, and scale transformations. Algebraic, lattice-based, controlled deformations The same structure, but on different scales, chains together in a multiplicative manner. Algebraic Torus Architecture　 Multiplicative Space / Scaling Geometry A cultural landscape where scales proliferate in a chain reaction. Mathematical Architecture space

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 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 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 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