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

In the world of architecture, defying gravity, a natural law, has long been both a dream and a challenge. Modern mathematical architecture translates abstract concepts such as chaos theory, topology, and higher-dimensional geometry into spatial ideas and visual forms, realizing innovative structural designs that transcend the conventional constraints of gravity. This article explores the possibilities of gravity-transcending structural design and provides a concrete explanati

"A four-dimensional complex surface with many holes, deep symmetry, and beautifully balanced curvature." K3 surfaces are smooth surfaces in complex 2D and real 4D, with a representative example being a quartic surface in projective space. 1. A type of Calabi-Yau K3 surfaces can be viewed as two-dimensional versions of Calabi-Yau manifolds; that is, highly balanced spaces where the curvatures cancel each other out as a whole. 2. The structure of the holes is rich. Unlike a sim

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

This approach involves updating predictions and probabilities whenever new information becomes available. First prediction ↓ Obtain evidence ↓ Update your forecast The probability is updated each time more information is added. Architecture where space gradually learns and adapts to its optimal state. 無数の可能性が重なり合った形 "Probability Field Architecture" " Architecture is only possible because information is constantly being updated ." Mathematical Architecture space

The sense of time, rhythm, and changes that occur within living organisms 1. Body clock 2. Time for Growth 3. Seasonal Time 4. Metabolism time Time that manifests as changes in life 成長し、変化し、劣化し、回復し、季節に反応する空間 Biological time is "the structure of time that living organisms possess within themselves." Mathematical Architecture space

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

"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 space in which countless triangular orders are hyperbolically folded, resulting in a space that possesses perfect symmetry as a whole. Surfaces of genus 3 It has a topology with three holes. 168 symmetries It possesses the greatest symmetry among Riemann surfaces of genus 3. The number "168" is extremely important. Related to hyperbolic geometry It's easier to understand if you think of it not as a plane, but as an order in a space with negative curvature. 「3つの大きな空洞を持つ双曲的な文

"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

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

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

"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

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

(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