Any flat map can be colored using a maximum of four colors, provided that adjacent regions are not the same color. "The first famous theorem proven by a computer" 隣接関係そのものが建築の形を決める The walls and ceiling are divided like a "three-dimensional map" using gold, crimson, blue-green, and purple acoustic panels. The four colored polygonal regions are continuous from the outer shell to the ceiling, walls, seating area, and circulation paths. Mathematical Architecture space

It is possible to determine whether many convex regions "have a common part as a whole" using only a small number of combinations. When you choose any three things, there is always a common element. A central point or shared space exists that satisfies all conditions. A theorem for finding the commonality of the whole from local overlaps. 複数の凸状ボリュームが重なり、中央の金色に光る共有アトリウムへ収束する The golden light represents the "common area" of each domain. Spaces with different uses exist independ

Values defined continuously within a closed subspace can be extended to the entire space while maintaining continuity, provided the conditions are favorable. This approach involves extending the "continuous conditions" such as light, temperature, sound, and density present in parts of existing buildings naturally into the city and surrounding space, rather than abruptly cutting them off at the boundary. 中央の明るいホールを「局所で定義された連続性」とし、屋根・床・テラス・階段・広場の水平レイヤーがそのまま外部へ拡張していく構成 A hall wh

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

When you draw closed lines that do not intersect on a plane, the plane is always divided into an "inside" and an "outside". It is only by placing a continuous boundary that the concepts of "inside" and "outside" are created. ONE CONTINUOUS BOUNDARY　CREATES INSIDE AND OUTSIDE. A single, non-intersecting closed curve forms the entire structure, clearly separating the central courtyard as the "inside" from the urban plaza as the "outside." The main entrance symbolizes the moment

There are always two points on Earth that are diametrically opposed to each other where the temperature and atmospheric pressure are the same. Even if the external form is asymmetrical, the antipodal points on either side of the center of the building share the same environmental conditions. 「形は異なっていても、正反対の場所が同じ状態になる」 Despite its asymmetrical shape, the hall offers the same experience at its antipodal points. The ends of the straight line passing through the golden central po

"A smooth space is broken down by a single point, line, or plane, and a curved surface is where structure and meaning converge." Singularity Surface Architecture: Architecture where points of failure generate space. 滑らかさではなく、破綻を設計する建築 「空間のエラー」が神聖な中心 Mathematical Architecture space

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

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

The field of spatial analysis requires handling complex data structures and diverse variables. Kenjiro Kimura's proposed spatial analysis method using multivariable polynomials is attracting attention as a technique that significantly improves accuracy and efficiency compared to conventional methods. This article clearly explains the characteristics and specific applications of Kimura's method, exploring the future of spatial analysis. 多変数多項式による空間解析ーあるホール What is spatial anal

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

"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 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

"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

"In a sufficiently large system, 'order' will inevitably emerge." “An order that appears without design.” 1. A pattern emerges despite the random arrangement. 2. Cities unilaterally acquire a "core" 3. "Necessity within coincidence" exterior Giant random grid city countless units Seemingly chaotic However, partial symmetry will always appear. The golden light reveals an "unavoidable structure". Interior Random passage labyrinthine circulation However, walking always converges

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

"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