A world of "not smooth spaces" Thinking in terms of distance and measure Viewing in terms of extremes and scales Approach it probabilistically Treat as a discrete structure "A space where you can't find peace anywhere."   「世界は本当に滑らかなのか？」 Differentiable = Ideal/Smooth Not differentiable = realistic, rough, complex 👉 Non-differentiable geometry is **"geometry that is close to reality"**

A situation where rules exist, but unpredictable actions occur. for example weather Water flow Movement of crowds of people Moving endlessly within complex shapes → somewhere between order and disorder "Architecture where getting lost itself becomes an experience." 秩序のある迷宮

A collection of points floating randomly in space A space that "exists, yet lacks coherence." "A city that exists but is disconnected" → "A space where continuity has been completely destroyed" “存在とは何か”を問う建築 A fantastical landscape of a disconnected city and futuristic skyscrapers.

Beautiful vs. Wild tame = "gentle" vs wild = "wild" ① The “extreme behavior” of space ② "Geometry where intuition doesn't work" Wild topology = "A continuous yet uncontrollably complex space." 未来的な有機的建築複合体

🌀 Main line flow Swirling curves: The spiral flow that dominates the entire screen creates a cosmic sense of movement. Fluid Wavy Lines: Red, pink, blue, and orange colors merge in a wave-like pattern, representing the flow of energy. Convergence towards the center: A composition in which all lines guide the viewer's gaze towards the central light (sun). 💧 The effect of vertical lines The dripping vertical lines visible at the edges create a surrealistic "melting" effect. T

Defining architecture itself as geometry and determining how waves behave. ① Definition of the space (hall) itself The interior of the hall is treated as a three-dimensional space. Ω⊂R3\Omega \subset \mathbb{R}^3Ω⊂R3 Boundaries (walls, ceilings, floors, columns, openings) ∂Ω\partial \Omega∂Ω Let's assume that. The coordinates of each point are x=(x,y,z)x = (x,y,z)x=(x,y,z) ② The basic equation for waves propagating in space (time-dependent) The fundamental form of sound, ligh

Slow zoom-in motion A slightly enhanced glowing effect. 24fps / Full HD Landscape prompt Vertical video, chaotic dense urban structures, cyberpunk atmosphere, dark tones, slow zoom in, cinematic lighting, ultra realistic マッピング picture Night view + building silhouettes

The original three-way balance design Light → Organic and natural connection Le Corbusier → Geometric Order, Pilotis, Roof Gardens Mies van der Rohe → Extreme Minimalism, Purification of Structure 構造＝ミース　　 秩序＝コルビュジエ　　外形＝ライト

Fusion concept Structure: Based on Mies van der Rohe's "Universal Space," the space is so transparent that iron and glass almost disappear. Form: Le Corbusier's "piloti" liberates the ground surface, while "organic terraces," reminiscent of Wright's architecture, appear to sprout from the ground, breaking through a rigid grid and blending into the surrounding nature. Light and Materials: The inorganic concrete and steel are permeated with the unique stone materials and war

Time does not circulate in a straight line, but rather in a "closed circle." Self-causal existence (causa sui) type time structure Are humans truly free? "They just think they're free." Time does not move forward, it cycles. ◆ Basic definition spatial area Ω⊂R3\Omega \subset \mathbb{R}^3Ω⊂R3 Time and place T(x)T(x)T(x) Density of existence (intensity of causality) Ψ(x)\Psi(x)Ψ(x) ◆ Core governing equations ∇⋅(C(x)∇Ψ(x))+ω2T(x)Ψ(x)=Ψ(Φ(x))\nabla \cdot \bigl( C(x)\nabla \Psi(x)

What is possible in architecture? et cetera

A " compassionate human" is a "caring person" who deeply empathizes with the suffering and sorrow of others, and actively seeks to alleviate their pain by standing by them and taking action. "Chikatillo" is "a beautifully decorated hellish closet." 未来都市の幻想的な光景 夢幻的な花園の中で 未来都市の光と影

In terms of cooking Finished dish → The process of separating the ingredients The rule that governs the whole Viewing the structure of the world 0 is "boundary" ■ Three things that govern nature ① Law (equation) World rules ② State (initial conditions) Initial state ③ Chance (fluctuations/noise) minute disturbances "Structure + Condition + Coincidence" What kind of sensibility is required of an architect? Ability to set conditions 感情に応じて変化する未来的空間

■ Mathematical Model of Space Generation Algorithms Let S be the spatial shape. Basic formula S=argmin⁡S[w1O(S)+w2Sym(S)+w3C(S)+w4P(S)+w5K(S)]S = \operatorname*{argmin}_{S} \Big[ w_1 O(S) + w_2 Sym(S) + w_3 C(S) + w_4 P(S) + w_5 K(S) \Big]S=Sargmin[w1O(S)+w2Sym(S)+w3C(S)+w4P(S)+w5K(S)] ■ Meaning (architectural translation) The shape of space S is determined by the shape that minimizes the evaluation values of "order, symmetry, continuity, proportion, and complexity." Archite

Features mathematics architecture abstraction Replacing real-world phenomena with mathematical formulas and symbols. Translating daily life and functions into spatial configurations. logic Build a logically sound proof. Building a foundation of structural and functional evidence creativity Discover new solutions that go beyond existing frameworks. Creating new spatial experiences within constraints element mathematical background Impact on space Parametric lofting A function

数学の基本定数 "The most beautiful mathematical formula in the world" "Resonance Dome" "Pool of Consciousness" "Connecting rays of light" "The Silent Corridor" テレパシーを感じる建築空間

The "atom" of the world of numbers A sequence at the boundary between order and chaos ウラムの螺旋

"The power to extract invisible structures" "A concept that compresses complexity" "A symbol of symmetry and balance" ...A mental apparatus that returns complex reality to a form that can be understood—a principle that translates spatial quantities into forms. The reason why square root ratios naturally appear in architecture is because humans themselves have a square root structure. 空洞としての数 Giacometti = making numbers into bones Michelangelo = embodying numbers in physical f

Complex space, rather than a "space of position" that most naturally represents rotation, vibration, waves, and quantum states, is a "space of vibrational states." Complex number form name formula coefficient Orthogonal form z = a + ib Real part a=ℜ(z), imaginary part b=ℑ(z) polar form z = r(cosθ + isinθ) Absolute value r = |z|, argument θ = arg⁡(z) Exponential function format z=reiθ Phasor format z=r∠θ A tool to simplify complex phenomena into a "simple form". It look

I thought it was a straight line, but it was actually a curve. In reality, friction heat noise External disturbance It gets in there. In other words, nature is always slightly curvilinear . ● Twist position (3D straight line) ● A world where the shortest distance is not a straight line Relationships become more complex when the space changes. Straight lines represent "shape," while curves represent "relationships." y = ax