A structure in which countless circles within a 3-dimensional sphere correspond neatly to a 2-dimensional sphere. "A space created by the intertwining of infinite circular corridors." ”思考スタイル”として再構成した比較想像図 ① Flowing curved surface type ② Silent minimalist type ③ Structural logic exposed type Fluid / Continuous / Dynamic Geometry 迷路ではなく流体空間 Mathematical Architecture space

An equation that smooths out the "curvature" of space over time. Imagine this: → There's a wrinkled surface → We'll make the shape uniform. → Something like heat diffusion in space → Smooths out curvature → Deforms the shape of space over time → Shape evolves → Space becomes simpler → Shape becomes smoother over time → “Chaos → Order” A monumental cultural hall inspired by Ricci Flow geometry, aerial drone perspective, the architecture expresses a continuous transformation f

A collection of exceptional symmetries that do not belong to any large pattern (an infinitely continuing family). Monster group Mathieu Group Conway Group Fisher group, etc. Sporadic group: "An unknown creature that suddenly appears (only one exists)." "A structure that deviates from theory, yet somehow works perfectly." 全体ルールが存在しないのに、崩壊しない構造 "Experiences are continuous, but space is not." "A cross-section where a different building emerges no matter where you cut it." Mathem

A concept of urban design that applies random movement to urban forms, probabilistically generated curved cities normal city + + + + + + + + + + + + + + + Brown City ~ ~ ~~ ~ ~~ ~ ~~ ~~~ Cities are "generated like terrain." ground Gentle, random undulations road No straight lines It continues to curve slightly. building Embedding in a curved surface In other words City = Mega-landscape parametric city 「ブラウン多様体都市」 The space itself is a performance device; the cross-section is

Basic image time 1 ⬜⬛⬜⬜ ⬜⬜⬛⬜ ⬛⬜⬜⬛ ↓ time 2 ⬜⬜⬜⬜ ⬜⬛⬛⬜ ⬜⬜⬜⬜ Changes over time Conway's Game of Life From the life-and-death changes of cells on a grid that follow simple rules, complex and unpredictable patterns emerge. 成長する建築 The key to a cellular automaton is to visually represent its characteristics: growth, discreteness, and local rules. Mathematical Architecture space

Shapes that cannot be explained in ordinary dimensions (1D, 2D, 3D) Famous dimension ① Koch curve Dimensions: Approximately 1.26 dimensions ② Sierpinski triangle Dimensions: Approximately 1.58 dimensions ③ Cantor set Dimensions: Approximately 0.63 dimensions "Architecture where scale collapses" 建物 ≒ 地形 ≒ 宇宙構造 Prompt 1 fractal architecture based on Hausdorff dimension, recursive self-similar structure, infinite detail facade, multi-scale geometry, organic yet mathematical form