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

"Infinity has varying degrees of magnitude." Cantor Dust fractal topology infinite structure All of these originate from Cantor's set theory. "A city that exists, yet hardly exists." 「都市を削ることで現れる都市」 Cantor Group Mathematical Architecture space