"Architectural design generated using probability and randomness" Buildings = Topography of probability distributions → Topographication Order × Randomness = Statistical Order 臨界状態（壊れる一歩手前） (Space becomes distorted) A space where a continuous function appears discontinuous → The architectural representation of phenomena Mathematical Architecture space

"Geometric spaces with completely different shapes actually contain the same information." Space A Space B Geometry: Counting Curves Geometry for studying hole structure Space A Space B (Complex curve) ←→ (Complex hole) 鏡宇宙を移動する体験 Twin buildings with different shapes Architecture A Architecture B Organic forms full of curves linear Flowing Corridor Courtyard type Movement distance, line of sight, and spatial volume are in perfect agreement. Mathematical Architecture space

Mathematics that deals with "shape (topology)" and "logic/programs" in the same language. Space = Transformable proof → Architecture that allows you to walk through a proof → Architecture that is a maze yet leads you to the same place ∞次元トポロジー Mathematics = multidimensional space → Loops, twists, non-Euclidean wires Mathematical Architecture space

"The study of mathematically dealing with patterns of randomly (accidentally) placed points, lines, and surfaces." Mathematical modeling of random spatial structures 建築と都市の中間 "Cities are architecture that grow like living organisms." "Architecture that has come into existence" rather than "architecture that has been designed" Mathematical Architecture space

"A phenomenon where seemingly unrelated fields of mathematics coincide at an unbelievable level." Monstrous Moonshine The coefficients in the expansion of the modular function are as follows: 196884 = 196883 + 1 196883 → Dimensions of representation of monster groups 1 → Self-evident expression "Architecture where structure and light are perfectly aligned" 広大な都市広場の中央に、完全に無機質な黒い直方体が静かに立っている。 The surface appears flat at first glance, but upon closer inspection, countless irregu

"A hotel that's fully booked but can still accommodate guests." 無限を説明するための思考実験 部屋は 1号室、2号室、3号室…と無限にある。すでに全部満室 Mathematical Architecture space