"A space created by gathering all the 'shapes (structures)' that satisfy certain conditions, and then classifying and organizing them." "A space in which geometric and algebraic objects are classified by 'grouping similar objects together as one.'" ● Circle Moduli ● Moduli of a donut (torus) Not "space itself," but "space of space." "A space that uses differences in shape as coordinates." Mathematical Architecture space

"A polygon with an infinite number of sides" "Apeirogon" comes from the Greek words apeiros (infinity) + gonia (horn). "A way of thinking that views a circle as a 'polygon that is infinitely divided'" 終わらない回廊都市 ● Architecture with an endless corridor ● Deconstruction of a circular hall ● Architecture where only the boundary exists Mathematical Architecture space

"A phenomenon where a state changes suddenly, almost as if it's flying, after having been changing slowly." The form "cusp" Space is gradually compressed. In a sense, "the view suddenly opens up." The flow of movement suddenly branches or reverses. Architecture that creates a continuous space, yet the experience is discontinuous. 連続変化 → 突然の空間ジャンプ The ball is in a valley. The terrain gradually changes. At a certain moment, it jumps into another valley. This "jumping" becomes

The outer space becomes incredibly complex. Strange topology 絡まり地獄 Hilbert Hotel Architecture A crazy space Mathematical Architecture space

It's continuous (not interrupted), yet it can't be differentiated anywhere (the slope cannot be defined). A space where details continue endlessly f(x)=n=0∑∞​ancos(bnπx) Curved surfaces vibrate infinitely; slabs become fractalized ; light creates abnormal shadows. Mathematical Architecture Mathematical Architecture space

"Cities may appear random, but in reality, they are made up of self-similarity (fractals) and nonlinearity (chaos)." ① Hierarchical design of scale 👉 This creates a "comfortable atmosphere" ② Network optimization 👉 Resilient to disasters and congestion ③ Blurring of boundaries 👉 Spaces with chaotic "fluctuations" "Designing growth rules" 「建築というより小都市」 "A cultural hall without a central point"