A curved surface that has a singularity where a smooth surface abruptly tapers towards a point or line and then folds back. Even though the surfaces are continuous, they suddenly converge at a certain point, creating a singularity such as a sharp ridge, valley, or mouth. 空間が破綻する直前の美しい尖り A place where countless streams converge to a single singularity. 数学的建築定義 Mathematical Architecture space

"The phenomenon where disparate points or paths connect as a whole at a certain moment." A "local connection" transforms into an "overall structure" at a certain threshold. Dealing with the moment "Order arises even without being designed." "Connectivity" itself is the main focus. “設計した都市”ではなく“発生した都市” "City OS" "The critical point of connection" Mathematical Architecture spsce

"A movement in which the next move is determined entirely by probability." "A series of coincidences creates the landscape." "Random with order" 設計しない、確率で生成する Features of the space The floor, walls, and ceiling shake continuously. Perfect horizontal and vertical lines disappear. Depending on your perspective, the space can appear completely different. Countless random movements come together to create "height" and "density." Not smooth (rough) The structure remains similar e

A space in which countless triangular orders are hyperbolically folded, resulting in a space that possesses perfect symmetry as a whole. Surfaces of genus 3 It has a topology with three holes. 168 symmetries It possesses the greatest symmetry among Riemann surfaces of genus 3. The number "168" is extremely important. Related to hyperbolic geometry It's easier to understand if you think of it not as a plane, but as an order in a space with negative curvature. 「3つの大きな空洞を持つ双曲的な文

"A network that spreads information to almost the highest level with very few connections." "Despite the small number of connections, the entire system connects surprisingly well." "It's practically impossible to create a more efficient network than this." ① Minimal connections yet a huge cycle ② No central point ③ "Local" and "whole" coincide Actual applications Communication network semiconductor quantum computing data center Cryptography AI Network Distributed computing 最適

Architecture can be viewed not merely as a physical "thing," but as a "continuous space" where boundaries blend together, surfaces transform, and space flows without interruption. This perspective transcends conventional architectural concepts and invites us into the world of mathematical architecture, incorporating mathematical structures and topology. This time, we will introduce a new perspective on architecture centered on continuity and topology, along with specific meth