(An energetic perspective) Energy (Hamiltonian) → Time evolution → Motion There is an "invisible topography (energy undulation)" in space, and particles flow through it. "Architecture that designs movement itself" 動いていないのに動いて見える "Dynamic Space Architecture" Mathematical Architecture space ■ Gumroad https://shomei.gumroad.com/l/apmao ■ Lemon Squeezy https://shomei.lemonsqueezy.com/ ■ Payhip https://payhip.com/MathematicalArchitectureS ■ BOOTH https://shomei-a.booth.pm

The world where form, sound, and vibration modes correspond. Visualization of spatial shape = eigenfunctions → "Architecture with overlapping frequency layers" 「音の干渉縞」 Humans become "particles in the sound field" The space itself is a mixer Mathematical Architecture space

Space itself is a "structure that possesses power." "Architecture that designs changes in space," rather than "architecture that creates form." The realm of designing "relationships themselves" → "Architecture that visualizes the distribution of invisible forces" 空間＝位置と運動のペア system Content Relationship with Symplectic Mandelbrot Shape generation ❌ Wrong Lehman Face multilayer space △ Related topology connection ◎ Core non-commutative interaction ◎ Deeply related Yang Mills pl

"Mathematics is the process of unifying disparate, localized pieces of information into a coherent, unified whole structure." ① Segmentation (local) ② Connection (restriction mapping) ③ Integration (gluing) "A collective building that retains differences in its components while perfectly aligning only its boundaries." ①形態 × ②構造 × ③運動 を統合 Core Geometry Mathematical Architecture space

"Geometry that deals with the relationships between motion and energy" Geometry that governs the motion of the universe Geometry of movement paths → Human movement × Space 流れが凍結した建築 If topology is about "preserving shape," then symplectic architecture is about "preserving motion." Mathematical Architecture :

"A structure in which distant places or spaces are directly connected within a building." The "instantaneous" connection of space → "architecture that eliminates distance" The internal space is topologically broken. Visual perception and movement patterns do not align. "Time" also becomes a design subject. Opening the sliding door of a Showa-era house reveals a futuristic city—this is a "disconnecting jump." "Architecture that breaks down and reconnects distance, continuity,

"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

"An integer version of complex numbers with the symmetry of a triangle (60°)" Eisenstein integers → triangular lattice (60°) → hexagonal tile (honeycomb structure) "The most stable planar structure" honeycomb crystal A configuration in which force is evenly distributed. "The structure chosen by nature" "Unifying everything under the rule of 60 degrees." 「中心を持たない文化」 Space that grows diagonally ↑ "Architecture where crystals proliferate like living organisms, losing their bound

Physical laws do not change even when a certain "transformation of perception" is applied. The forces of the universe = gauge symmetry In architecture, mathematics is incredibly powerful. Yang-Mills theory Wilson Loop Holographic principle Chern–Simons theory Gauge/Gravity compatible When viewed from a distance A single massive mass of fluid As you get closer A collection of countless misaligned spaces As we got closer You can see the "flow (force) of light" running along the

Space + Time = Spacetime Black Hole ● ↓↓↓ ───∪∪∪─── Gμν + Λgμν = c48πGTμν Black Hole Architecture physics concepts architectural elements Spacetime distortion Nonlinear grid of exterior walls Gravity well Settlement pattern towards the center Event horizon ring-shaped facade The bending of light Light facade (reflection and convergence) physics concepts architectural elements Spacetime distortion Nonlinear grid of exterior walls Gravity well Settlement pattern towards the cen

A structure in which points are arranged in a regular and infinite pattern in space. A perfectly formed supercrystal → A gigantic symmetrical city → A cosmic-scale urban grid 無限に続く構造 静かな建築 structure = light 24 Dimensions of Light Mathematical Architecture space

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

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