"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

"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

Mathematics that understands probability distributions and statistical models as "curved spaces" Geometric spaces with different curvatures Information Geometry Architecture It's completely different from fractal architecture. theory space fractal self-similarity chaos non-linear information geometry statistical surface theory shape Mandelbrot Set Jagged, self-similar Hyperbolic Geometry Divergence and sharp distortion information geometry Smooth, statistical terrain 都市に現れた、滑

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