Hausdorff dimension

Shapes that cannot be explained in ordinary dimensions (1D, 2D, 3D)

Famous dimension

① Koch curve

• Dimensions: Approximately 1.26 dimensions

② Sierpinski triangle

• Dimensions: Approximately 1.58 dimensions

③ Cantor set

• Dimensions: Approximately 0.63 dimensions

"Architecture where scale collapses"

建物 ≒ 地形 ≒ 宇宙構造

Prompt 1

fractal architecture based on Hausdorff dimension, recursive self-similar structure, infinite detail facade, multi-scale geometry, organic yet mathematical form, highly detailed exterior, drone perspective, soft natural light, strong shadows, parametric design, futuristic cultural hall, no text, ultra high resolution, cinematic, 16:9

Prompt 2

hausdorff dimension architecture, extreme recursive self-similar megastructure, scale ambiguity, infinite detail illusion, collapsing dimensionality, boundary between inside and outside dissolving, organic fractal geometry fused with parametric design, glowing microstructures, surreal landscape, cinematic lighting, ultra high resolution, no text, 16:9

“Space itself is a fractal.”

Mathematical Architecture

space