Hausdorff dimension

Yuki
Apr 16
1 min read

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"

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