Isometric
Describing scaling where proportions remain constant regardless of size—each dimension changes at the same rate. Contrasts with allometric scaling where proportions change with size.
Used in the Books
This term appears in 2 chapters:
"... how properties change with size through power-law relationships: Y = aX^b, where b is the scaling exponent. When b equals one, the relationship is isometric - double the size, double the property. When b differs from one, it's allometric - double the size, and the property changes by 2^b."
"...linearly with volume (not volume^(2/3)). Scaling consequence: The fractal structure enables lung surface area to scale as body mass^0.98 (nearly isometric), despite volume scaling as mass^1.0. This keeps oxygen delivery capacity matched to metabolic demand across body sizes - mice and elephants have pro..."
Biological Context
If organisms scaled isometrically, a scaled-up ant would have the same proportions as a normal ant. But physical constraints prevent this—strength scales with cross-sectional area while weight scales with volume, requiring allometric changes in larger organisms.