Fractal
A geometric pattern that repeats at every scale—the same basic shape appears whether you zoom in or out. Fractals have non-integer dimensions and infinite detail.
Used in the Books
This term appears in 7 chapters:
"...l model for the origin of allometric scaling laws in biology. Science, 276(5309), 122-126. - Theoretical framework explaining Kleiber's Law through fractal network theory of resource distribution systems Shrew Metabolic Data: Etruscan shrew (Suncus etruscus). Wikipedia. Retrieved 2025."
"...ches: Each should have radius r where 10³ = 2r³ - Solution: r = 10 / ∛2 = 7.94 cm Each bifurcation reduces radius by ~21% (1 - 1/∛2 = 0.206). The fractal consequence: Trees exhibit self-similar branching across scales (trunk → branches → twigs). Each level follows Murray's Law."
"Faster pruning = faster reallocation = more resources to high-productivity branches = more fruit. Fractal Branching: Scale-Free Architecture Tree branching follows fractal patterns: the architecture repeats at multiple scales. The trunk splits into ..."
"They emerge from fundamental physical and geometric constraints. The three-quarters power reflects fractal-like branching networks - circulatory systems in biology, communication networks in organizations - that distribute resources through three-dimension..."
"Book 7, Chapter 2: Fractal Geometry - Self-Similarity Across Scales Introduction In 1904, Swedish mathematician Helge von Koch constructed a peculiar geometric object."
And 2 more chapters...
Biological Context
Branching patterns in lungs, blood vessels, and trees are approximately fractal—similar branching appears at every level from major vessels to capillaries. Fractal geometry allows organisms to maximize surface area within limited volume. Coastlines and mountain ranges also show fractal properties.