Definition
Fractal
A Fractal is a complex geometric shape that exhibits self-similarity across different scales. If a fractal is subdivided into parts, each part is (at least approximately) a reduced-size copy of the whole.
Characteristics
Fractals differ from Euclidean geometry in that their dimensions are often non-integers, and their perceived length or surface area can increase as the resolution of measurement increases. This is famously illustrated by the Richardson effect, which notes that the measured length of a coastline (like that of Britain) grows as the ruler used to measure it becomes smaller.
Biological Applications
Living organisms utilise fractal structures to solve biophysical problems, particularly in distributing resources across three-dimensional space using one-dimensional networks.
- Scaling Laws: As explored by Geoffrey West, fractal branching in circulatory systems and bronchial tubes leads to universal scaling laws. For instance, the number of heartbeats in a mammal’s lifetime is roughly constant (1.5–2 billion) regardless of body mass.
- Multifractals: Real-world systems are often multifractals—they exhibit repetitive structure at every scale, but the specific patterns vary across scales.
Multifractal Symbiosis
From a computational perspective, the genome exhibits fractal-like properties due to the process of symbiogenesis. Because genomes are built by repeatedly copying and merging sub-sequences (which are themselves replicators), they develop a hierarchical, self-similar structure.
Observation
DNA is highly compressible precisely because it is a system that evolves through “multifractal symbiosis”. It is an aggregate of cooperating replicators all the way down, resulting in the power-law scaling of repeated sequences found in genomic data.