Biology

Mendel’s laws of inheritance (dominance, segregation, independent assortment) are the cornerstones of classical genetics. However, when viewed from the perspective of quantum fractal biology, these laws are merely a simplified projection of a “linear” model. The fractal approach proposes that inheritance is a multiscale network woven with energy motifs and shaped by quantum resonances.

Reveals how biological systems can be explained at the intersection of fractal mathematics and quantum mechanics. These notes systematically cover how quantum effects integrate with fractal structures both at the cellular level and in genetic information transfer.

1. Basic Idea: Evolution = Flow of Motifs, Selection = Resonance Alignment Classical Evolution: Mutation + Selection + Drift + Migration Spiral–Fractal Evolution Theory: Motif Variation + Resonance Alignment + Fractal Propagation + Spiral Time Short Formula: Evolution = 𝑑𝑀 / 𝑑𝑡 ,Selection = ℛ(𝑀, 𝒞) 𝑀: spiral–fractal motif (genome + structure + behavior) 𝒞:

Genome = Encoded Energy–Information Map of the Spiral–Fractal Motif 1. FUNDAMENTAL AXIOMS OF GENETICS A1 — The gene is the linear code of the spiral–fractal motif. The DNA sequence is not a “text,” but a 1-dimensional projection of the spiral–fractal motif. 𝐺 ≡ Π(𝑀) 𝑀: spiral–fractal motif Π: projection operator A2 — Genetic information is

This model defines the beginning of life not as a single biological event (e.g., fertilization, first cell division, or heartbeat), but as the locking of multi-scale biological oscillators into a fractal resonance network.

When we interpret faulty protein synthesis in cancer cells from a motif–depth perspective, the processes known in classical biology as “mutation” and “misfolding” can actually be seen as the distorted unfolding of motif depth:

A new foundational biological theory that describes the living cell through spiral flows, fractal motifs, and multi-scale resonances.

Fractal biology connects the following properties of living systems to a single principle: geometry, function, evolution, energy flow, information processing capacity.

The fundamental assumption of this report is: Spacetime is a fractal fluid. The central spiral nodes of this fluid transform into different physical structures at different scales: at the galactic center → black hole, in a stellar system → stellar magnetic dynamo, in a cell → centrosome. These three structures are scale-transformed versions of the same mathematical motif.

Below is a full mathematical report defining the cell membrane from a fractal mechanics perspective, following the chain: motif → structure → field → equation → scaling law.