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.
Protein folding is one of biophysics’ most complex problems, and the classical approach describes this process as a minimization problem on a multidimensional free energy landscape. This study reformulates protein folding within the Fractal Mechanics (FM) framework, modeling the folding process as a spiral–hierarchical collapse of a fractal wave function. The proposed model defines a local spiral wave number (k-local) for each amino acid and a hierarchical resonance parameter (q) for each structural scale, suggesting that folding is driven not only by energy but also by resonance and fractal continuity. Comparative analysis with the classical funnel model shows that FM offers novel advantages, particularly in explaining rapid folding, misfolding, and aggregation phenomena.
This report covers the application of atomic-level circuit motifs to biochemical molecule design. Basic assumption: Each atomic bond is the physical equivalent of a circuit element; each functional group is a circuit segment; Each molecule is a fractal scaled circuit architecture. This approach provides isomorphic coupling of biochemical functions with the Elementary Circuit Topology I developed. The analgesic effect is a low-pass filter + gain reduction + feedback function in the biological circuit. Therefore, the circuit response of the molecule to be designed must also carry these functions.