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.
Fractal Symmetry Breaking, distinct from classical symmetry breaking, refers to an approach that accounts for the inter-scale distortion dynamics of motifs, rather than just the breaking of a symmetry at a single scale.
Fractal statics is an approach that combines the classical static concept of “equilibrium” with fractal geometry and multiscale structures. In classical statics, for an object to remain in equilibrium, the sum of forces and moments must be zero. In fractal statics, however, these equilibrium conditions are satisfied not just for a single scale, but across all sub-scales and self-repeating fractal motifs of the system.
Spiral-Fractal time functions break the classical linear understanding of time, defining it as a multiscale, cyclical, and resonant structure. This approach creates new computational possibilities in both physical systems and biological/social processes.
The fine-structure constant (𝛼 ≈ 1/137) is a dimensionless constant that determines the strength of electromagnetic interactions. This constant manifests in the fine details of atomic spectra (e.g., the energy levels of hydrogen).
Fractal Magnetic Field Theory is a brand-new field theory that integrates the time-derivative structure of classical Maxwell fields with the scale-derivative structure of fractal mechanics. Below are the axioms, field equations, operators, physical interpretations, and circuit equivalents of the complete theory. This stands as the natural extension of fractal circuit theory.
This model explains the “reading” process in biological systems through spiral–fractal resonance chains. DNA decoding, enzyme substrate selection, and ribosomal protein synthesis are all unified under the same universal reading operator.
This paper formally proves Goldbach’s conjecture within the framework of Fractal Arithmetic and the Riemann Hypothesis. In fractal arithmetic, each natural number is defined as a fractal wave function composed of motif, scale, orientation, and resonance components. The Riemann Hypothesis is a necessary consequence under fractal arithmetic axioms. This regularity makes the spiral–fractal density function of prime distribution equal to 𝐷(𝑁) = 1 in every interval.
Fractal surface activity: Catalyst surfaces are not homogeneous; they possess fractal roughness and porous structures. The distribution of active sites is measured by the fractal dimension 𝐷.