Classical analysis treats nature as an instantaneous cross-section; it takes a “photograph” of nature with fixed parameters, stationary equations, and single-scale processes. Fractal analysis, however, treats nature within process, through interactions between scales, resonance, and feedback loops—essentially, it takes a video of nature.
Kant is one of the most critical turning points of modern philosophy: by determining the limits of reason, he opposed both dogmatism and skepticism. However, his emphasis on the unknowability of the “thing-in-itself” and the rigid autonomy in his understanding of morality carries both strong and controversial aspects.
Feynman diagrams are tools of quantum field theory that visually represent particle interactions; from the perspective of fractal mechanics, these diagrams can be interpreted as a projection of fractal networks that explain particle behavior through multi-scale wave-resonance motifs.
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.
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).