Classical quantum mechanics describes atomic orbitals using sinusoidal-phase and exponentially decaying wave functions. However, this approach is insufficient to explain the multiscale spiral structures observed in nature, such as magnetic field lines, plasma flows, galaxy arms, and DNA helices. In this study, we propose a spiral–fractal wave function that redefines the fundamental form of the wave function:
Fractal Ontology is a framework that explains how existence emerges at the most fundamental level. Fractal Mechanics describes how a motif unfolds across scales once it has formed. However, it does not answer the following question:
According to fractal mechanics, society is: a combination of motifs, the interaction of scales, the repetition of cycles, resonance fields, direction vectors forming a multi-layered fractal system. Society is not a single “whole”; it is a network of motifs repeating across scales.
Fractal psychology explains the human mind through: Motif (core personality), Scale (layers of the self), Cycle (emotional periods), Resonance (environment–mind harmony), Direction (vector of personal evolution). The mind is not a single whole; it is a network of motifs repeating across scales.
According to fractal mechanics, chemistry is not the sum of random behaviors of atoms and molecules. Chemistry is the repeating pattern of the energy–field–probability motif across scales.
This interpretation treats chemistry as a fractal structure along the chain: atom → molecule → macromolecule → crystal → matter. Below, each fundamental concept of chemistry is reconstructed through the five laws of fractal mechanics.
According to fractal mechanics, mathematics is: The universal language that describes the repeating structure of motifs across scales. In other words, mathematics is not the science of numbers, but the science of how scales behave.
I now explain how fractal mechanics is applied to the discipline of history, interpreting the period from the mid-19th century to the present entirely through my model’s laws of motif–scale–cycle–resonance.
This is not a classical historical narrative; it is a higher-scale analysis that reveals the fractal structure of history and divides eras into mathematical motifs.
Fractology is a new philosophical system that explains being, consciousness, knowledge, and meaning through scale-independent fractal laws.
Inflation is no longer:
Psychology,
Money supply alone,
or supply-demand imbalance.
Inflation = incompatibility among fractal energy, pressure, geometry, curvature, and coupling constant.
Economy is a fractal field theory.
Inflation is its phase transition.
When we speak of “the political interpretation of Fractal Mechanics,” we are entering the most powerful—and most dangerous—dimension of my Fractal Mechanics Theory. Because the issue here is not parties, individuals, or ideologies; it is scale, power, institutions, and the architecture of society.
For this very reason, I will construct a completely general, universal, impersonal, and neutral framework—yet one that remains deeply analytical. This interpretation refers to no country, party, individual, or contemporary political figure; it speaks only through the scale behavior of systems.