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In this study, a spiral–fractal number system that goes beyond classical analysis and arithmetic is unified with quantum field theory. The aim is to transform the particle–wave duality into a motif–resonance duality and to redefine quantum dynamics on spiral coordinates.
Gravity, in the classical sense, is not the “mutual attraction of masses”; rather, it is the pushing/pulling of matter caused by differences in orientation within the spiral density field of spacetime. So attraction → spiral field gradient.
The interpretation below is a universal physical framework that connects fractal mechanics to the classical–quantum–field theory triad.
Space-time is a fractal fluid. Gravity = large-scale flow of this fluid, Quantum = small-scale fractal vibration, SFD = fundamental wave solution of this fluid. The theory is built on three pillars: Fractal geometry, Fluid dynamics, Spiral-fractal wave function
Classical physics defines water as: H₂O molecules, Hydrogen bonds, Liquid phase, Thermal motion. Fractal mechanics defines water as: Water = a multiscale, self-similar hydrogen bond fractal exhibiting collective behavior. This fractal can be analyzed across four layers: Geometric Fractal (Void Structure), Energy Fractal (Vibrational Modes), Information Fractal (Collective Wave Field), Structural Fractal (EZ water / Structured Water)
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:
Particle structures → linear motion
Quantized structures → wave motion
So what about fractal structures → ?
This third category is not properly defined anywhere in classical physics. But when viewed from within fractal mechanics, the answer is very clear:
The model below unifies the starting point (FREB) and the ending point (FRAMET) of fractal evolution within a single mathematical circle and precisely determines the position of the black hole within this circle.
Below is a comprehensive technical report explaining the term FRAMET in its scientific, fractal-mechanical, and conceptual integrity. This report systematically presents the core of the fractal evolution model.
This essentially means constructing the alphabet of fractal physics. I will now build it from the foundation—starting with the motif. Each term will be explained both mathematically and intuitively.