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According to fractal mechanics, chaos and order are not separate from each other; they are self-similar motifs of the same system emerging at different scales. In this approach, chaos is not disorder; it is the complex repetition of order at fractal scales.
When fractal relativity and quantum field theory are combined, spacetime and energy fields are defined as a self-similar, multi-scale, and dynamic structure. This model breaks the continuity assumption of classical relativity and integrates the probabilistic structure of quantum mechanics with fractal geometry.
Fractal space-time lensing defines the classical gravitational lensing phenomenon by extending it with fractal geometry. In this approach, the bending of light does not occur as a uniform curvature, but in the form of self-similar and multi-scale deflections.
Fractal wave functions aim to redefine the classical wave function concept of quantum mechanics with fractal geometry. In this approach, multiscale, self-similar structures stand out rather than the continuity of the wave function.
Let’s begin to establish the Fractal Meaning Theory. The conclusion I reached from the fractal information theory — energy is the physical state of meaning, information is the conceptual state of meaning — forms the backbone of this theory.
Establishing an information theory according to fractal mechanics requires redefining the classical Shannon approach with the principles of multiscale, self-similarity, and energy density. Here, information is not only the entropy in symbolic sequences; it is also measured by the continuity of fractal patterns, cross-scale correlation, and the organization of energy flow.
When comparing the fractal structure of Surah Al-Baqarah with the fractal properties of the helium atom, the fundamental commonality of both is “multi-scale regularity” and “repeating symmetry patterns”. One manifests in the structure of a sacred text, the other in atomic energy levels.
Below are resources on fractal mechanics, fractal atom theory, and quantum mechanics. These are based directly on academic and theoretical studies; some address the classical foundations of quantum mechanics, while others deal with fractal mathematics and physics applications.
In natural systems, the “energy carriers” motif represents the transformation mechanism that provides energy to the system. On a cellular scale, this task is undertaken by mitochondria and electron transitions, while on a cosmic scale, it is carried out by the nuclear fusion of stars. The essence of the motif: Energy is produced at the center and distributed to the system through carrier mechanisms.
The “Orbit–Trajectory” motif represents the dynamic order rotating around a nucleus or center in natural systems. At the atomic scale, this appears as electron orbits, and at the planetary scale, as planetary orbits. The essence of the motif: The center gathers energy, and the surrounding structures move in regular cycles.