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.
If we critique Engels’ philosophy (especially historical materialism and dialectics) by comparing it with the perspective of fractal mechanics, the resulting picture takes shape as follows:
The science of fractal statistics must be built directly upon fractal analysis, transcending the linear and Gaussian assumptions of classical statistics. The goal here is to mathematically describe and measure the scale-dependent, self-similar, multifractal structures in nature and systems.
When the fractal analysis of Surah Ali ‘Imran is examined through structural repetitions, symmetry groups, and multi-scale patterns; the surah acts as a continuation of Surah Al-Baqarah, branching out fractally to process the themes of prophethood, faith, and tawhid (monotheism). In particular, the distinction between muhkam (clear/decisive) and mutashabih (allegorical/ambiguous) verses establishes an order that spreads from the center to the periphery, like fractal wave functions.
The “hydrogen universe scenario” refers to a cosmological concept where only hydrogen exists in the universe and neutrons are absent. In this scenario, matter, chemistry, and life could not have emerged with their present-day diversity.
A step-by-step guide to Fractal Calculus. These notes include both the mathematical background and physical interpretations.
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.