Fractal Calculus
A step-by-step guide to Fractal Calculus. These notes include both the mathematical background and physical interpretations.
Fractal Meaning Theory
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.
Information Theory According to Fractal Mechanics
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.
Energy, Meaning Duality in the Context of the Fractal Structure of Surah Al-Baqarah and the Fractal Properties of the Helium Atom
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.
Fractal Analysis of Surah Al-Baqarah
The fractal analysis of Surah Al-Baqarah is structurally based on “ring composition” and multi-scale thematic symmetry. In this surah, the verses are connected to each other through mutual echoes and symmetrical repetitions among the introduction–development–conclusion sections.
Towards Fractal Physics
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.
Common Motifs in Nature at Different Scales 5 – The Energy Carriers Motif
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.
Common Motifs in Nature at Different Scales 4 – Orbit–Trajectory Motif
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.
Descartes’ Thoughts According to Fractal Mechanics
Interpreting Descartes’ thoughts according to fractal mechanics makes it possible to reread his “quest for certainty” and “methodical doubt” approach as multi-scale motifs. Although Descartes’ proposition “Cogito ergo sum” appears as an absolute starting point on a single plane, from a fractal perspective, it is understood as the core of consciousness motifs repeating at different scales.
Interpretation of Gabriel Garcia Marquez’s Works from the Perspective of Fractal Literature
Gabriel Garcia Marquez’s works can be read from the perspective of fractal literature through their repeating motifs, cyclical time, and narrative structures that reproduce themselves in a self-similar manner. The motifs seen in his texts, from “One Hundred Years of Solitude” to “Chronicle of a Death Foretold,” exhibit the same structural patterns at both the micro and macro levels, much like fractal geometry.