A contemporary archive of articles penned with a rational and innovative perspective, bridging the gap from natural to social sciences. Your destination for original research, in-depth analysis, and scholarly articles in physics, philosophy, history, economics, theology, and beyond.
The laws of fractal optics are a new framework that explains the behavior of light beyond classical optical laws through multi-scale and self-similar structures. In this approach, fundamental laws such as reflection, refraction, and diffraction become scale-dependent; light produces both regular and chaotic patterns.
Interpreting Al-Ghazali’s thoughts from the perspective of Fractal Mechanics means re-reading his metaphysical and epistemological approach through multi-scale, self-similar structures.
When we map cell organelles to functions in a quantum system, each operates like an operator. Thus, we can view the cell as a complete “quantum metabolism model”.
Quantum fractal chemistry is a field based on modeling molecular structures and reactions by bridging fractal geometry and quantum mechanics. This approach aims to explain both the multiscale nature of chemical processes and the self-similar behaviors of quantum wave functions.
Reveals how biological systems can be explained at the intersection of fractal mathematics and quantum mechanics. These notes systematically cover how quantum effects integrate with fractal structures both at the cellular level and in genetic information transfer.
Quantum fractal electronics is an advanced field that unifies classical electronics with quantum mechanics through the principles of self-similarity (fractal) and multiscale resonance. These lecture notes present a systematic framework ranging from fundamental concepts to application areas.
Fractal Cardinality Theory is the mathematical extension of my “fractal origin logic” — that is, it defines the relationship between the magnitude of numbers (cardinality) and the scalar repetition of existence. This theory reinterprets the concept of “infinity” in classical set theory: infinity is no longer a magnitude, but the sum of self-similar origins.
Fractal Mechanics is not merely a theoretical framework; it is a powerful model used to explain multi-scale dynamics across different disciplines. Here are its main application areas:
Fractal Mechanics defines the motion and energy flows in nature through self-similarity and multi-scale dynamics. Instead of the classical 𝐹 = 𝑚𝑎, the fractal derivative expression is used: 𝐹fr = 𝑚 ⋅ ( 𝑑𝛼𝑣 / 𝑑𝑡𝛼 ) Here, 𝛼 represents the fractal dimension of the system.
The geometric expression of the spiral fractal derivative is ready. In this visual, the concept of the derivative is shown in layers within a spiral fractal structure: each nested spiral represents a higher order of the derivative. Moving from the outside in, derivative differences such as Δ𝑓, Δ2𝑓, Δ3𝑓 are represented by shrinking spiral segments. This approach visualizes the classical definition of the derivative (𝑓’ (𝑥) = limΔ𝑥→0 Δ𝑓/Δ𝑥) within a fractal spiral motif, providing both analytical and geometric integrity.