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.
Dyson spheres are mathematical structures built upon infinite energy density and vacuum fluctuations in the classical sense. According to fractal mechanics, however, these spheres are not single-scale; they are explained by multi-scale self-similarity motifs. That is, a Dyson sphere is not a flat sphere, but an energy lattice containing fractal sub-spheres on every edge.
According to fractal mechanics, the void is not “nonexistence”; it is a multi-layered carrier of self-similar energy and information flows. Both the void within the atom and the void in space are filled with fractal motifs: they gain structure through invisible but constantly changing flows of entanglement.
The constancy of the speed of light can be explained with different interpretations beyond classical physics, according to both relativistic and fractal mechanics. Let us unfold this through patterns and energy flow: