Recursive Fractal Structures And Harmonic Intervals Drive Multi-Frequency Synchronization.
Creators: name: Kirjonen, Miikka Markus
name: Kirjonen, Miikka Markus
Publisher: name: Zenodo
Year: 2025
Subjects: subject: interval harmonics
subject: wave interference
subject: phase field coupling
subject: harmonic overtones
subject: quantum topological phenomena
subject: spatiotemporal spectrum
subject: recursive feedback
subject: harmonic intervals
subject: multi-scale synchronization
subject: spin–lattice
subject: spin liquid
subject: topological invariant
subject: pattern formation
subject: tritone
subject: integer
subject: magnons
subject: topology
subject: topological
subject: quantum spin liquid
subject: Cognitive Science
subject: Cognitive Science/methods
subject: Cognitive Science/statistics &amp; numerical data

description: We introduce a Recursive Spatiotemporal Morphogenetic Framework by RSM, that unifies fractal morphogenetic fields with interval harmonics—including tritones and topological integer relationships—to explain coherent pattern formation across quantum, mechanical, and neural domains. By weaving together phonon–magnon interactions and recursive morphogenetic fields, RSM demonstrates how fractal expansions, wave interference, and topological invariants combine to produce stable, coherent phenomena in systems ranging from quantum spin liquids to neural networks and material spintronics.

In this approach, phase field coupling and harmonic intervals emerge as critical drivers for multi-scale synchronization: fractal recursion organizes wave excitations and feedback loops, thereby revealing how multi-frequency coherence underlies phenomena like spin–lattice synergy, neural synchrony, and advanced functional materials. Through this lens, we uncover new perspectives on the interplay of coherence and decoherence, showing that fractal morphogenetic fields and harmonic interactions can unify quantum spin excitations with neural dynamics.

Finally, the recursive nature of RSM underpins potential applications in quantum computing, spintronics, and cognitive science, where morphological fractals and harmonic wave couplings converge. By crystallizing these concepts in a single framework, RSM highlights a universal language of recursive feedback, fractal topologies, and musical intervals that orchestrates coherence across the spatiotemporal spectrum.

This approach incorporates:





Phonon–magnon interactions extended by fractal morphogenetic feedback loops,




Recursive PDE expansions that sustain emergent coherence in quantum spin liquids, neural networks, and macro-scale wave phenomena,




Higher-order coupling in non-linear equations capturing complex resonance behaviors.




By uniting fractal recursion, harmonic intervals, and topological invariants, RSM illuminates the synergy behind multi-frequency synchronization—ranging from quantum spin excitations to neural synchrony.



This Paper illuminates,





How recursive fractal structures and harmonic intervals drive multi-frequency synchronization. 




That potential applications span quantum computing, spintronics, and cognitive science,




The synergy between morphological fractals and harmonic couplings.




Fractal Morphogenetics , Musical Overtone Harmonics and Topological Integers.



By tying in phonon–magnon interactions, fractal recursion, and phase field coupling, we unify multi-scale synchronization in quantum, mechanical, and biological systems. Ultimately, this paper underscores how recursive feedback, fractal topologies, and harmonic intervals collectively orchestrate coherence across the spatiotemporal spectrum, bridging harmonic overtones with quantum topological phenomena.