Fractal Neural Dynamics and Memory Encoding Through Scale Relativity.

Area of Science:

• Computational Neuroscience
• Theoretical Physics
• Neurobiology

Background:

• Classical models of synaptic plasticity (e.g., Hebbian learning, spike-timing-dependent plasticity) often neglect the distributed and wave-like nature of neural activity.
• Scale Relativity Theory (SRT) offers a framework for describing neural propagation in a non-differentiable spacetime with fractal properties.

Purpose of the Study:

• To develop a computational framework grounded in Scale Relativity Theory (SRT) to explain structured memory representations.
• To link nonlinear wave dynamics with emergent memory structures in a biologically plausible manner.

Main Methods:

• Modeled neural activity using nonlinear Schrödinger-type equations derived from SRT.
• Coupled synaptic plasticity via a reaction-diffusion rule based on local activity intensity.
• Performed simulations in 1D and 2D domains using finite difference schemes and analyzed results with spectral entropy, cross-correlation, and Fourier methods.

Main Results:

• The model reproduced neurobiological features like CA1 place fields, entorhinal grid cells, and V1 orientation maps.
• Interacting waveforms demonstrated interference-dependent plasticity, modeling memory competition and contextual modulation.
• The system exhibited robustness to noise, gradual potentiation, hysteresis, and multi-scale memory structures through cross-frequency coupling.

Conclusions:

• Wave-driven dynamics in fractal spacetime offer a novel hypothesis for distributed memory formation.
• The theoretical framework successfully reproduces biological motifs but requires further validation against established models and empirical testing.
• Future work should incorporate neuromodulatory and glial influences and propose experimental tests.