Fractal Neural Dynamics and Memory Encoding Through Scale Relativity

TL;DR

This paper proposes a new computational model for memory encoding using fractal neural dynamics and wave-like activity in non-differentiable space-time.

Contribution

It introduces a novel framework based on Scale Relativity Theory to explain distributed memory formation through nonlinear wave dynamics.

Findings

The model reproduces biological features like place fields, grid cells, and orientation maps.

Interference-driven plasticity and cross-frequency coupling generate complex memory structures.

The system shows robustness to noise and learning dynamics similar to empirical observations.

Abstract

Background/Objectives: Synaptic plasticity is fundamental to learning and memory, yet classical models such as Hebbian learning and spike-timing-dependent plasticity often overlook the distributed and wave-like nature of neural activity. We present a computational framework grounded in Scale Relativity Theory (SRT), which describes neural propagation along fractal geodesics in a non-differentiable space-time. The objective is to link nonlinear wave dynamics with the emergence of structured memory representations in a biologically plausible manner. Methods: Neural activity was modeled using nonlinear Schrödinger-type equations derived from SRT, yielding complex wave solutions. Synaptic plasticity was coupled through a reaction–diffusion rule driven by local activity intensity. Simulations were performed in one- and two-dimensional domains using finite difference schemes. Analyses included spectral entropy, cross-correlation, and Fourier methods to evaluate the organization and complexity of the resulting synaptic fields. Results: The model reproduced core neurobiological features: localized potentiation resembling CA1 place fields, periodic plasticity akin to entorhinal grid cells, and modular tiling patterns consistent with V1 orientation maps. Interacting waveforms generated interference-dependent plasticity, modeling memory competition and contextual modulation. The system displayed robustness to noise, gradual potentiation with saturation, and hysteresis under reversal, reflecting empirical learning and reconsolidation dynamics. Cross-frequency coupling of theta and gamma inputs further enriched trace complexity, yielding multi-scale memory structures. Conclusions: Wave-driven dynamics in fractal space-time provide a hypothesis-generating framework for distributed memory formation. The current approach is theoretical and simulation-based, relying on a simplified plasticity rule that omits neuromodulatory and glial influences. While encouraging in its ability to reproduce biological motifs, the framework remains preliminary; future work must benchmark against established models such as STDP and attractor networks and propose empirical tests to validate or falsify its predictions.

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