Exploring potential size-dependent effects of Fibonacci-based acoustic binary strings on cells as measured by cell death and cell aggregation patterns

This paper presents a preliminary investigation into potential size-dependent effects of Fibonacci-based acoustic signals on cells. Cellular responses to externally applied acoustic excitation were evaluated through measurements of reduced cell viability and changes in spatial aggregation patterns. To analyze these effects mathematically, binary Fibonacci sequences were converted into acoustic drive signals, and their spectral properties were examined. These signals distribute energy across multiple frequencies in a deterministic but non-periodic manner that exhibits fractal-like characteristics, with an estimated pointwise dimension of approximately 1.7. Experimental observations using three unicellular model systems (Chlorella vulgaris, Saccharomyces cerevisiae, and Haematococcus pluvialis) suggest that different cell sizes exhibit their strongest responses at different tested frequencies. An exploratory mathematical relationship between cell size and acoustic wavelength, size = (λ + 0.835)/0.8988 (R² = 0.8819), was observed and is presented as a hypothesis-generating trend that warrants further investigation. The range of statistical significance observed across experiments (p-values ranging from approximately 0.003 to 0.1) indicates that additional studies are required to assess reproducibility and elucidate underlying mechanisms. While these initial findings suggest possible directions for future research, substantial further investigation would be necessary to determine any potential relevance to therapeutic applications.