On the Response of Proteinoid Ensembles to Fibonacci Sequences

This work investigates the integration of Fibonacci patterns and Golden Ratio principles into proteinoid-based systems, connecting fundamental mathematical concepts with contemporary biomimetic approaches. Proteinoids are thermal proteins that can self-assemble and have enzyme-like capabilities. They provide a distinct platform for biomimetic information processing. Our study examines the impact of integrating Fibonacci sequences and the Golden Ratio (ϕ = 1.618) into the design and synthesis of proteinoids on their structural organization and response characteristics. We developed two categories of stimuli: auditory signals generated using frequencies derived from the Fibonacci sequence, and electrical patterns that correspond to the proportions of the Golden Ratio. The proteinoid microsphere assemblies were subjected to these stimuli, and their electrical and structural responses were recorded and analyzed. The results indicate that proteinoid systems reveal unique reactivity to acoustic stimuli based on the Fibonacci sequence, exhibiting heightened sensitivity to particular combinations of frequencies and demonstrating nonlinear amplification effects. The proteinoid assemblies exhibited distinctive temporal dynamics and emergent oscillatory behaviors when exposed to voltage patterns inspired by the Golden Ratio, which were not detected with ordinary input signals. These findings provide opportunities for developing advanced bioinspired information transfer and security systems and might improve our understanding of information processing in early chemical systems.