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AbstractBranching patterns occur throughout nature and are often described by the Fibonacci numbers. While the regularity of these branching patterns in biology can be described by the Fibonacci numbers, the branches (leaves, petals, offshoots, limbs, etc.) are often variegated (size, color, shape, etc.). To begin to understand how these patterns arise, we considered different branching patterns based on p-Fibonacci sequences. In our model, different branching patterns were created based on a specific number of decreasing-sized branches that arise from a main branch (termed the degree of branching). It was assumed that the ratio between the sizes of pairs of consecutive branches (ordered by size) equals the ratio of the largest branch size to the sum of the largest and smallest branch sizes. Generation of these branching structures illustrates that pattern self-similarities occur across different degrees of branching and multiple dimensions. Conclusion: studying geometric branching patterns based on p-Fibonacci sequences begins to show how the regularity in branching patterns might occur in biology.

A flexible nanocomposite of cobalt hexacyanoferrate (CoHCF) and commercial carbon cloth (CC) was prepared by facile electrodeposition of CoHCF on a flexible CC surface. As a kind of flexible integrated electrode without polymer binders, the flexible CC–CoHCF nanocomposites were directly used for nonenzymatic H2O2sensing. Several techniques such as scanning electron microscopy, energy dispersive X-ray spectroscopy, Fourier transform infrared spectroscopy and electrochemistry were employed for the characterization of the electrode. It was found that CoHCF nanoparticles (about 100 nm) uniformly deposited on the CC surface. Electrochemical experiments demonstrated that the flexible CC–CoHCF nanocomposite electrode exhibited good electrocatalytic activity towards the oxidation of H2O2. Based on the amperometric experiments, the proposed nonenzymatic sensor showed a linear response to H2O2detection in the range of 0.002–9.04 mM with a detection limit of 0.7 μM, which was superior to most of the previous results. Such a good result renders it a promising candidate for routine testing.