Detection of a Fractal Element with Complex-Conjugated Power-Law Exponents in Living Systems: Analysis of the Temporal Evolution of Impedance Measurements in the Unblown Bud Plumeria Flower (Frangipani Plumeria)

Abstract

In this paper the proposed theoretical model describing 3D-branching systems in the intermediate range of frequencies was applied in the first time for description and further fitting of the complex impedance in a living system, as unblown bud plumeria flower (Frangipani Plumeria). The proposed fitting function that follows from the applied model allows to describe completely with high accuracy (the fitting error is less than 0.25%) the whole stages of the temporal evolution of the bud plumeria flower in room conditions (T = 30 ± 1 ℃, with relative humidity located in the interval [50% ≤ H ≤ 70%] during 19 days (25.03.21–12.04.21) of the impedance evolution measurements. The reason of selection of this plumeria flower taken in the form of the unblown bud is related to the fact that all possible conducting channels form approximately 3D-heterogeneous branching structure. The fitting function contains the power-law exponent with complex-conjugated parts and serves as the first evidence of detection of the fractal element in the living systems. Two stages as normal and quasi-chaotic were detected during 123 measurements. The basic fitting parameters that can detect these stages have been found. The qualitative explanation of the processes that take place in this living system and does not contradict with measured data is given.Keywords3D-branshing/fractal systemsImpedance measurements in the unblown bud flowerNew fractal element with complex-conjugated power law exponents