Abstract
The aim of this study was to explore the golden ratio (Φ) based scaling relations existing between the golden ring volume, the golden measure equation (GME) and transversal dynamics of growth ring formation. Magnitudes of the golden ring volume, the golden ring cube and parameters of the GME were experimentally quantified based on X-ray densitometer data of Douglas-fir and white spruce. Thereafter, transversal dynamics of the parameter-fitted equations were analysed. The Φ (1·618) was satisfied by both species with 95% confidence. The first order derivative of the GME agreed with the transversal momentum of growth ring formation. The second order derivative was deduced to have potential in explaining transversal physiological transitions from earlywood to latewood and juvenile to mature wood. The structure and formation of growth rings are shown to be self-optimised based on Φ and this finding may explain why wood has higher strength-to-weight ratio in comparison with other materials.
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