Is the golden ratio a universal constant for self-replication?

PloS One
Yu Liu, David J T Sumpter

Abstract

The golden ratio, ϕ = 1.61803…, has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its mathematical origins in Fibonacci's sequence for "rabbit reproduction". Recently, it has been claimed that ϕ determines the ratio between the number of different nucleobases in human genome. Such empirical examples continue to give credence to the idea that the golden ratio is a universal constant, not only in mathematics but also for biology. In this paper, we employ a general framework for chemically realistic self-replicating reaction systems and investigate whether the ratio of chemical species population follows "universal constants". We find that many self-replicating systems can be characterised by an algebraic number, which, in some cases, is the golden ratio. However, many other algebraic numbers arise from these systems, and some of them-such as [Formula: see text] and 1.22074… which is also known as the 3rd lower golden ratio-arise more frequently in self-replicating systems than the golden ratio. The "universal constants" in these systems arise as roots of a limited number of distinct char...Continue Reading

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Citations

Dec 14, 2018·Journal of Virology·Ryan H GumpperMing Luo
Dec 25, 2021·PsyCh Journal·Daniela De BartoloMarco Iosa

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