Modeling Transistor Growth: Moore’s Law Revisited Exploiting the Golden Ratio

This paper revisits Moore’s Law, the well-known empirical law which predicted the doubling of the number of transistors on a silicon chip every two years, by proposing an alternative model of transistor growth based on the golden ratio (𝝋 ≈ 𝟏. 𝟔𝟏𝟖), a fundamental constant often found in natural and biological systems. We analyze a dataset covering the period 1971-2025 and compare the traditional exponential growth pattern of Moore’s Law, whose sustainability is threatened by physical limits on hardware architectures and atomic-scale transistor dimensions, with a scaling law model inspired by 𝝋. The results show that while Moore’s Law overestimates transistor growth in recent years, the proposed scaling law based on the golden ratio aligns more closely with actual data, updating predictions about every 6.6 years. This suggests a shift towards more sustainable, biologically inspired technological development, with significant implications for fields such as Information Communication Technology (ICT), Artificial Intelligence (AI), quantum computing and neuromorphic computing.