Authors: Blair D. Macdonald
As a fractal structure emerges — repeating a simple rule — it appears to share directproperties familiar to classical economics, including production, consumption, andequilibrium. Fractal geometry is found universally and is said to be one of the bestdescriptions of our reality — from clouds and trees to market price behaviour. Thispaper investigated whether the mathematical principles behind ‘the market’ — marginalism — is an aspect or manifestation of a fractal geometry or attractor. Total and marginal areas (assumed to stand for utility) and the cost of production were graphed as the fractal grew and compared to a classical interpretation of diminishing marginal utility theory and the market supply and demand. PED and PES were also calculated and analysed with respect to (iteration) time and decay. It was found that the fractal attractor demonstrates properties and best models classical economic theory, and from this, it was deduced that the market is a fractal attractor phenomenon where allproperties are inextricably linked. The fractal, at equilibrium, appears to be a convergent — zeta function — series, able to be described by Fourier analysis and involves Pi, i, e, 0, and 1 (of Euler’s identity) in one model. It also demonstrated growth, development, evolution and Say’s Law — production before consumption. Insights from the fractal on knowledge and knowing are also revealed, with implications on what exactly ‘science’ is and what ‘art’ is. A connection between reality and quantummechanics was identified. It was concluded marginal; classical economics is an aspectof fractal geometry.
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