Subjective observation via informational invariance results in creation of fractals and self‐similar processes of fractional order
Abstract
Purpose
The purpose of this paper is to explain why fractal, self‐similarity, and fractional Brownian motions are so pervasive in human systems.
Design/methodology/approach
The analysis involves mainly relative observation, Minkowskian observation, Euclidean observation, and fractional calculus.
Findings
It is shown that observation with informational invariance, which is a modeling of subjectivity, creates fractal, and self‐similarity.
Research limitations/implications
This result could have an application to the quantitative analysis of volatility in finance, for instance.
Practical implications
The paper supports the use of fractional dynamics to describe human systems.
Originality/value
The paper provides practical arguments that may explain why fractals are so pervasive in natural science, and mainly in systems involving human factors.
Keywords
Citation
Jumarie, G. (2010), "Subjective observation via informational invariance results in creation of fractals and self‐similar processes of fractional order", Kybernetes, Vol. 39 No. 7, pp. 1167-1183. https://doi.org/10.1108/03684921011062764
Publisher
:Emerald Group Publishing Limited
Copyright © 2010, Emerald Group Publishing Limited