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Subjective observation via informational invariance results in creation of fractals and self‐similar processes of fractional order

Guy Jumarie (Department of Mathematics, University of Québec at Montréal, Montréal, Canada)

Kybernetes

ISSN: 0368-492X

Publication date: 10 August 2010

Abstract

Purpose

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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

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The analysis involves mainly relative observation, Minkowskian observation, Euclidean observation, and fractional calculus.

Findings

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It is shown that observation with informational invariance, which is a modeling of subjectivity, creates fractal, and self‐similarity.

Research limitations/implications

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This result could have an application to the quantitative analysis of volatility in finance, for instance.

Practical implications

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The paper supports the use of fractional dynamics to describe human systems.

Originality/value

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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

Download as .RIS

Publisher

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Emerald Group Publishing Limited

Copyright © 2010, Emerald Group Publishing Limited

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