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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

–

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

  • Cybernetics
  • Systems theory
  • Information theory

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

:

Emerald Group Publishing Limited

Copyright © 2010, Emerald Group Publishing Limited

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