Information vs. Dimension: An algorithmic perspective

Jan Reimann

doi:10.1142/9789813228238_0004

Information vs. Dimension: An algorithmic perspective

Jan Reimann

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

This paper surveys work on the relation between fractal dimensions and algorithmic information theory over the past thirty years. It covers the basic development of prefix-free Kolmogorov complexity from an information theoretic point of view, before introducing Hausdorff measures and dimension along with some important examples. The main goal of the paper is to motivate and develop the informal identity “entropy = complexity = dimension” from first principles. The last section of the paper presents some new observations on multifractal measures from an algorithmic viewpoint.

Original language	English (US)
Title of host publication	Structure And Randomness In Computability And Set Theory
Publisher	World Scientific Publishing Co.
Pages	111-151
Number of pages	41
ISBN (Electronic)	9789813228238
DOIs	https://doi.org/10.1142/9789813228238_0004
State	Published - Jan 1 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)
Computer Science(all)

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10.1142/9789813228238_0004

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Information vs. Dimension: An algorithmic perspective

Abstract

All Science Journal Classification (ASJC) codes

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