Scale, Patterns, and Fractals

Cristian Suteanu
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Cristian Suteanu: Saint Mary’s University, Department of Geography and Environmental Studies, Department of Environmental Science

Chapter Chapter 7 in Scale, 2022, pp 207-252 from Springer

Abstract: Abstract This chapter applies the concepts associated with scale to a broader context. It introduces fundamental concepts regarding invariance, patterns, and pattern analysis from a perspective centered on scale, presents the main types of symmetry, and highlights the role of symmetry in our exploration of the environment. In particular, scale symmetry is shown to have scale as ratio operating at its core. Given its relevance for our understanding of the natural environment, scale symmetry is further addressed in more details. Fractals and fractal dimension are introduced and defined. An effective method for fractal analysis is described step by step, and the key role of scale as ratio that lies at the core of the method is discussed. Practical aspects regarding the application of the method are described and explained. Scalebound and scale-free patterns are defined, explained, and illustrated with examples.

Keywords: Scale; Pattern; Invariants; Pattern analysis; Environment; Scale invariance; Scale symmetry; Fractal; Self-similar; Self-affine; Power law; Fractal dimension; Box-counting method; Scaling regimes; Multifractals (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-15733-2_7

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DOI: 10.1007/978-3-031-15733-2_7

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