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Fractal dimension

In geometric measure theory, fractal dimensions enable consistent statistical indexes of complexity in patterns. Since fractal patterns can be scale-variant, measuring space-filling capacity should be possible in non-integer (fractal) dimensions.

History, Examples & Estimating from real-world data

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Overview

Introduction

History

Mathematical definition

D is not a unique descriptor

Fractal surface structures

Examples

Estimating from real-world data

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Map overview Semantic statistics

Fractal dimension

Nodes77
Edges76
Triples85
Avg. degree1.97
Density0.025974
Components1

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Fractal dimension

Top relations

related to Examples · 19
Fractal dimension → Although, Bigl, Bigr, Box-counting, Correlation, For, Generalized, Hausdorff, Higuchi, In, Information, Lyapunov, Packing, Parabolic Hausdorff, Rényi, Several, The, The Hausdorff, Uncertainty
related to D is not a unique descriptor · 11
Fractal dimension → As, Diffusion-limited, Fig, For, Fractal, Koch, L-system, Mandelbrot, Many, Sierpinski, The
related to External links · 11
Fractal dimension → Brady Haran, Compute Fractal Dimensions Archived, Fractal AnalysisBowley, Fractals, Java Applet, Nottingham, Roger, Sixty Symbols, TruSoft's Benoit, University, Wayback MachineIntroduction
related to history · 11
Fractal dimension → Britain, Hausdorff, Julia, Koch, Mandelbrot, See Fractal, Sierpiński, The, There, These, Various
related to Estimating from real-world data · 10
Fractal dimension → An, Fractal, In, Lempel, Many, Nonetheless, Practically, Riemann, To, Ziv
related to Introduction · 10
Fractal dimension → Benoit Mandelbrot, But, Euclidean, Fig, For, Fractal, If, Several, The, Thus
related to Fractal surface structures · 6
Fractal dimension → It, Mean, Numerous, RA, RRMS, The
related to Mathematical definition · 6
Fractal dimension → For, In, Now, Similarly, Such, The
is a · 1
Fractal dimension → index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale

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Important terminology

fractal dimension dimensions self-similarity displaystyle mandelbrot scaling detail koch fractals length patterns complexity two number infinite sets curve mathematical see

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Fractal dimensionis aindex for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale0.90text
Fractal dimensionrelated to D is not a unique descriptorAs0.60section
Fractal dimensionrelated to D is not a unique descriptorThe0.60section
Fractal dimensionrelated to D is not a unique descriptorKoch0.60section
Fractal dimensionrelated to D is not a unique descriptorMany0.60section
Fractal dimensionrelated to D is not a unique descriptorFig0.60section
Fractal dimensionrelated to D is not a unique descriptorFor0.60section
Fractal dimensionrelated to D is not a unique descriptorFractal0.60section
Fractal dimensionrelated to D is not a unique descriptorSierpinski0.60section
Fractal dimensionrelated to D is not a unique descriptorMandelbrot0.60section
Fractal dimensionrelated to D is not a unique descriptorDiffusion-limited0.60section
Fractal dimensionrelated to D is not a unique descriptorL-system0.60section

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