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Fractal

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly…

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Etymology

Introduction

History

Definition and characteristics

Common techniques for generating fractals

Applications

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Fractal

Nodes213
Edges212
Triples275
Avg. degree1.99
Density0.00939
Components1

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Fractal

Top relations

related to Further reading · 111
Fractal → About, Academic Press Professional, Addison Wesley, Advanced Research, Arthur, Available, BASIC, Benoit, Bernt, Bielefeld, Boston, CA, Changsha, Chaos, Clarke, Clifford, Co, Computer Graphical Journey, Corte Madera, Dietmar
see also · 36
Fractal → Analogy, Banach, Boundary, Brownian, Concept, Creation, Cycles, Detailing, Filtration, Functional, Generalization, Hausdorff, Interdisciplinary, Mathematics, Method, Motion, Open, Philosophical, Process, Recurringly
related to Common techniques for generating fractals · 22
Fractal → Because, Brownian, Burning Ship, Cantor, Haferman, Harter-Heighway, IFS, Images, Iterated, Julia, Koch, L-systems, Lyapunov, Lévy, Mandelbrot, Menger, Nova, Peano, Random, Sierpinski
related to External links · 14
Fractal → Art, August, Congress Web Archives, February, Fractals, Hidden Dimension, Hunting, Library, Mandelbrot, November, Oriental Five Elements Fractal, PBS NOVA, Roughness, TED
related to history · 14
Fractal → According, African, Geometry, Gottfried Leibniz, In, Indeed, July, Karl Weierstrass, Leibniz, Pickover, Royal Prussian Academy, Sciences, The, Thus
related to Fractals in cell biology · 10
Fractal → As, Diego Krapf, Fractals, Ian Wong, Multiple, Nerve, Richard Taylor, Similarly Matthias Weiss, The, These
has application · 8
Fractal → ArchaeologyArchitectureClassification, BionicsFractal, Coastline, GPU, MARPATGeographyGeologyMorton, MedicineNeuroscienceOrganic, Menten, Michaelis
related to Definition and characteristics · 8
Fractal → Authors, Besicovitch, Hausdorff, Hilbert, However, In, Mandelbrot, One
related to Physiological responses: Fractal Fluency · 8
Fractal → Fluency, Fractal Expressionism, Humans, Jackson Pollock's, Neuroscience, Pollock, This, When
related to Simulated fractals · 8
Fractal → Also, As, Images, L-systems, Modeled, Models, Some, The

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Important terminology

fractals patterns dimension isbn mandelbrot self-similarity geometric scales one mathematical self-similar also new topological similar set curve many form two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Fractalis ageometric shape containing detailed structure at arbitrarily small scales0.90text
Fractalis arough or fragmented geometric shape that can be split into parts0.90text
in the infinite regress in parallel mirrors or the homunculusinstance ofpeople have pondered self-similarity informally0.80text
the little man inside the head of the little man inside the headinstance ofpeople have pondered self-similarity informally0.80text
the Koch snowflakeinstance offractal curve0.80text
one would never find a small enough straight segment to conform to the curveinstance offractal curve0.80text
because the jagged pattern would always re-appearinstance offractal curve0.80text
at arbitrarily small scalesinstance offractal curve0.80text
essentially pulling a little more of the tape measure into the total length measured each time one attempted to fit it tighterinstance offractal curve0.80text
tighter to the curveinstance offractal curve0.80text
How Long Is the Coast of Britaininstance ofwhen Benoit Mandelbrot started writing about self-similarity in papers0.80text
the Hilbert curve.Because of the trouble involved in finding one definition for fractalsinstance ofthis requirement is not met by space-filling curves0.80text

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