Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Fractal_dimension> ?p ?o }
- Fractal_dimension abstract "A fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured. It has also been characterized as a measure of the space-filling capacity of a pattern that tells how a fractal scales differently from the space it is embedded in; a fractal dimension does not have to be an integer.The essential idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions. In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastline's measured length changes with the length of the measuring stick used (see Fig. 1). In terms of that notion, the fractal dimension of a coastline quantifies how the number of scaled measuring sticks required to measure the coastline changes with the scale applied to the stick. There are several formal mathematical definitions of fractal dimension that build on this basic concept of change in detail with change in scale.One non-trivial example is the fractal dimension of a Koch snowflake. It has a topological dimension of 1, but it is by no means a rectifiable curve: the length of the curve between any two points on the Koch Snowflake is infinite. No small piece of it is line-like, but rather is composed of an infinite number of segments joined at different angles. The fractal dimension of a curve can be explained intuitively thinking of a fractal line as an object too detailed to be one-dimensional, but too simple to be two-dimensional. Therefore its dimension might best be described not by its usual topological dimension of 1 but by its fractal dimension, which in this case is a number between one and two.".
- Fractal_dimension thumbnail Britain-fractal-coastline-200km.png?width=300.
- Fractal_dimension wikiPageExternalLink Fractals.htm.
- Fractal_dimension wikiPageExternalLink fracdim.
- Fractal_dimension wikiPageExternalLink www.trusoft-international.com.
- Fractal_dimension wikiPageID "285907".
- Fractal_dimension wikiPageLength "34556".
- Fractal_dimension wikiPageOutDegree "90".
- Fractal_dimension wikiPageRevisionID "679543900".
- Fractal_dimension wikiPageWikiLink Arc_length.
- Fractal_dimension wikiPageWikiLink Assouad_dimension.
- Fractal_dimension wikiPageWikiLink Attractor.
- Fractal_dimension wikiPageWikiLink Benoit_Mandelbrot.
- Fractal_dimension wikiPageWikiLink Box-counting_dimension.
- Fractal_dimension wikiPageWikiLink Box_counting.
- Fractal_dimension wikiPageWikiLink Brady_Haran.
- Fractal_dimension wikiPageWikiLink Calculus.
- Fractal_dimension wikiPageWikiLink Category:Chaos_theory.
- Fractal_dimension wikiPageWikiLink Category:Dimension_theory.
- Fractal_dimension wikiPageWikiLink Category:Dynamical_systems.
- Fractal_dimension wikiPageWikiLink Category:Fractals.
- Fractal_dimension wikiPageWikiLink Coalescence_(chemistry).
- Fractal_dimension wikiPageWikiLink Colloid.
- Fractal_dimension wikiPageWikiLink Complexity.
- Fractal_dimension wikiPageWikiLink Correlation_dimension.
- Fractal_dimension wikiPageWikiLink Diffusion-limited_aggregation.
- Fractal_dimension wikiPageWikiLink Diffusion_limited_aggregation.
- Fractal_dimension wikiPageWikiLink Entropy_(information_theory).
- Fractal_dimension wikiPageWikiLink Euclidean_geometry.
- Fractal_dimension wikiPageWikiLink Felix_Hausdorff.
- Fractal_dimension wikiPageWikiLink Fractal.
- Fractal_dimension wikiPageWikiLink Fractal_analysis.
- Fractal_dimension wikiPageWikiLink Fractal_derivative.
- Fractal_dimension wikiPageWikiLink Fractals.
- Fractal_dimension wikiPageWikiLink Gaston_Julia.
- Fractal_dimension wikiPageWikiLink Hausdorff_dimension.
- Fractal_dimension wikiPageWikiLink Helge_von_Koch.
- Fractal_dimension wikiPageWikiLink Higuchi_dimension.
- Fractal_dimension wikiPageWikiLink How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension.
- Fractal_dimension wikiPageWikiLink Infinity.
- Fractal_dimension wikiPageWikiLink Information_entropy.
- Fractal_dimension wikiPageWikiLink Integer.
- Fractal_dimension wikiPageWikiLink Julia_set.
- Fractal_dimension wikiPageWikiLink Koch_snowflake.
- Fractal_dimension wikiPageWikiLink L-System.
- Fractal_dimension wikiPageWikiLink L-system.
- Fractal_dimension wikiPageWikiLink Lacunarity.
- Fractal_dimension wikiPageWikiLink Lebesgue_covering_dimension.
- Fractal_dimension wikiPageWikiLink Lewis_Fry_Richardson.
- Fractal_dimension wikiPageWikiLink Limit_(mathematics).
- Fractal_dimension wikiPageWikiLink List_of_fractals_by_Hausdorff_dimension.
- Fractal_dimension wikiPageWikiLink Local_connected_dimension.
- Fractal_dimension wikiPageWikiLink Logarithm.
- Fractal_dimension wikiPageWikiLink Mandelbrot_set.
- Fractal_dimension wikiPageWikiLink Minkowski–Bouligand_dimension.
- Fractal_dimension wikiPageWikiLink Multifractal.
- Fractal_dimension wikiPageWikiLink Multifractal_analysis.
- Fractal_dimension wikiPageWikiLink Multifractal_system.
- Fractal_dimension wikiPageWikiLink Packing_dimension.
- Fractal_dimension wikiPageWikiLink Particle_aggregation.
- Fractal_dimension wikiPageWikiLink Pattern.
- Fractal_dimension wikiPageWikiLink Power_law.
- Fractal_dimension wikiPageWikiLink Probability_distribution.
- Fractal_dimension wikiPageWikiLink Proportionality_(mathematics).
- Fractal_dimension wikiPageWikiLink Rectifiable_curve.
- Fractal_dimension wikiPageWikiLink Regression_lines.
- Fractal_dimension wikiPageWikiLink Rényi_entropy.
- Fractal_dimension wikiPageWikiLink Sample_(statistics).
- Fractal_dimension wikiPageWikiLink Scaling_(geometry).
- Fractal_dimension wikiPageWikiLink Self-similarity.
- Fractal_dimension wikiPageWikiLink Set_(mathematics).
- Fractal_dimension wikiPageWikiLink Sierpinski_triangle.
- Fractal_dimension wikiPageWikiLink Sierpiński.
- Fractal_dimension wikiPageWikiLink Slope.
- Fractal_dimension wikiPageWikiLink Space.
- Fractal_dimension wikiPageWikiLink Space-filling_curve.
- Fractal_dimension wikiPageWikiLink Topological_dimension.
- Fractal_dimension wikiPageWikiLink Uncertainty_exponent.
- Fractal_dimension wikiPageWikiLink University_of_Nottingham.
- Fractal_dimension wikiPageWikiLink Wacław_Sierpiński.
- Fractal_dimension wikiPageWikiLink File:32_segment_fractal.jpg.
- Fractal_dimension wikiPageWikiLink File:Blueklineani2.gif.
- Fractal_dimension wikiPageWikiLink File:Fractaldimensionexample.PNG.
- Fractal_dimension wikiPageWikiLink File:KochFlake.svg.
- Fractal_dimension wikiPageWikiLink File:Onetwosix.png.
- Fractal_dimension wikiPageWikiLinkText "Fractal (q = 1)".
- Fractal_dimension wikiPageWikiLinkText "Fractal Dimension Analysis".
- Fractal_dimension wikiPageWikiLinkText "Fractal dimension".
- Fractal_dimension wikiPageWikiLinkText "Rényi dimensions".
- Fractal_dimension wikiPageWikiLinkText "dimension".
- Fractal_dimension wikiPageWikiLinkText "fractal dimension".
- Fractal_dimension wikiPageWikiLinkText "theory of fractal dimensions".
- Fractal_dimension align "right".
- Fractal_dimension alt "Coastline of Britain measured using a 100 km scale".
- Fractal_dimension alt "Coastline of Britain measured using a 200 km scale".
- Fractal_dimension alt "Coastline of Britain measured using a 50 km scale".
- Fractal_dimension caption "(11.5 x 200 = 2300 km)".
- Fractal_dimension caption "(28 x 100 = 2800 km)".
- Fractal_dimension caption "(70 x 50 = 3500 km)".
- Fractal_dimension footer "Figure 1. As the length of the measuring stick is scaled smaller and smaller, the total length of the coastline measured increases.".