Utente:Spock/Sandbox: differenze tra le versioni

Versione delle 12:41, 24 dic 2006

Versione delle 12:52, 24 dic 2006

Riga 108:

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! δ<br />(exactvalore valueesatto) || δ<br />(valuevalore) || NameNome || IllustrationIllustrazione || width="40%" | RemarksCommenti

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|MeasuredMisurato||align="right"|1.24||[[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension|CoastlineCosta ofdella GreatGran BritainBretagna]]||align="center"| [[Image:Gb4dot.svg|100px]] ||

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|<math>\textstyle{\frac {4}{3}}</math> || align="right" | 1.33 || [[Boundary of Brownian motion]] || align="center" |[[Image:Front mouvt brownien.png|150px]] || (Cf [[Wendelin Werner]])<ref>[http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Amath%2F0010165 Fractal dimension of the brownian motion boundary]</ref>.

Riga 120:

| || align="right" | 1.40 || [[diffusion-limited aggregation|Clusters of clusters 2D]] || align="center" | || When limited by diffusion, clusters combine progressively to a unique cluster of dimension 1.4. (Cf Sapoval)

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| MeasuredMisurato|| align="right" | 1.52|| [[CoastlineCosta ofdella NorwayNorvegia]] || align="center" |[[Image:Norgeskart.png|100px]] ||

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| MeasuredMisurato|| align="right" | 1.55 || [[Random walk with no self-intersection]] || align="center" | [[Image:2D self-avoiding random walk.png|150px]]|| Self-avoiding random walk in a square lattice, with a « go-back » routine for avoiding dead ends.

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| <math>\textstyle{\frac {5} {3}}</math>|| align="right" | 1.66|| [[3D Polymer]] || align="center" | || Similar to the brownian motion in a cubic lattice, but without self-intersection (Cf Sapoval).

Riga 130:

| <math>\textstyle{\frac {91} {48}}</math> || align="right" | 1.8958 || [[2D Percolation cluster]] || align="center" | [[Image:Amas de percolation.png|150px]] || Under the percolation threshold (59.3%) the percolation-by-invasion cluster has a fractal dimension of 91/48 (Cf Sapoval). Beyond that threshold, le cluster is infinite and 91/48 becomes the fractal dimension of the « clearings ».

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| <math>\textstyle{\frac {ln(2)} {ln(\sqrt{2})}}</math> || align="right" | 2 || [[BrownianMoto motionbrowniano]] || align="center" | [[Image:Mouvt_brownien2.png|150px]]|| OrO randomcamminata walkcasuale. Thele dimensioni di Hausdorff dimensionssono equalsuguali a 2 in 2D, in 3D ande in alltutte le greateraltre dimensionsdimensioni (K.Falconer "The geometry of fractal sets").

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| <math>\textstyle{\frac {ln(13)} {ln(3)}}</math> || align="right" | 2.33 || [[CauliflowerCavolfiore]] || align="center" | [[Image:Blumenkohl-1.jpg|100px]]|| EveryOgni branchramo carries aroundporta 13 branchesrami 3 timesvolte più smallerpiccoli.

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| || align="right" | 2.5 || Balls of crumpled paper || align="center" | [[Image:Paperball.jpg|100px]] || When crumpling sheets of different sizes but made of the same type of paper and with the same aspect ratio (for example, different sizes in the [[ISO 216]] A series), then the diameter of the balls so obtained elevated to a non-integer exponent between 2 and 3 will be approximately proportional to the area of the sheets from which the balls have been made. [http://classes.yale.edu/fractals/FracAndDim/BoxDim/PowerLaw/CrumpledPaper.html] Creases will form at all size scales (see [[Universality (dynamical systems)]]).

Riga 139:

| || align="right" | 2.50 || [[diffusion-limited aggregation|3D DLA Cluster]] || align="center" | [[Image:3D diffusion-limited aggregation2.jpg|100px]] || In 3 dimensions, clusters formed by diffusion-limited aggregation, have a fractal dimension of around 2.50 (Cf Sapoval).

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| || align="right" | 2.97 || LungSuperficie surfacepolmonare || align="center" |[[Image:Thorax Lung 3d (2).jpg|100px]] || TheGli alveoli ofdi aun lungpolmone formformano auna fractalsuperficie surfacefrattale closedi todimensione vicina a 3 (Cf Sapoval).

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