File:3fractals2.jpg
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Summary
Description3fractals2.jpg |
These are examples of multiplicative cascade fractals. To create these distributions there are a few steps to take. Firstly, we must create a lattice of points which will be our underlying probability density field. Then we will populate this lattice with randomly placed points, insisting that the probability that the points be placed are proportional to the cell probability. The fractal is constructed as follows: The space is split into four equal parts, each part is then assigned a probability from the set without replacement. Where . Each subspace is then divided again and assigned probabilities randomly from the same set and this is continued to the level. At the level the probability of a cell being occupied is the product of the cell's and its parents and ancestors up to level 1 i.e. all the cells above it. In constructing this model down to level 8 we produce a array of cells each with its own probability. To then place particle in the space we invoke a Monte Carlo rejection scheme. Choosing x and y coordinates randomly we simply test if a random number between 0 and 1 is less or greater than the cell probability. We typically dust the probability density field with 5,000 points in a space of 256 x 256. Model I (left plot): Model II (middle plot): Model III (right plot): |
Date | 9 August 2007 (original upload date) |
Source | Own work |
Author | User:Csabiu |
Licensing
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
Attribution: Csabiu | ||
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Original upload log
Transferred from en.wikipedia to Commons using For the Common Good.
Date/Time | Dimensions | User | Comment |
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14:10, 9 August 2007 | 1,990 × 732 (504,822 bytes) | w:en:Csabiu (talk | contribs) | () |
13:30, 9 August 2007 | 1,990 × 732 (504,822 bytes) | w:en:Csabiu (talk | contribs) | (These are examples of multiplicative cascade fractal.) |
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current | 09:55, 22 June 2012 | 1,990 × 732 (493 KB) | wikimediacommons>Hydriz | Transferred from en.wikipedia: see original upload log above |
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