fractal dimension

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fractal dimension

(mathematics)
A common type of fractal dimension is the Hausdorff-Besicovich Dimension, but there are several different ways of computing fractal dimension. Fractal dimension can be calculated by taking the limit of the quotient of the log change in object size and the log change in measurement scale, as the measurement scale approaches zero. The differences come in what is exactly meant by "object size" and what is meant by "measurement scale" and how to get an average number out of many different parts of a geometrical object. Fractal dimensions quantify the static *geometry* of an object.

For example, consider a straight line. Now blow up the line by a factor of two. The line is now twice as long as before. Log 2 / Log 2 = 1, corresponding to dimension 1. Consider a square. Now blow up the square by a factor of two. The square is now 4 times as large as before (i.e. 4 original squares can be placed on the original square). Log 4 / log 2 = 2, corresponding to dimension 2 for the square. Consider a snowflake curve formed by repeatedly replacing ___ with _/\_, where each of the 4 new lines is 1/3 the length of the old line. Blowing up the snowflake curve by a factor of 3 results in a snowflake curve 4 times as large (one of the old snowflake curves can be placed on each of the 4 segments _/\_). Log 4 / log 3 = 1.261... Since the dimension 1.261 is larger than the dimension 1 of the lines making up the curve, the snowflake curve is a fractal. [sci.fractals FAQ].
References in periodicals archive ?
Table 1 Fractal Information Dimension Estimates Information Dimension Information Dimension (Nonrandom) (Random) P/P(a) E/R(b) P/P E/R Subject 1 1.
This considerably simplified the information dimension in combat.
Additionally, he has held executive management positions at Oracle Corporation, XDB Systems, and Information Dimensions Inc.
amp; PHILADELPHIA -- At the 30th annual SAS(R) Users Group International (SUGI) conference in Philadelphia, SAS, the leader in business intelligence and analytics, unveiled integrated business intelligence (BI) applications that will allow organizations to visualize and analyze data relationships in new ways by considering both location and traditional business information dimensions together.
HTH is pleased to add new real-time service and information dimensions to traditional economic protection afforded by insurance policies," said Angelo Masciantonio, Chief Executive Officer of HTH.
Bill Forquer, formerly President of Information Dimensions, Inc.
Granger has also held sales and marketing positions with Information Dimensions, Price Waterhouse, Citicorp Information Services, and ADP Network Services.
Leonti held Regional Field Sales Management positions with Hummingbird Communications, Information Dimensions, and was Regional Director for Excalibur Technologies.
So we know first hand the tremendous potential the Middle East holds for our future growth as more organizations see the value of tapping the knowledge in their large, multilingual collections of complex documents," said Bill Forquer, president of Information Dimensions.
It was originally developed by Information Dimensions, which was acquired by Open Text Corporation in June 1998 and is now a completely integrated division of Open Text.
Information Dimensions delivers the world's fastest way to publish these collections on the web, BASIS Intranet Solution.

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