meaning of fractal dimension

1. fractal dimension 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]. FRAD Frame Relay Access Device. fragile brittle fragment fragmentation fragmentation 1. segmentation. 2. The process, or result, of splitting a large area of free memory on disk or in main memory into smaller non-contiguous blocks. This happens after many blocks have been allocated and freed. For example, if there is 3 kilobytes of free space and two 1k blocks are allocated and then the first one at the lowest address is freed, then there will be 2k of free space split between the two 1k blocks. The maximum size block that could then be allocated would be 1k, even though there was 2k free. The solution is to "compact" the free space by moving the allocated blocks to one end and thus the free space to the other. As modern file systems are used and files are deleted and created, the total free space becomes split into smaller non-contiguous blocks composed of "clusters" or "sectors" or some other unit of allocation. Eventually new files being created, and old files being extended, cannot be stored each in a single contiguous block but become scattered across the file system. This degrades performance as multiple seek operations are required to access a single fragmented file. Defragmenting consolidates each existing file and the free space into a continuous group of sectors. Access speed will be improved due to reduced seeking. The rate of fragmentation depends on the algorithm used to allocate space and the number and position of free sectors. A nearly-full file system will fragment more quickly. MSDOS and Microsoft Windows use the simplest algorithm to allocate free clusters and so fragmentation occurs quickly. A disk should be defragmented before fragmentation reaches 10%. See garbage collection.

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