Fractal Dimension


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Fractal Dimension

A number that quantitatively describes how an object fills its space. In Euclidean, or Plane geometry, objects are solid and continuous. That is, they have no holes or gaps. As such, they have integer dimensions. Fractals are rough and often discontinuous, like a wiffle ball, and so have fractional, or fractal dimensions.

Fractal Dimension

A description of how a discontinuous object fills the space it occupies. For example, a basketball is not smooth; rather it has lines and grooves all over it. Because it is not a perfect sphere, it requires fractal dimensions to explain how it exists.
References in periodicals archive ?
Ao, "Fractal dimension for porous metal materials of FeCrAl fiber," Transactions of Nonferrous Metals Society of China, vol.
IVAN was used to grade for retinal calibers [50], and the retinal vascular fractal dimension was graded by the International Retinal Imaging Software (IRIS-Fractal), which was the standard of the time [51].
Fernandez et al., "Determination of fractal dimension of physiologically characterized neurons in two and three dimensions," Journal of Neuroscience Methods, vol.
Phase synchronization index in the alpha (8~12Hz) and beta (15~35Hz) frequency bands, as well as power, fractal dimension, and sample entropy during pre- and postfatigue contractions were tested using paired sample t-tests.
Fractal dimension mapping us to ascertain geomorphic domains where variability of fractal dimension of the earth surface represents the roughness of the land form topography and is an assessment of texture of topography.
In order to describe the decomposed waveform further and classify the EGG signals easily, this algorithm uses fractal dimension algorithm proposed by Katz (Kartz, 1988), to process the waveform obtained by decomposing the EGG signals, thus obtaining the fractal weft of sub waveform.
In order to quantify the content of collagen, Fractal Dimension analysis (FD) was performed (Ozaki et al.) on slides stained with Sirius Red and photographed by a polarized light microscope (Leica DM 4000B) coupled to a Leica DFC500 camera with 100x magnification (Ozaki et al.), belonging to the Faculty of Dentistry--FOA / UNESP, Aracatuba--SP.
For each record, the fractal dimension was calculated by the R/S analysis method, so that every subject received two different fractal dimension values for each of the 20 records.
T represents a point in the [R.sup.n] space, [DELTA]t represents the offset of the point [DELTA] t represents the Euclidean distance, F(x) represents the Gaussian random distribution function, and the fractal dimension is defined by [L.sub.H](t)
Fractal dimension [14] was obtained by Blanket algorithm which is put forward by Peleg; then the block with defects was marked, and the defect was localized.