![]() They found that the FDs of the gray matter surfaces were 2.35 for the younger brain and 2.29 for the senile brain. (1997) studied senile brain atrophy by comparing the young brain (NMR data) and the older brain with visible senile changes (photo data). Their method may be applied to extract progressive tumor development information by comparing it to normal brain data. (2000) used FD to detect and locate brain tumors. (2000) quantified the edge irregularities of brain lesions to evaluate the degree of tumor malignancy in human brain MR images. The results showed a close correspondence between structure and function. (2002) studied the microangioarchitecture of human brain vessels during the fetal period and found that FD increased from 1.26 in the fourth month to 1.53 in the fifth month and 1.6 in the sixth and seventh months. Differences in FD between the normal gyral patterns and those in epilepsy were compared, and the abnormality expressed by FD in epilepsy was determined. The investigators found a high degree of symmetry in FD between the right and left hemispheres in the subjects aged from 23 to 53, whereas no gender-related difference was observed. (1996) studied the convolution of cerebral cortex by measuring variance in the WM surface in human brain MR images, and obtained the FD in a narrow range from 2.24 to 2.41. Their results showed significant age-related FD changes in the frontal regions and gender-related FD alterations in the left superior frontal and right inferior frontal regions. (2001) investigated the influence of age and gender on structural complexity and cortical sulcus developmental trends in children and adolescents by measuring FD of the surface of the brain sulcal/gyral convolution in MR images using the algorithm of Thompson et al. The investigators concluded, based on their observation of low variance in the FD, that there was a stable FD value for normal brain, which could be used as a control for pathological studies. (1996) quantified morphometric variance of the surfaces of the supracallosal sulcus, the cingulate and marginal sulci, the anterior and posterior rami of the calcarine sulcus, and the parietooccipital sulcus in cryoplaned specimen photographs of human brain, and found that the FDs of these structures were in a narrow range around 2.10. They determined the mean FD of all subjects to be 1.402, and found that the manic-depressive patients had higher FD than controls, whereas the schizophrenic patients had lower FD than controls. (1994) measured the complexity of the boundaries between the white matter (WM) and gray matter (GM) in human brain magnetic resonance (MR) images and applied the results to a controlled study of schizophrenic and manic-depressive patients. It has been used successfully in quantifying brain cell morphologies ( Porter et al., 1991 Smith et al., 1991, 1993 Takeda et al., 1992 Smith and Behar, 1994 Soltys et al., 2001) and the shape of the brain ( Bullmore et al., 1994 Cook et al., 1995 Free et al., 1996 Thompson et al., 1996 Rybaczuk et al., 1996 Rybaczuk and Kedzia, 1996 Kedzia et al., 1997, 2002 Pereira et al., 2000 Iftekharuddin et al., 2000 Blanton et al., 2001). FD serves as an index of the morphometric complexity and variability of the object being studied.įractal analysis has recently been applied to study a wide range of objects in biology and medicine ( Kenkel and Walker, 1996 Cross, 1997 Heymans et al., 2000 Losa, 2000), especially in brain structures and processes. Fractal analysis provides a useful tool to quantify the inherent irregularity of a fractal object by a number, i.e., FD, which is usually a fractional value. Fractal properties include self-similarity, scale invariance, infinite amount of details, etc. Fractal objects are everywhere in nature, such as coastlines, clouds, trees, and snowflakes. Unlike the more familiar Euclidean structures, magnifying a fractal results in the resolution of more details. Mathematically, a fractal structure is defined as a set that has a fractal dimension (FD) exceeding its topological one. Unsourced material may be challenged and removed.Fractal, first introduced by Mandelbrot (1982), is a concept to characterize spatial or temporal phenomena that are continuous but not differentiable. Please help improve this section by adding citations to reliable sources. Other properties Main cardioid and period bulbs These algebraic curves appear in images of the Mandelbrot set computed using the "escape time algorithm" mentioned below. The set is defined in the complex plane as the complex numbers c. It is popular for its aesthetic appeal and fractal structures. ![]() ![]() The Mandelbrot set ( / ˈ m æ n d əl b r oʊ t, - b r ɒ t/) is a two dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. The Mandelbrot set within a continuously colored environment ![]() Fractal named after mathematician Benoit Mandelbrot ![]()
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