found: Work cat.: Cabral, T.M. Fractal analysis of breast masses in mammograms, 2012(The primary objective of this book is to present fractal analysis as an approach for the classification of breast masses ... Fractals are irregular geometric patterns made up of sets of infinitely smaller but identical patterns. Fractal theory gives insights into tumor morphology and provides a mathematical platform for the analysis of complex and irregular tumor patterns. The fractal dimension (FD) may be used as a quantitative measure of the complexity of the contour or boundary and gray-scale variability exhibited by an object)
found: Journal of applied functional analysis, Oct. 2009:p. 571 (The basic elements related to fractal creation/generation and analy[s]is are: 1) an object; 2) a generator (initiator); 3) iteration and 4) the emerged form. Fractal analysis is concerned with the study of the emerged form. For example, the object may be a line. This line may be subject to different rules or a generator (i.e, divide the line by a third) and iterated for an established amount of times. At the conclusion of those iterations, which theoretically could be infinite, an emergent form would appear. The resulting form/object will not be the same as the original object as it is not a replication but a mutation. However, the paradox is that the abstract fractal actually has self-similarity and scalelessness so in essence it is a replication, but, is mysteriously different)
found: Reproductive biology and endocrinology, via WWW, May 21, 2013:v. 8, 2010, art. 86, pp. 4-5 (Fractal analysis is a contemporary method of applying nontraditional mathematics to patterns that defy understanding with traditional Euclidean concepts. Fractal analysis measures complexity using the fractal dimension. A fractal dimension is, in essence, a scaling rule comparing how a pattern's detail changes with the scale at which it is considered. The fractal dimension is a valuable parameter to describe the complexity)
found: Gynecologic oncology, Oct. 1999:p. 78 (Usually, the structure of an object can be described utilizing tools of common geometry. A square, for example, can be described by the measure of its sides. However, "complicated" objects, particularly naturally occurring objects such as clouds, mountains, and coastlines, do not apparently appear as a sum of triangles and lines. Such objects are better described using fractal geometry. Fractal geometry has been known as a mathematical concept for many years ... Its tools were applied successfully to characterize irregularly shaped and complex figures by a mathematical value wherever Euclidean geometry fails. One of the advantages of fractal analysis is the ability to quantify the irregularity and complexity of objects with a measurable value, which is called the fractal dimension)
found: Dentomaxillofacial radiology, May 2001:p. 179 (Fractal analysis is a mathematical technique that can aid in the quantification of complex structures. The spatial properties of a fractal object are `statistically self-affine'. In general, the higher the dimension, the more complex the shape)
found: Journal of number theory, Sept. 2008:pp. 2663, 2665 (Fractal analysis for sets of non-differentiability of Minkowski's question mark function. ... In this paper we study various fractal geometric aspects of the Minkowski question mark function Q. ... These observations mark the starting point for the fractal geometric analysis of the function Q in this paper)
