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A fragmented geometric shape that can be split into parts, each of which approximates a reduced-size copy of the whole, a property which is called self-similarity. Fractals provide the mathematics behind structures in the natural universe—e.g., frost crystals, coastlines, etc.—which cannot be described by the language of euclidean geometry. Fractal analysis is providing new ways to interpret biomedical phenomena. It has been used for classifying histopathology, enzymology, and signal and image compression
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Measure-valued images, associated fractal transforms and the affine self-similarity of images.
This paper presents the SIC algorithm working with the DWT to detect the change point of self-similarity in real-time.
The deeper we go into such graphs, the higher we increase the magnification, the more levels of self-similarity we uncover, always with shapes arising that resemble figures viewed much earlier.
This self-similarity strikes an ancient chord in our culture.
HUTCHINSON, Fractal and self-similarity, Indiana Univ.
To avoid these difficulties, or at least replace them with more tractable ones, self-similarity was used in the analysis of an intermediate fixed boundary in place of the changing boundary.
At the theoretical level, the self-similarity property underlying the fractal model assumes that the form or pattern of the spatial phenomena remains unchanged throughout all scales, which further implies that one cannot infer the scale of the spatial phenomena from its form or pattern.
On the other hand, self-similarity establishes a classification.
conditions, self-similarity is one of the concepts from chaos theory
Jencks' new architecture of complexity has several key characteristics, principally self-similarity, non-linearity, and organisational depth.
This quality, called self-similarity, results from repeatedly building up a form from small component units, so that the overall pattern appears identical at all levels of magnification.
For example, when reconstructing a larger office algorithms may exploit the geometric self-similarity of the scene, storing a model of a chair and its multiple instances only once rather than multiple times.