Self-Similar

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Self-Similar

When small parts of an object are qualitatively the same, or similar to the whole object. In certain deterministic fractals, like the Sierpinski Triangle, small pieces look the same as the entire object. In random fractals, small increments of time will be statistically similar to larger increments of time. See: Fractal.

Self-Similar

In mathematics, describing a condition in which the parts of an object are substantially the same as its whole. See also: Fractals.
References in periodicals archive ?
Section 3 gives a brief introduction to self-similarity and the relationship between the wavelet coefficients and the Hurst parameter.
Kenneth Hsu has even discovered fractal qualities of self-similarity across scales in the music of Bach and Mozart (1993).
To solve this combined spherical and conical plastic indentation problem, the self-similarity method was used here for the Rockwell indenter geometry.
Statistical self-similarity and fractional dimension.
The other elements defining the grammar and completing self-similarity are the type of the fragments -theory or practice- and the subtype of the theoretic fragments - presentation, model, and examples.
Examples of self-similarity can be seen when a coastline or a snowflake
Self-similarity is a state in which parts resemble (but are not identical to) other parts and sometimes to the whole.
The concept of Self-Similarity was originally developed by Efros and Leung (Efros and Leung, 1999).
Iterated Function Systems allow to formalize the notion of self-similarity or scale invariance of some mathematical object.
Among the topics are modeling and simulating deep brain stimulation in Parkinson's Disease, the role of self-similarity for computer aided detection based on mammogram analysis, and image registration for biomedical information integration.
The topics include fractional Brownian motion and related processes, parametric estimation for fractional Ornstein-Uhlenbeck type processes, sequential inference and non-parametric inference for processes driven by fractional Brownian motion, parametric estimation for processes driven by a fractional Browning sheet, and self-similarity index estimation.
When fractals are demonstrated in nature, they have what is called statistical self-similarity.