self-similarity

1. The property of having a substructure analogous or identical to an overall structure. For example, a part of a line segment is itself a line segment, and thus a line segment exhibits self-similarity. By contrast, no part of a circle is a circle, and thus a circle does not exhibit self-similarity. Fractals such the Sierpinski triangle are self-similar to an arbitrary level of magnification; many natural phenomena, such as clouds and plants, are self-similar to some degree.

2. See more at fractal

Example Sentences

The study, published in December in Journal of Ecology, refutes claims that the self-similarity which is observed within individual trees can be extended to whole forest canopies and landscapes.

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If self-similarity extended from the small twigs of a single tree to entire forest ecosystems, it would help ecologists describe complex landscapes in much simpler ways, and potentially directly compare the complexity of very different ecosystems, such as coral reefs and forest canopies.

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By contrast, a regular cauliflower often displays self-similarity in at least seven fractal scales, meaning a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral nested in, ultimately, another spiral.

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The defining characteristic of a fractal, such as the Mandelbrot set, “is self-similarity,” Dr. Hart said.

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Fractal music also displays self-similarity at varying scales, but applied to, say, pitch and tempo.

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