Fractal

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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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Ferrari (2007) establishes a formal definition of self-similarity, as follows:

Please note we are speaking of self-similarity over time, not space.

Consciousness and brain science: mechanisms by which nature knows through us

Because this figure demonstrates self-similarity when you zoom in on the sides, students can begin discussing concepts of similarity.

Using Disney's Frozen to motivate mathematics: bringing fractals into the classroom

1999; Niklas and Enquist, 2001), following the elastic self-similarity model (Niklas, 1994).

Growth, biomass, and allometry of resprouting shrubs after fire in scrubby flatwoods

The example for Wavelet transformation window length T = 1000 for self-similarity parameter H values of 0.

Real-time estimation of traffic self-similarity parameter in Simulink with wavelet transform

Many images exhibit approximate self-similarity and this structure has proven very useful in applications in image compression, representation and analysis (Hutchinson, 1981; Barnsley and Demko, 1985; Barnsley et al.

Minkowski-additive multimeasures, monotonicity and self-similarity

Thus even the classical non-equilibrium flows can show self-similarity if properly scaled.

Scaling of turbulent boundary layers with pressure gradients

Fractals have two basic characteristics suitable for modeling the topography and other spatial surfaces in the Earth's surface: self-similarity and randomness.

The investigation of mashhad's heat island by using satellite images and fractal theory (box counting method)

m]) can be used as a scaling function to study the self-similarity of the phase morphology at different solidification temperatures.

Off-line and in-line analysis of phase morphology and evolution during solidification process of PP/PEOc blend in an internal mixer

The plots of the residual analysis shown in Figure 4 don't reveal systematic curves; this fact shows a good fit in the linear pattern of the bi-logarithmic representations and therefore, the characteristic of statistical self-similarity is evidenced in these coastlines.

Fractal analysis of the complexity of Panama City coastlines, Central America

Zooming in to the intricate boundary reveals more and more detail and self-similarity with subtle variations.

The Mandelbrot set

Other topics include synthesis and mesogenic properties of a novel hyperbranched triphenylene-based discotic liquid crystal, bistable technology in flat panel displays, the synthesis and properties of ultraviolet-curable sealant for liquid crystal display panels, and the self-similarity of electrochemically-deposited copper films on porous silicon.