"Objects (in particular, figures) that have the same appearance when they are seen on fine and coarse scales." (David Rincón & Sebastià Sallent, Scaling Properties of Network Traffic, 2008)
"A collection of objects that have a power-law dependence of number on size." (Donald L Turcotte, "Fractals in Geology and Geophysics", 2009)
"A fractal is a geometric object which is self-similar and characterized by an effective dimension which is not an integer." (Leonard M Sander, "Fractal Growth Processes", 2009)
"A fractal is a structure which can be subdivided into parts, where the shape of each part is similar to that of the original structure." (Yakov M Strelniker, "Fractals and Percolation", 2009)
"A fractal is an image that comprises two distinct attributes: infinite detail and self-similarity." (Daniel C. Doolan et al, "Unlocking the Hidden Power of the Mobile", 2009)
"A geometrical object that is invariant at any scale of magnification or reduction." (Sidney Redner, "Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks", 2009)
[Fractal structure:] "A pattern or arrangement of system elements that are self-similar at different spatial scales." (Michael Batty, "Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies", 2009)
"A set whose (suitably defined) geometrical dimensionis non-integral. Typically, the set appears selfsimilar on all scales. A number of geometrical objects associated with chaos (e. g. strange attractors) are fractals." (Oded Regev, "Chaos and Complexity in Astrophysics", 2009)
[Fractal system:] "A system characterized by a scaling law with a fractal, i. e., non-integer exponent. Fractal systems are self-similar, i. e., a magnification of a small part is statistically equivalent to the whole." (Jan W Kantelhardt, "Fractal and Multifractal Time Series", 2009)
"An adjective or a noun representing complex configurations having scale-free characteristics or self-similar properties. Mathematically, any fractal can be characterized by a power law distribution." (Misako Takayasu & Hideki Takayasu, "Fractals and Economics", 2009)
"Fractals are complex mathematical objects that are invariant with respect to dilations (self-similarity) and therefore do not possess a characteristic length scale. Fractal objects display scale-invariance properties that can either fluctuate from point to point (multifractal) or be homogeneous (monofractal). Mathematically, these properties should hold over all scales. However, in the real world, there are necessarily lower and upper bounds over which self-similarity applies." (Alain Arneodo et al, "Fractals and Wavelets: What Can We Learn on Transcription and Replication from Wavelet-Based Multifractal Analysis of DNA Sequences?", 2009)
"Mathematical object usually having a geometrical representation and whose spatial dimension is not an integer. The relation between the size of the object and its “mass” does not obey that of usual geometrical objects." (Bastien Chopard, "Cellular Automata: Modeling of Physical Systems", 2009)
"A fragmented geometric shape that can be split up into secondary pieces, each of which is approximately a smaller replica of the whole, the phenomenon commonly known as self similarity." (Khondekar et al, "Soft Computing Based Statistical Time Series Analysis, Characterization of Chaos Theory, and Theory of Fractals", 2013)
"A natural phenomenon or a mathematical set that exhibits a repeating pattern which can be replicated at every scale." (Rohnn B Sanderson, "Understanding Chaos as an Indicator of Economic Stability", 2016)
"Geometric pattern repeated at progressively smaller scales, where each iteration is about a reproduction of the image to produce completely irregular shapes and surfaces that can not be represented by classical geometry. Fractals are generally self-similar (each section looks at all) and are not subordinated to a specific scale. They are used especially in the digital modeling of irregular patterns and structures in nature." (Mauro Chiarella, Folds and Refolds: Space Generation, Shapes, and Complex Components, 2016)
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