"A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales [...]" (Benoît Mandelbrot, "The Fractal Geometry of Nature", 1982)
"A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." (Benoît Mandelbrot, "The Fractal Geometry of Nature", 1982)
"In the mind's eye, a fractal is a way of seeing infinity." (James Gleick, "Chaos: Making a New Science, A Geometry of Nature", 1987)
"Fractals are geometric shapes that are equally complex in their details as in their overall form. That is, if a piece of a fractal is suitably magnified to become of the same size as the whole, it should look like the whole, either exactly, or perhaps after a slight limited deformation." (Benoît B Mandelbrot, "Fractals and an Art for the Sake of Science", 1989)
"Fractals are patterns which occur on many levels." (Györgi Ligeti, [interview] 1999)
"Mathematical fractals are generated by repeating the same simple steps at ever decreasing scales. In this way an apparently complex shape, containing endless detail, can be generated by the repeated application of a simple algorithm."
[fractal:] "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)
"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)
"A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales […]" (Benoît B Mandelbrot)
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