"Chaos does provide a framework or a mindsetor point of view, but it is not as directly explanatory as germ theory or plate tectonics. Chaos is a behavior - a phenomenon - not a causal mechanism. [...] The situation with fractals is similar. The study of fractals draws one’s eye toward patterns and structures that repeat across different length or time scales. There is also a set of analytical tools - mainly calculating various fractal dimensions - that can be used to quantify structural properties of fractals. Fractal dimensions and related quantities have become standard tools used across the sciences. As with chaos, there is not a fractal theory. However, the study of fractals has helped to explain why certain types of shapes and patterns occur so frequently." (David P Feldman,"Chaos and Fractals: An Elementary Introduction", 2012)
"Fractals are different from chaos. Fractals are self-similar geometric objects, while chaos is a type of deterministic yet unpredictable dynamical behavior. Nevertheless, the two ideas or areas of study have several interesting and important links. Fractal objects at first blush seem intricate and complex. However, they are often the product of very simple dynamical systems. So the two areas of study - chaos and fractals - are naturally paired, even though they are distinct concepts." (David P Feldman,"Chaos and Fractals: An Elementary Introduction", 2012)
"Fractals' simultaneous chaos and order, self-similarity, fractal dimension and tendency to scalability distinguish them from any other mathematically drawable figures previously conceived." (Mehrdad Garousi, "The Postmodern Beauty of Fractals", Leonardo Vol. 45 (1), 2012)
"One of the most important artistic properties of fractals is the randomness governing the process of making them. Each fractal is essentially generated by a basic formula and one or more gradients that identify the colors of the fractal. Sometimes, however, fractals are generated by tens of different formulas and gradients." (Mehrdad Garousi, "The Postmodern Beauty of Fractals", Leonardo Vol. 45 (1), 2012)
"The concept of infinity embedded in fractals' identity provides an infinity of possibilities to explore in a single image. The repetition of a formula is the key to becoming more familiar with it. When trying a completely new formula, all fractal artists are engaged in the same activity - a random playing around." (Mehrdad Garousi, "The Postmodern Beauty of Fractals", Leonardo Vol. 45 (1), 2012)
[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)
"Only at the edge of chaos can complex systems flourish. This threshold line, that edge between anarchy and frozen rigidity, is not a like a fence line, it is a fractal line; it possesses nonlinearity." (Stephen H Buhner, "Plant Intelligence and the Imaginal Realm: Beyond the Doors of Perception into the Dreaming of Earth", 2014)
"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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