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- W2356601896 abstract "Fractals give us a way to visually and quantitatively observe various abstract and real-world phenomena. Mathematician Benoit Mandelbrot coined the word “fractal” in 1975 (Stewart, Clark, Mandelbrot, et al., 5) while working at IBM but other mathematicians had studied these geometric structures long before him. During the 18th and 19th centuries, Calculus was gaining mass appeal. Most mathematicians of this period believed that all continuous curves could have tangent lines drawn at any point on the function, except at cusps. In 1872, Mathematician Karl Weierstrass, described a family of curves that were continuous but not differentiable at any point (Stewart, Clark, Mandelbrot, et al., 6-7). This discovery surprised mathematicians because it challenged current ideas about mathematics (Eglash, 12). Mathematicians were somewhat uncomfortable with the idea of continuous curves that could repeat, or iterate, themselves infinite times within a finite space. Two questions arose from this period: What are the dimensions of these curves, and can we measure the lengths of these “pathological curves” as they iterate over and over again in a finite space? In the early 20th century, Mathematician Felix Hausdorff, helped make the idea of fractional dimension clear, believing fractals to be in an in-between dimension as they were not quite two-dimensional objects or one-dimensional mathematical structures. His main contribution to this area of mathematics was the Hausdorff dimension (Barnsley, p. 171):" @default.
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- W2356601896 date "2016-01-01" @default.
- W2356601896 modified "2023-09-26" @default.
- W2356601896 title "Analysis of Fractals from a Mathematical and Real-World Perspective" @default.
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