$ultra fractal 6 personal images$

$ultra fractal 6 personal images$

The science of rights, squares, cones and so on is made of approximations. Nature is more complicated than classical geometry. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space… Put simply, that there are some geometric shapes, which he called “fractals”, that are equally “rough” at all scales. Mandelbrot ended up doing a great piece of science and identifying… a fundamental idea. Gaston Julia’s 111th Birthday Google Doodle (February 2, 2004)Īs computed scientist Stephen Wolfram wrote: In 2004, Google credited Julia, Mandelbrot’s former teacher, with having laid the cornerstone of the branch of mathematics from which they developed the PageRank technology. Special effects for movies routinely use fractals to enhance their looks. In 1995, the mathematician prefaced the book Fractals in Petroleum Geology and Earth Processes, a multiple authorship effort exploring methods of crude oil reserves estimation, topographical effects of drilling and other related fields. Where Mandelbrot did not tread, or not too much-and he already did much-others would. Nassim Taleb, whose books are easier to read for non-mathematicians, was hugely inspired by Mandelbrot. In The Misbehavior of Markets: A Fractal View of Financial Turbulence (2006), he showed that one could not predict the future stock market values due to, inter alia, non-linearity and the absence of periodicity in market cycles, even if chaotic fluctuations did not happen completely at random. In Fractals and Scaling in Finance (1997), he demonstrated that finance operators relied on unreliable tools but managed to “get it” by tweaking said tools from guesswork. His sets made famous, Mandelbrot went back to what he deemed their most interesting application: the markets. Such sets had a much higher degree of recursion and self-similarity than the other Julia sets. Using them to generate Julia sets, he isolated a sub-class of these which remained invariant no matter their scale. Mandelbrot was lucky enough to have access to brand new IBM computers, still an academic luxury at the time. Over his long career, he was tasked with studying and teaching on complementary sets called the Julia sets and Fatou dusts, two complementary mathematical sets, the first ones worked on earlier by mathematician Gaston Julia who had been one of his teachers. A student of the French école polytechnique, then a teacher at Harvard, Mandelbrot was a polymath who got a master degree in aeronautics but remained fascinated by the stock markets for all his life. The fractals are widely attributed to mathematician Benoît Mandelbrot (1924-2010). Just like an “infiniteception.” But you need a fractal phenomena to witness it. An infinity of infinites within an infinite. What does it mean to be finite-occupying a limited portion of space, having been born at such time and place, likely dying at some time and place- when even the smallest portion of space can hold infinity? It looks like the universe is made of an infinite number of parts which also have an infinite number of parts. No wonder why so many non-mathematicians “feel” that fractals make them dwell on the meaning of life. The pattern similarity across an indefinite number of occurrences and levels echoes the infinite. The point is this: it is theoretically possible to calculate an infinite number of iterations by zooming continuously and indefinitely within a finite space. A supercomputer could come up with more iterations, a super quantum computer with even more, and so on. As you can guess, the limited number of iterations is only due to the limitation of computing power.

$ultra fractal 6 personal images$

Ultra fractal 6 personal images