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By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.
Mathematicians are not so different from naturalists. Rather than studying organisms, they study equations and shapes using their own techniques. They twist and stretch mathematical objects, translate them into new mathematical languages, and apply them to new problems. As they find new ways to look at familiar things, the possibilities for insight multiply.
That’s the promise of a new idea from two mathematicians: Laura DeMarco, a professor at Northwestern University, and Kathryn Lindsey, a postdoctoral fellow at the University of Chicago. They begin with a plain old polynomial equation, the kind grudgingly familiar to any high school math student: f(x) = x 2 – 1. Instead of graphing it or finding its roots, they take the unprecedented step of transforming it into a 3-D object.
https://www.quantamagazine.org/20170103-fractal-dynamics-from-3d-julia-sets/
(Score: 2) by butthurt on Sunday January 15 2017, @03:30PM
Fractals are named for their property of having a fractional number of dimensions, hence a 3-D fractal is a contradiction in terms.
https://ocw.mit.edu/high-school/humanities-and-social-sciences/godel-escher-bach/lecture-notes/MITHFH_geb_v3_2.pdf [mit.edu]
(Score: 3, Informative) by Anonymous Coward on Sunday January 15 2017, @06:47PM
Not necessarily a contradiction. There are differing ways [cut-the-knot.org] of defining “dimension”. Fractals have a fractional Hausdorff-Besicovich dimension, but the Brouwer dimension is always an integer.