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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: 3, Interesting) by FatPhil on Sunday January 15 2017, @01:28PM
Erm, nope. The real numbers are not a closed field, the closed field is the complex numbers, and a polynomial over the complex field is intrinsically a four dimensional thing. Restricting things like this to the subset of the complex numbers that is unchanged by conjugation is simply an artifice.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 0) by Anonymous Coward on Sunday January 15 2017, @03:09PM
The math doesn't matter, and 3D fractals are mostly decorative curiosities.