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: 0) by Anonymous Coward on Sunday January 15 2017, @10:24AM
For our VR headsets while buffering hardcore 3D porn, eh?
(Score: 0, Funny) by Anonymous Coward on Sunday January 15 2017, @11:13AM
The real reason this made news.
DeMarco then went off to do pioneering work applying techniques from dynamical systems to questions in number theory, for which she will receive the Satter Prize — awarded to a leading female researcher — from the American Mathematical Society on January 5.
I've met DeMarco, she's charismatic, and frankly she's too pretty for mathematics. It's completely unsurprising that the pretty one earned a prize for working in a field dominated by ugly people.
(Score: -1, Offtopic) by Anonymous Coward on Sunday January 15 2017, @11:32AM
Laura DeMarco's 370lb Deadlift [youtube.com]
Just joking. This is a completely different person.
(Score: 0) by Anonymous Coward on Sunday January 15 2017, @04:51PM
Hawt.
(Score: 1, Funny) by Anonymous Coward on Sunday January 15 2017, @04:16PM
So what are you saying - that pretty people can never be appreciated for their non-beauty-related skills and accomplishments? Perhaps you should start gathering data to support this hypothesis of yours and see if it's actually true.
(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.
(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.