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Do you find some mathematical activities useless?
04-24-2018, 05:27 PM
Post: #46
RE: Do you find some mathematical activities useless?
(04-23-2018 03:04 PM)pier4r Wrote:  a good example of apparently not useful quest. [...] Now I wonder what the guy learned. because I am pretty sure one can get quite some patterns doing this.

Probably not much. He used quite arbitrary choices for both the range of the coefficients and the window of acceptance so the alleged patterns in the resulting images would surely reflect this and would probably be quite different with other choices.

Also, this technique of getting fractal-like images from roots of polynomials is nothing new, just Google Images for "Littlewood polynomial roots fractal" for some classical images and links to relevant articles (Borwein et al. popularized this in some of their excellent books on Experimental Mathematics).

Last but not least, what's an "useful" quest ? Is the quest for beautiful, artistic images "useful" ? Is it "useless" ? What about mathematically-generated art ?

I recently wrote my own 2D fractal generator program, a simple personal affair developed in 30-plus-year-old hardware, OS, and programming language, just for the sheer fun of it all, and despite me being into fractals since reading the first seminal article that made the cover of Scientific American that many decades ago, I've been utterly astonished by what the simplest of formulas, a simple palette, and a simple coloring algorithm can produce, i.e. absolutely unexpected images, indefinitely zoomable and explorable, that no one but me has ever seen since the Universe began, among a multi-infinity of them existing (or not) in some Platonic realm.

Everytime I use my program I casually discover scores of them, totally different from the previous ones, which leaves me gasping in amazement.

Is this a "useless" quest ? Not for me.


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RE: Do you find some mathematical activities useless? - Valentin Albillo - 04-24-2018 05:27 PM

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