would it be true to say there are only parabolas out there, some very dense, which might make them not clearly visible in some plots?
Alexander Powell
from the pic, It appears to have some sort of self-similarity which means some concept of fractal is near
Noah Turner
...
Michael Green
I think you're seeing aliasing from sampling at integers. Here's what it looks like if you sample at .001 with n = 1001.
Aiden Reed
Better pic, I accidentally included x=0
Thomas Butler
Looks like adjacent parabola have b's that differ by 0.3
Gabriel Sanders
Nevermind, guess it's not that simple.
Nicholas Sanchez
confirmed aliasing
Henry Bailey
interesting thought. Wouldn't that mean that using a much larger number would increase the "resolution" though and remove that effect?
Camden Gonzalez
First rule of using a tool is to know the limitations...
Parker Peterson
Oh fug Brimes are bretty weird :DDDDDDD
Zachary Wilson
those dips occur whenever the function is at a point where k divides n.
Jason Campbell
wrong
Logan Price
>confirmed aliasing Is it? Other way to express OPs function r = (n mod k) is r = ( n - k*floor(n/k) ) Take k's from some range separated by some m and calculate r. A parabola emerges. eg.: n = 627739 a = range(1550, 1619, 4) // range taken from one of my parabolas in the graph, m=4 [n - k*floor(n/k) for k in a]
Kevin Evans
The sampling rate is 1 Hz (I'm just going to assume x is in seconds for my own sake) so to remove aliasing you'd need to shift most of the power within ~.5Hz. I'm not really sure how changing n affects the fourier transform though, and I can't really make heads or tails of the fractal(?) pattern.
The prime factors of 62773913 are 7919 and 7927 so no.
David Collins
I don't think people who are saying aliasing understand the question.
Asher Reed
Anyone understand what this noise shit is in the bottom of this plot?
William Anderson
>Anyone understand what this noise shit is in the bottom of this plot? screams of all of the lost souls of sperm wasted during the fapping you did instead of studying math
William Jenkins
I didn't really mean it as an answer, just part of the discussion.
Carson Rodriguez
No, I think it's right. Integers are always the same distance apart. See >implying I wasn't fapping to math the whole time
Jonathan Barnes
I mean, aliasing is one way of looking at the problem but it doesn't immediately answer "why are there parabolas?" and "where are the minima?"
Luis Cooper
I think that if you express k as k = m*q+l and pick some integer m, then iterating over q gives you a parabola, right? OPs function is: r = ( n - k*floor(n/k) ) pick some m and substitute k = m*q+l and plot r and you have a parabola Question is why? Maybe there are some properties of floor function that I'm missing
Plot3D ain't magic, it samples points and tries to interpolate a surface. You can try increasing the number of points it uses but some finer detail is always going to slip through.
Kayden James
Bear in mind it's only every x points, as in , where it's every 4 points. I've been messing around with floor() a lot lately and I'll see if I can find a MATlab plot I made the other day that I think might be relevant
Elijah Howard
I know, but it was coming through in contour plot too and I didn't want to use my brain to try to figure out why it might be happening.
Nolan Hernandez
>Bear in mind it's only every x points, as in , where it's every 4 points. Not only. I've found parabolas every 1 (small ones), 2, 4, 7, and 8 points. I didn't look further.
>it was coming through in contour plot too Same situation.
Aiden Rodriguez
You're late but still correct.
Lincoln Roberts
gotta go to werk hope this thread still lives in 12 hours
Aaron Mitchell
Bumping just for you
Hudson Barnes
OP here
I know that especially for high k, the pattern can becomes less chaotic and the pic can or could look linear where the data points jump by a similar amount. With a Listplot of integers in Mathematica, it's certainly not an image glitch, it's exact.
Whether by aliasing you mean the first or second effect, I'd expect that may be a simple way to compute the "nice dip looking" structures.
It won't be a fractal in any technical sense, as I just plot integers. And it's not tied to factoization in any naive sense, as it happens with a kinds of numbers.
In fact I just stumbled upon it by looking at numbers from the RSA challenge. And in fact I actually observed it with the related function floor(n/k)-n/k which somewhat naturally has a same pattern as the mod function, except all values are in a range of 1.
John Foster
I'd expect there may be a simple way to compute*
Noah Perez
bump
Oliver Adams
pump
Cooper Rodriguez
Back from work. I found something related but I still haven't read into it, and I'm not sure if I want to until I try looking some more into it on my own. Here's the link anyway, you'll have to start from part one but I'm giving the link to part 5 because there are plots showing this. divisorplot.com/5.html
i would expect to see something like this for nonprime n, especially n with lots of small prime factors.
>They are also there when n is prime
that is much more puzzling. it should be a line up to the multiples of n. check for bugs.
Grayson Stewart
other numbers are consistent with that too. The first number he posted only has 2 prime factors but still exhibits parabolas.
Also, if you look closely (like in the first image I posted ), you see that there are really hundreds of little parabolas. The ones that we're looking at are really just the largest ones.
This would indicate it's an aliasing effect. See my pic as well. The interesting part is it's not an artifact of the computer, it's produced by the mod(N,x) function (where N is constant) sampled over equally spaced real values of x. There's something interesting here, I'll be checking this thread for a better answer.