This has been challenging to me:

This has been challenging to me:

Can someone explain why, given an in n, the function

f_n(k) := n mod k

has those parabolic parts with clear minima in them?

Where are they located. They are also there when n is prime, so it's not about factors in any straight forward fashion.

Other urls found in this thread:

youtube.com/watch?v=yVkdfJ9PkRQ
divisorplot.com/5.html
math.stackexchange.com/questions/2110014/the-fractional-part-of-n-logn
en.wikipedia.org/wiki/Moiré_pattern
twitter.com/NSFWRedditVideo

bump
I am monitoring this thread

yup, me too

Each parabola seems to go by increments of four.

Forgot pic.

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?

from the pic, It appears to have some sort of self-similarity which means some concept of fractal is near

...

I think you're seeing aliasing from sampling at integers. Here's what it looks like if you sample at .001 with n = 1001.

Better pic, I accidentally included x=0

Looks like adjacent parabola have b's that differ by 0.3

Nevermind, guess it's not that simple.

confirmed aliasing

interesting thought. Wouldn't that mean that using a much larger number would increase the "resolution" though and remove that effect?

First rule of using a tool is to know the limitations...

Oh fug Brimes are bretty weird :DDDDDDD

those dips occur whenever the function is at a point where k divides n.

wrong

>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]

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.

I don't think people who are saying aliasing understand the question.

Anyone understand what this noise shit is in the bottom of this plot?

>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

I didn't really mean it as an answer, just part of the discussion.

No, I think it's right. Integers are always the same distance apart. See >implying I wasn't fapping to math the whole time

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?"

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

Video related
youtube.com/watch?v=yVkdfJ9PkRQ

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.

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

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.

>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.

youtube.com/watch?v=yVkdfJ9PkRQ

same reason for this

>it was coming through in contour plot too
Same situation.

You're late but still correct.

gotta go to werk
hope this thread still lives in 12 hours

Bumping just for you

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.

I'd expect there may be a simple way to compute*

bump

pump

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

thanks for the bumps btw

I also found this:
math.stackexchange.com/questions/2110014/the-fractional-part-of-n-logn

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.

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.

Is this all related to this?

looks kinda like JUST

Depends on what "this" is.

Are you talking about the Moire pattern in your pic? Then no, it's something different.
en.wikipedia.org/wiki/Moiré_pattern

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.