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Using the modulus operation on a constant over a continuous set of real numbers produces what at first appears to be an orderly, linear graph when zoomed out.

However, when zooming in, the plot quickly becomes chaotic, with changes in direction that don't fall on the x-axis at varying frequencies. What am I looking at and what sort of math does this touch on?

Jake Bromberg
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    The correct graph is like the one you are looking when you zoomed out. When you zoom in what you are seeing is the consequence of lost of precision of the computer. – jjagmath Jul 09 '22 at 21:07

2 Answers2

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The graph isn't too hard to explain.

We are looking at infinitely many line segments.

Let $c$ be given. Then when $c/x$ is in between the integers $k$ and $k+1$ we have

$$f(x)=c-xk$$

This creates infinitely many jump discontinuities because $c/x$ gets infinitely large as $x$ gets close to zero. Therefore, we need infinitely many line segments.

Mason
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  • Here's a graph on desmos. – Mason Jul 09 '22 at 21:29
  • Is there any pattern to the increasingly chaotic frequencies as we approach 0? – Jake Bromberg Jul 09 '22 at 23:22
  • @JakeBromberg There's nothing chaotic there. There's only line segments with a very ordered pattern, it only looks chaotic because the software you used didn't plot it correctly. – jjagmath Jul 10 '22 at 12:39
  • Nothing chaotic. As $x$ gets small computing which integers $c/x$ falls between becomes computationally more expensive and your software isn't rendering this so well... but the word "chaos" is usually reserved for a different type of phenomenon. – Mason Jul 10 '22 at 18:20
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Does the graph of $x^{2}+y^{2}=10$ looks like a slant line to you?

Well it's curve right? (a circle)
See this,
enter image description here

  • 20% zoom
    enter image description here
  • 2000% zoom

But why does it looks like a diagonal line now?
That's usual, as when the precision of the formula increase, the graph changes. When you zoom in, the graph keeps dividing into minute particles, like atoms.
I think I don't need to explain any more about these.

Just the same,

Your zoomed graph is totally different from the usual graph, as it's only a minute part of the graph.
Afterall there is nothing to do with modulo or any other, it's all about the graph, #thinkcreative

Neptotech -vishnu
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