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An Interesting Pattern in the Prime Numbers: Parallax Compression

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Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#61

Post by tathougies »

tzahola wrote: post #9
ythn wrote: post #7

Earlier quoted context omitted.

Come on, does every cool thing need a stamp of approval by "experts" before publication? "SQLite looks nice, but I would have double checked with Oracle engineers before announcing this as something novel"

Well, to some extent, yes. Otherwise you’d end up like the MD who’ve “rediscovered” numerical integration (the trapezoid method) and got it published in the journal of diabetes or whatever.

> Otherwise you’d end up like the MD who’ve “rediscovered” numerical integration (the trapezoid method) and got it published in the journal of diabetes or whatever.

This was shocking because calculus is a required subject in American high schools, and this American doctor presumably went to American high school, not because the doctor didn't check in with mathematicians. Frankly, it would be equally shocking if the doctor had asked a mathematician if integration were a thing, because presumably a doctor is an educated member of society.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#62

Post by brador »

kibwen wrote: post #37

These runes would serve excellently as a written alphabet for an alien species in fiction (or maybe for modrons or other Lawful creatures in D&D).

I'd like to see the triangle fractal as a starting state for Conways "Game of Life".

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#63

Post by anderskaseorg »

The drawing is incorrect.

More specifically, it’s a drawing of OEIS A054521 (black if gcd(row, col) == 1, red otherwise), not of the parallax compressed primes. The two drawings do not match as claimed. The first place where they differ is row 9, column 1, which is drawn as black even though none of 217, 226, 235, 244, 253, 262 are prime.

It’s clear that gcd(row, col) == 1 is a necessary condition for there to be any primes in that cell (which consists of the numbers col + 3row² − 3row, col + 3row² − 2row, col + 3row² − row, col + 3row², col + 3row² + row, col + 3row² + 2row), but it’s not sufficient. There’s no way it could be sufficient, because there are only constantly many (six) numbers tested in every cell, but the asymptotic density of the primes goes to 0 and the asymptotic density of A054521 goes to 6/π².

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#64

Post by Whitespace »

It wasn't exactly clear to me when I read the article, so here's my explanation:

- take a line of integers, color them black if prime, red otherwise

- hexagonally arrange them in a spiral (similar to Ulam's spiral)

- cut the hexagon into six equilateral triangles

- overlap the triangles (rotate where necessary)

- if any pixels are black, color the whole thing black, if none are black, color it red

- interesting pattern arises

- interesting pattern already exists as per http://oeis.org/A054521

Edit: They may be packing more than 6 numbers into a pixel, looks like 75. Unsure how that would look visually, but you extend the above to use 75 or any other number. Unsure why 75 was chosen, maybe it's the only interesting one?

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#65

Post by mathythrowaway »

anderskaseorg wrote: post #63

The drawing is incorrect. More specifically, it’s a drawing of OEIS A054521 (black if gcd(row, col) == 1, red otherwise), not of the parallax compressed primes. The two drawings do not match as claimed. The first place where they differ is row 9, column 1, which is drawn as black even though none of 217, 226, 235, 244, 253, 262 are prime. It’s clear that gcd(row, col) == 1 is a necessary condition for there to be any…

Their picture is correct, but only because they are doing something more ridiculous than this. Every one of the squares in their picture represents 75 numbers, not 5 numbers.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#66

Post by gowld »

ssewell wrote: post #43
_rpd wrote: post #33

Earlier quoted context omitted.

The claim is that it is the same pattern independent of the number of integers per dot.

If the numbers of integers-per-dot was set to 1, the sequence would simply highlight prime numbers as they progress through the pyramid shape since “Parallax Compression” would no longer apply.

The triangle is a hexagon folded onto itself. That's what the "parallax" part is.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#67

Post by gowld »

mathythrowaway wrote: post #57

This just shows the reduced residues mod n. There are n squares in the nth row from the top. Color the kth square of the nth row black if gcd(k,n)=1, color it red otherwise.

How is that?

Isn't it plotting a prime spiral, not GCD?

Obviously prime implies gcd=1, but the "kth" square isn't "k", because it's a spiral counting up from the center.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#68

Post by anderskaseorg »

mathythrowaway wrote: post #65
anderskaseorg wrote: post #63

The drawing is incorrect. More specifically, it’s a drawing of OEIS A054521 (black if gcd(row, col) == 1, red otherwise), not of the parallax compressed primes. The two drawings do not match as claimed. The first place where they differ is row 9, column 1, which is drawn as black even though none of 217, 226, 235, 244, 253, 262 are prime. It’s clear that gcd(row, col) == 1 is a necessary condition for there to be any…

Their picture is correct, but only because they are doing something more ridiculous than this. Every one of the squares in their picture represents 75 numbers, not 5 numbers.

Click on the definition of T, and you see exactly the A054521 formula.

T = (n, k) => { return (GCD(n, k) == 1) ? 1 : 0; }

The given code doesn’t use primes, primesSet, or isPrime at all.

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#69

Post by [deleted] »

ssewell wrote: post #43
_rpd wrote: post #33

Earlier quoted context omitted.

The claim is that it is the same pattern independent of the number of integers per dot.

If the numbers of integers-per-dot was set to 1, the sequence would simply highlight prime numbers as they progress through the pyramid shape since “Parallax Compression” would no longer apply.

[deleted]

Re: An Interesting Pattern in the Prime Numbers: Parallax Compression

#70

Post by mathythrowaway »

gowld wrote: post #67
mathythrowaway wrote: post #57

This just shows the reduced residues mod n. There are n squares in the nth row from the top. Color the kth square of the nth row black if gcd(k,n)=1, color it red otherwise.

How is that? Isn't it plotting a prime spiral, not GCD? Obviously prime implies gcd=1, but the "kth" square isn't "k", because it's a spiral counting up from the center.

No, it isn't plotting a prime spiral. Each square in their triangle is a block of 75 numbers. Within the nth row the numbers are sorted by residue mod n.
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