Rotation effects of negative (whitespace) of moiré patterns from multiples of [2,3,5,7,11,13,17,19]. With each increment they are tilting at different 'rates' so the whole represents rotation of straight artifacts at several speeds at once.

woah, yeah, what is up with the galaxies spin motion/transformation? there's gotta be a good explanation

I did the same thing - but you can just put your cursor in the number box and hold up / down arrow key.

Very! I saw the distant galaxies spin.

I did the same thing and saw galaxies

          .....   ......   ......   ....   ..    ..   ......
         ..       ..   ..  ..   ..   ..    ...   ..   ..     
         ..       ..   ..  ...  ..   ..    .. .. ..   ..     
          .....   ......   ......    ..    .. .. ..   ..  ...
           .....  ...      .. ..     ..    ..   ...   ..   ..
              ..  ..       ..  ..    ..    ..    ..   ...  ..
         ......   ..       ..   ..  ....   ..    ..    .....

Feistel networks are another way to map your index from linear sequence to a pseudorandom permutation.

That's neither random nor O(1). I think everybody reading the link immediately understands what you mean, but I whished this community would use its technical terminology more carefully.

this deserves more upvotes

Nothing too surprising more or less same thing as all other vertical columns. 546=2*3*7*13 and all numbers in the range [242, 250] can be divided by one of those 4 primes same for [296, 304] . If x is divisor of a and b, then it will also divide a+n*b meaning you get an empty column. 2 and 3 already makes more than half the columns non primes, fill in the gaps with few more primes and you get the wide empty columns. If the width is multiple of many different small primes it's more likely to happen.

In a similar way 210=2*3*7*5 also gives wide empty columns (if you ignore ignore first row where 2,3,5,7 themselves are primes)

It helps if you think of it in terms of where the non primes are located instead of where the primes are. Multiples of 2, 3, 5 form a very regular pattern. Wrap it around in a grid and you get straight lines which are either straight vertical or slightly shifted depending on the divisors of width. Stack a couple of repetitive patterns and you still get a repetitive pattern. If the positions which are not primes form a regular pattern, the inverted image also forms recognizable pattern. Of course the primes don't form perfectly regular pattern and but most the visible repetition are result of small prime multiples.

Those are just columns that happen to share factors with 546 and happen to line up together. 546 is a very composite number (lots of factors!)

546n + 242 is always even

546n + 243 is always divisible by 3

546n + 244 is always even

546n + 255 is always divisible by 7.

Etc.

It's similar to how in base 10 you never see a prime ending in 0,2,4,6,8 or 5 since those numbers are clearly divisible by 2 or 5. In 546's case you have a lot of factors so even more gaps.

You also get the pattern appearing again since the number is even and the non-even factors repeat their pattern starting from the halfway point.

I am interested to know how you discovered this! Was it by happenstance or did you know to look for this?

The reason behind that is similar to how all prime numbers above 2 are of the form 2n+1 since all other numbers are divisible by 2. Eg. all prime numbers >2 are odd.

In this case you're seeing the extension of this to include multiples of 3. That is, all prime numbers above 6 are of the form 6n+1 or 6n+5, all other numbers are either divisible by 2 or 3.

You can extend these patterns. Whenever you have a composite number you'll get periodic points where factors are known. Eg. to extend it one step further you could say all prime numbers above 30 are of the form 30n + [1,7,11,13,17,19,23,29], all others are divisible by 2, 3 or 5.

From this you can also quickly iterate towards to the prime number formula for the frequency of primes. eg. Only half of numbers above 2 can be prime (1/2), the rest are multiples of 2. Over 6 you have half of two thirds of numbers that can possibly be prime, the rest are multiples of 2 or 3. Over 30 only 1/2 x 2/3 x 4/5 could possibly be prime. etc. This converges to the prime number theorem!

Anyway if anyone ever expresses amazement that's good to see but mathematically it's well known. Prime numbers have patterns in their frequency, specifically where there's period multiples of factors there can't possibly be primes. It's the basis for prime number theory and patterns in primes have been known since Erasthosenes was back in BC times. So if you see a pattern here just remember that the pattern comes from looking at a period of a composite number and within that composite number there's guaranteed periodic gaps in primes where the factors of that number repeat.

This btw is something mathematicians deal with a lot. People seem to think prime numbers have no patterns and any view of them that reveals patterns is a surprising which is a weird misconception. Prime numbers absolutely have patterns. It's the basis for prime number theory.

A prime number greater than 3 must leave a remainder 1 or 5 when divided by 6. In other words:

If n is prime and n > 3, then n ≡ 1 (mod 6) or n ≡ 5 (mod 6).

Or more succinctly:

n ≡ ±1 (mod 6).

So when the total number of columns is a multiple of 6, all the primes greater than 3 line up on the nth columns for n = 1, 5, 7, 11, etc.

Thanks! Do you mean you’d like to be able to input any number you like?

The numbered values are editable inputs. You can click into them and type in the amount you’d like. If you couldn’t tell they were editable inputs, that’s valuable feedback! I’ll redesign them to make it more obvious that you can do so, and don’t have to just click the +/- buttons.

The cake is a lie.

You sure about that? I see some clear diagonal lines at 431 cols: https://imgur.com/a/rNKjTtr

I think you'll find this to be the case with any prime.