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comment by alpha0
alpha0  ·  3302 days ago  ·  link  ·    ·  parent  ·  post: ∞ new works | ~:4(2)

Product matrix of reduced residues (rings). Recursive. The patterns you see are the deep structure of the algebraic space of N.

(Used Java but that was an arbitrary choice).





neptath  ·  3302 days ago  ·  link  ·  

Oh. I'm going to pretend I know what those words mean :P Looks awesome, anyhow, thanks!

alpha0  ·  3302 days ago  ·  link  ·    ·  

Sorry, assumed you would google it.

Basically, let say you have a set of numbers {1, 2, 3, .., n}. And you remove all numbers -- except 1 -- in that set that have a common factor with n. example {1, 2, 3, 4, 5, 6} => {1, 5}. So {1, 5} is the reduced residue set of 6.

And lets call the product of all primess up to a certain prime as a primorial. (This is just like a factorial, except that we only multiply primes in the range. So, 6 is a primorial since it is 2 * 3.

Now just make a multiplication matrix with that r.r.s. and enter the product of the x and y mod the primorial. That matrix is what is generating those images.

neptath  ·  3300 days ago  ·  link  ·  

Whoa. Mathematics is always amazing when it's made into art!

(Usually I would, just google it, but you took the time to explain it, so thanks, have a badge!)

alpha0  ·  3298 days ago  ·  link  ·  
neptath  ·  3296 days ago  ·  link  ·  

Looks like a Persian rug to me. Thanks!

alpha0  ·  3295 days ago  ·  link  ·  

Good observation. Most of Persian Architecture and Art are in fact group theoretic pattern systems.

alpha0  ·  3300 days ago  ·  link  ·  

+Thanks. (I'll pick one just for you, then.)

b_b  ·  3302 days ago  ·  link  ·  

So then the complexity of the emerging pattern increases with n, I assume?

alpha0  ·  3302 days ago  ·  link  ·  

It appears the answer is no.

What seems to be happening is that it simply gets more resolved. Superimposing generations of n, e.g. {1, 2, 6, 30, 210, 2310, ..., ∞#} and applying the same selection criterio manifest self similarity.