pouët.net

huhu,
i actually wanted to ask this at the newbie table at revision (would be my first visit to a demoparty), but i just couldn't wait:

beforehand: this hardly would count as prod - it would maybe fall into the "wild" category, at best. it's about math and not entertaining :)

i am the kind of guy, that can spend hours in a blank room thinking about numbers... and i spent countless hours doing exactly that. And i think i came across something interesting, maybe even important. it has much similarity with pascal's triangle.

here is the thingy
(googled a text editor, because this BBS doesn't support [center][/center] :) )

up until now, i only used pen&paper for this, now i would like to get a bigger data-set of this thingy. i was thinking of giving each number an associated pixel and decide the "color-value" by "how big the number is" - maybe with some tweaking, depending on how the result looks. (for example decide the intensity value by the difference of magnitude to neighboring numbers... or whatever)

i want to do this, because i hope i can draw additional information out of such a picture - and maybe understand numbers a bit more :)

i think i need an array, that can hold an object and an array of its own type(?) to compress the structure into something a code can execute.
i can code myself a bit, but i didn't code for over 4 years >_> and i feel a bit lost at this moment :/

tbh: i don't even know how to start with this... and that is why i am asking here :)

i could imagine that this would be a rather simple thing to code? i am not sure.

hopefully my post is readable and i am not too far "offtopic"

oh, and i am not even sure, if this thing is new or already well known... how would you google something like that? o_O

Looks like you are factoring the natural numbers.

but yeah, maybe look at Processing for turning ideas into graphics.

I found your sequence in the OEIS: https://oeis.org/A050873

ty very much,
that is definitely the same sequence. but there are a few differences:

they got to it with the GCD(GreatestCommonDivisor)
(i never thought of this... :))

which is on the one hand very nice, because they can compress all information down to:

or for 12 rows:


but on the other hand: the information contained and building this sequence is not extracted out of the sequence. (i wanted to do it that way)

i would still try to put a formula on it without the GCD

oh... and they have a lame name for the sequence: "A050873", but that doesn't rly matter ^-^

(mhm... from 2011, this thingy is super new, still)

i looked around a bit and found this image, which looks pretty much exactly how i imagined it (just in small)

source: wolfram(under applications)

but i feel uncomfortable using the GCD, because i am not sure about some properties of this sequence:

i have no idea what happens at the very first point (1/1), afterwards it gets simpler, but there are still things, that are unclear to me.

for example at the point (2/4) the GCD is 2 and i would get 2 as well, but i don't know if this point creates a new "branch", that descents down the center while skipping 3 rows.

this branch would overlap with the (1/2) branch at the point (4/8): the GCD would be 4, but i would get 5, because of the overlapping branches (i did not do this in my 1st example, because i didn't want to get too complicated^^)

and i would like to see how the result would differ, if i consider every point creating a new branch. i wouldn't be able to do this with the GCD?

btw, is there any way of getting wolfram mathematica for free? :D (i'm poor, can't rly buy anything)

ok, just saw they have a "trial" now... last time i checked, they didn't :)

first of: sry 4 spamming :)

i just thought about the things i called "branches" and the idea of each "point" creating a new "branch" -> and how to assign a value to a point accordingly. (while i was showering ^-^)

because i felt, like i made a mistake. i think my example of assigning a "5" to the point (4/8) is entirely wrong. i think i made the mistake even before, at the point (2/4).

i should not assign a single value to a point, but a set of values.

(i doubt i can put my thoughts in understandable words, yet)

if i look at the point (2/4) i see 2nd (1/2) and 1st (2/4). [(1/2),(2/4)]
the next point on the (1/2) branch would be (3/6), here i would assign 2 times the (1/2) and the (3/6) once [(1/2),(1/2),(3/6)]
now, for the next point (4/8), i know what i want to "have", but i don't know how to actually "see" it [(1/2),(2/4),(1/2),(4/8)]

i have the feeling that these assigned values would be "less wrong".

if i could find a way to put a formula on this, each "branch" would have the same structure and information density as the whole thing, just with different symbols representing the information.

this would fit perfectly in my "understanding of the underlying structure in our number-system"

mhm... *kopfkratz*
but how do i get there with "logic"? O_o

i prolly need a few more years from now on :)

but thanks a lot @reenigne - that link helped me _a lot_
i have a way bigger data-set now i can interpret.

(spam)
ah! i found it! the 3rd (1/2) at the point (4/8) is inside the (2/4) set!

Crystal Math