Which rule did I follow to draw these arrows?

Which rule did I follow to draw these arrows?

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en.wikipedia.org/wiki/Synchronizing_word
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Draw the arrow from smaller to bigger number? I bet you are from murrica lol

Then 1 would be connected to all other numbers.

numbers with only arrows pointing away (1, 4, 8, 2.) are added together. 1+2=3 kind of shit.
I cant figure any reasoning for 11, 14 and 13 though. just seems like extra shit thats randomly placed instead of actually using any rule.

You are onto something with your "only pointing away", maybe there are other groups of numbers?

I could add the next number, but I couldn't find a nice planar grpah for it.

Odd numbers only point towards higher odd numbers, hmm.

This is actually connected to

All even numbers are pointing towards themselves +1

If I have the rule right, if you add 16 it won't be connected to anything?

Odd numbers only touch odds

Evens touch evens

so, only numbers which dosn't point at another (11, 14, 7, 13) points towards 15. Don't have the ones that only points at others (1,4,8,2) to point towards a new number ?
I could figure out this: if you start at 1 then go to 11 by following the arrows that makes 1+3+11=15, same for 2+6+7=15

16 would be connected to several numbers, but the picture would change so much that it doesn't really look like te same thing anymore.

No it wouldn't, fuck off

sorry for poor english btw
I'm stuck with 14 and 13 unfornately, maybe by substracting and not adding

No more arrows need to be drawn in that picture.
Actually each number has it's own relationship to the number 15

16 would point to 3, 5, 6, 9, 10 and 12
No arrows would point towards it.

1+2=3, 2+4=6, 4+8=12, 8+1=9, 2+8=10, 1+4=5 => 1, 2, 4, 8 are used to form 3, 9, 5, 6, 8, 12

The rule of random
The rule of baiting
or the rule of being a huge autistic faggot (prob this)

10, not 8

Bullshit, it wouldn't point to those and you know it

(9+3+10)/2=11, (10+6+12)/2=14, (9+5+12)=13
here you go for the last ones

1 2 4 and 8 are used to form to other numbers, if one wants to put it that way.
How do you reach 13 14 and 15?

Not a general rule, but you had a good start, maybe this helps.

Summ of incoming numbers devided by quantity of numbers -1

check this

bruh I am pretty sure it's just golden ratio shit idk go fuck yourself silly with your conical shell

It's about the arrows, not the numbers.
The picture would still be valid, if you remove a number as well as any arrows that come from or go to it.

Okay, so the pink numbers are just there, and are independent. The blue are the sum of the two pink numbers pointing to them. The cyan are the the sum of the 3 blue numbers pointing to them, divided by 2

I got it.
The bit representation is the key to solving this problem.
You used the value 15 at first. Then you calculated the connections by subtracting the node number from 15. The bits that still were set afterwards were added seperately to the node number and connected to create the graph.
Example:
Node number 1:
15 = 1111 - 1 = 0001 = 14 1110
the second, third and fourth bit were still set so that means:
0001 + 0010 = 0011 => 3
0001 + 0100 = 0101 => 5
0001 + 1000 = 1001 => 9

That's what I thought except OP says 16 would point toward 3, 5, 6, 9, 10, and 12

Yay, you get a cookie.

That was probably a troll.

No 16 would definitively point to those numbers.

Not if the rule is each number points to any number that has the same binary representation except for one extra bit set

draw the picture you fag

okok you were all right. I failed, I deserve to die, yadda yadda yadda.

ARE YOU HAPPY NOW?

haha, yes I am.

...

for all i \in I

wrong, fag

lmao'ing at all the "rules"in this thread

this is at least a starting point for a formal "rule" for OP's Graph

I think I just had a mathgasm.
this originally started as cells having 4 connections, then it became having the states of those cells represeted by binary numbers.
now it's..whatever this is.

Name one Node where the facts stated by me fail!

If the difference of two numbers is a power of 2 (including the number 1), then there's an arrow from the smaller to the bigger number.

If you crave another mathgasm try this:
en.wikipedia.org/wiki/Synchronizing_word

The first fact is not an equivalence
It is just an implication from left to right

He can't, because you did not formulate a formal rule as tries to do,

you just stated the problem in formal speech.

thats not the same

Yall motherfuckas are just jelly bc I solved the problem and yall just sucked op's dick

Ur welcome

only green allowed

I started with the mission to create an alphabet and rulesets for a cellular automata, went through some stuff to help me viszualize what I'm doing and have come full circle.

If this was it then there would be an arrow from 4 to 8

Whats that cellular automata supposed to do?

Actually the problem was 'which rule did I use?'
and I used "change one bit in the binary representation", not a formal rule.

2^2 doesnt occur in the uniq. det. sum of 8!

8 = 2^3

The rule of thumb

It's supposed to make one node+ one connection in generation 0
for example O-
each cell has 4 possible connections
in the next generation new cells are created where there are connections pointing.
O-O
A cell will always try to grow more connections.
The rules where the new connection is grown depend on how many connections there already are

Trace the number back to ones with only arrows pointed away. So 3 comes from 1 and 2, and 7 comes from 5/6/3, which come from 1, 2, and 4. The root ones are all powers of 2.

so the original graph are all possible moves.
really 1 , so 0001 might mean "right connection"
and it will point to one number which was the 1s bit in common and another added
1001 might be "right+ down" in the next gen

Then what would be it's uniquely determined sum?

Sounds really cool
Keep your head up!

thank you,
trying to wrap my head around which rulesets actually make sense
been drawing outcomes by hand so far...