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Number of needed nodes to create collison free network.

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  Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-18 03:15 -0700
    Re: Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-18 04:45 -0700
    Re: Number of needed nodes to create collison free network. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-07-18 12:57 +0100
      Re: Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-18 05:30 -0700
        Re: Number of needed nodes to create collison free network. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-07-18 13:43 +0100
          Re: Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-18 08:49 -0700
            Re: Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-18 11:10 -0700
              Re: Number of needed nodes to create collison free network. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-07-18 20:00 +0100
                Re: Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-18 12:28 -0700
                  Re: Number of needed nodes to create collison free network. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-07-18 21:32 +0100
    Re: Number of needed nodes to create collison free network. "Michael Haufe (TNO)" <tno@thenewobjective.com> - 2014-07-19 04:41 -0700
      Re: Number of needed nodes to create collison free network. jonas.thornvall@gmail.com - 2014-07-19 07:37 -0700

#25430 — Number of needed nodes to create collison free network.

I was a bit tired tonight thinking about this, and very diffuse in my problem statement. I try be a bit more coherent below.

But I think i need some help to formulate the problem in a more coherent manner.
It is about how many corner/node names needed to create a collsion free network. Warning i am not that good formulate the actual problem.

So i may need some help formulate the problem in a more coherent manner.

I will start using the easiest case a square.

A square is a unique individual that use different name for each corner.
The arrangement of the corners is free, a square and its corner can never be revisited.

Now i want to build a oneway network out from a cental starting square. I push squares together, creating outward nodes from a central square that will be collision free. ***You only push together corners holding same name*** thus a interconnected corner/node is named 1,2,3,4,5... and so on.

To be collision free means that a corner can not point to two corners holding same name, but it can itself hold the same name as a corner it pointing to because it is a oneway path network.

How many corner names needed to create a collision free network.

1. Triangle
2. Tetrahedron
3. Square
4. Cube
And other polygons and platonic solids, is this group theory, computational complexity?

Maybe it is self evident but i just do not see it.

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#25431

Den fredagen den 18:e juli 2014 kl. 12:15:35 UTC+2 skrev jonas.t...@gmail.com:
> I was a bit tired tonight thinking about this, and very diffuse in my problem statement. I try be a bit more coherent below.
> 
> 
> 
> But I think i need some help to formulate the problem in a more coherent manner.
> 
> It is about how many corner/node names needed to create a collsion free network. Warning i am not that good formulate the actual problem.
> 
> 
> 
> So i may need some help formulate the problem in a more coherent manner.
> 
> 
> 
> I will start using the easiest case a square.
> 
> 
> 
> A square is a unique individual that use different name for each corner.
> 
> The arrangement of the corners is free, a square and its corner can never be revisited.
> 
> 
> 
> Now i want to build a oneway network out from a cental starting square. I push squares together, creating outward nodes from a central square that will be collision free. ***You only push together corners holding same name*** thus a interconnected corner/node is named 1,2,3,4,5... and so on.
> 
> 
> 
> To be collision free means that a corner can not point to two corners holding same name, but it can itself hold the same name as a corner it pointing to because it is a oneway path network.
> 
> 
> 
> How many corner names needed to create a collision free network.
> 
> 
> 
> 1. Triangle
> 
> 2. Tetrahedron
> 
> 3. Square
> 
> 4. Cube
> 
> And other polygons and platonic solids, is this group theory, computational complexity?
> 
> 
> 
> Maybe it is self evident but i just do not see it.

Kind of an update, i just realised that every node of a cube could hold 6 naturals depending on the taken path.

(Well given the above and my naive assumption that we can create a cubed network with no collision just using 6-7 names so storing a node 3 bits?
Is it true that an arrangement arround a centralised cube where every named corner intersection/nodes can hold 6 different natural number depending on the path we take and as we add cubes we add up natural numbers.

Now is it true that from this *centralised* cube any natural number arranged along the cube path can be reached in 3th root/(2*6)+1 **steps** using 3 bits?

Well the 2 is because the centralised arrangement and the 6 the number of natural numbers stored at each node.

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#25432

jonas.thornvall@gmail.com writes:

> I was a bit tired tonight thinking about this, and very diffuse in my
> problem statement. I try be a bit more coherent below.
>
> But I think i need some help to formulate the problem in a more coherent manner.
> It is about how many corner/node names needed to create a collsion
> free network. Warning i am not that good formulate the actual problem.
>
> So i may need some help formulate the problem in a more coherent manner.
>
> I will start using the easiest case a square.
>
> A square is a unique individual that use different name for each corner.
> The arrangement of the corners is free, a square and its corner can
> never be revisited.
>
> Now i want to build a oneway network out from a cental starting
> square. I push squares together, creating outward nodes from a central
> square that will be collision free. ***You only push together corners
> holding same name*** thus a interconnected corner/node is named
> 1,2,3,4,5... and so on.

Personally, I'd call them colours.  There's a long tradition of problems
involving colouring graphs (and therefore maps).

> To be collision free means that a corner can not point to two corners
> holding same name, but it can itself hold the same name as a corner it
> pointing to because it is a oneway path network.

Are you talking about a tessellation?  I.e. must the shapes fill the
plain?  If not, I think there needs to be much more said about the
constraints, but since the question you ask seems to be for a single
number it looks like you do mean to refer to infinite tessellations.

But then again you mention the tetrahedron, and space can't be filled
using regular tetrahedrons.  Maybe the shapes do not have to be all the
same?

> How many corner names needed to create a collision free network.

Presumably you mean the minimum number.

I'd turn the description round: given a pattern of touching shapes (here
you can say an infinite tessellation if that is what you mean, or
specify other constraints on the pattern), what is the minimum number of
colours needed to colour the nodes so that the corners of every shape
have distinct colours.

(This raises another question -- how many distinct shapes are needed
when you take the coloured corners into account?  To me, that seems like
the more interesting problem, but that's just a gut feeling.)

> 1. Triangle
> 2. Tetrahedron
> 3. Square
> 4. Cube
> And other polygons and platonic solids, is this group theory,
> computational complexity?

(I note in passing that the platonic solids are regular tessellations of
the sphere, so the problem can be asked *of* them as well as *about*
them if you relax the constraint that the pattern must be on the plain.)

It's most closely related to graph theory, I'd say, but group theory and
ordinary geometry are involved.  Computational complexity will come up
if you ask about the computational aspects.

Anyway, one thing is for sure, it's not javascript!  I've answered here
without setting followup-to because the obvious place is sci.maths, but
that become a cesspit of nonsense though there is the occasional bit if
real math that gets done.  If you can face it, post there.

-- 
Ben.

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#25433

Den fredagen den 18:e juli 2014 kl. 13:57:17 UTC+2 skrev Ben Bacarisse:
> jonas.thornvall@gmail.com writes:
> 
> 
> 
> > I was a bit tired tonight thinking about this, and very diffuse in my
> 
> > problem statement. I try be a bit more coherent below.
> 
> >
> 
> > But I think i need some help to formulate the problem in a more coherent manner.
> 
> > It is about how many corner/node names needed to create a collsion
> 
> > free network. Warning i am not that good formulate the actual problem.
> 
> >
> 
> > So i may need some help formulate the problem in a more coherent manner.
> 
> >
> 
> > I will start using the easiest case a square.
> 
> >
> 
> > A square is a unique individual that use different name for each corner.
> 
> > The arrangement of the corners is free, a square and its corner can
> 
> > never be revisited.
> 
> >
> 
> > Now i want to build a oneway network out from a cental starting
> 
> > square. I push squares together, creating outward nodes from a central
> 
> > square that will be collision free. ***You only push together corners
> 
> > holding same name*** thus a interconnected corner/node is named
> 
> > 1,2,3,4,5... and so on.
> 
> 
> 
> Personally, I'd call them colours.  There's a long tradition of problems
> 
> involving colouring graphs (and therefore maps).
> 
> 
> 
> > To be collision free means that a corner can not point to two corners
> 
> > holding same name, but it can itself hold the same name as a corner it
> 
> > pointing to because it is a oneway path network.
> 
> 
> 
> Are you talking about a tessellation?  I.e. must the shapes fill the
> 
> plain?  If not, I think there needs to be much more said about the
> 
> constraints, but since the question you ask seems to be for a single
> 
> number it looks like you do mean to refer to infinite tessellations.
> 
> 
> 
> But then again you mention the tetrahedron, and space can't be filled
> 
> using regular tetrahedrons.  Maybe the shapes do not have to be all the
> 
> same?
> 
> 
> 
> > How many corner names needed to create a collision free network.
> 
> 
> 
> Presumably you mean the minimum number.
> 
> 
> 
> I'd turn the description round: given a pattern of touching shapes (here
> 
> you can say an infinite tessellation if that is what you mean, or
> 
> specify other constraints on the pattern), what is the minimum number of
> 
> colours needed to colour the nodes so that the corners of every shape
> 
> have distinct colours.
> 
> 
> 
> (This raises another question -- how many distinct shapes are needed
> 
> when you take the coloured corners into account?  To me, that seems like
> 
> the more interesting problem, but that's just a gut feeling.)
> 
> 
> 
> > 1. Triangle
> 
> > 2. Tetrahedron
> 
> > 3. Square
> 
> > 4. Cube
> 
> > And other polygons and platonic solids, is this group theory,
> 
> > computational complexity?
> 
> 
> 
> (I note in passing that the platonic solids are regular tessellations of
> 
> the sphere, so the problem can be asked *of* them as well as *about*
> 
> them if you relax the constraint that the pattern must be on the plain.)
> 
> 
> 
> It's most closely related to graph theory, I'd say, but group theory and
> 
> ordinary geometry are involved.  Computational complexity will come up
> 
> if you ask about the computational aspects.
> 
> 
> 
> Anyway, one thing is for sure, it's not javascript!  I've answered here
> 
> without setting followup-to because the obvious place is sci.maths, but
> 
> that become a cesspit of nonsense though there is the occasional bit if
> 
> real math that gets done.  If you can face it, post there.
> 
> 
> 
> -- 
> 
> Ben.

I do mean connecting just one shape Ben in such a way all outgoing nodes have individual names. There is no problem if the current corner connect to a corner using the same name, but all the outgoing paths should lead to unique named corner/crosspoint.

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#25434

jonas.thornvall@gmail.com writes:
<snip>
> I do mean connecting just one shape Ben in such a way all outgoing
> nodes have individual names. There is no problem if the current corner
> connect to a corner using the same name, but all the outgoing paths
> should lead to unique named corner/crosspoint.

OK, I had a stab at it, but I don't know what you mean.

-- 
Ben.

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#25436

Den fredagen den 18:e juli 2014 kl. 14:43:11 UTC+2 skrev Ben Bacarisse:
> jonas.thornvall@gmail.com writes:
> 
> <snip>
> 
> > I do mean connecting just one shape Ben in such a way all outgoing
> 
> > nodes have individual names. There is no problem if the current corner
> 
> > connect to a corner using the same name, but all the outgoing paths
> 
> > should lead to unique named corner/crosspoint.
> 
> 
> 
> OK, I had a stab at it, but I don't know what you mean.
> 
> 
> 
> -- 
> 
> Ben.

I am not that mathematicly inclined so i do not have the sufficient language to communicate the problem. But i will try to program it for a square.
Given the square you can the Origo each corner/cross section have four nodes "those nodes around each corner could hold natural numbers *4*. 

But since it is a one way path leading from Origo to the individual "it seems a waste of space and time to use 4 digit we could had managed with just two? Because the paths out from square is oneway thus two pointing to the square itself? But we could store four  natural numbers centered around each "corner" cross section. 

I distinguish between cross section names and node names maybe that what people find weird? 

To find one of the four natural numbers stored around each corner/cross section you must take an extra step out.


So could i managed below with just 2 digits and still have unique optimal path leading out from each chosen square? 

2    1    2     1    2    1 

4    3    4     3    4    3

2    1    2     1    2    1
             O
4    3    4     3    4    3

2    1    2     1    2    1 

4    3    4     3    4    3


Admittedly i feel a bit dizzy about this, but can we chose an optimal path to find any of the  4 numbers stored around each of the cross sections using two digits?


1   2   1   2   1   2    

1   2   1   2   1   2 

1   2   1   2   1   2
          O
1   2   1   2   1   2

1   2   1   2   1   2

1   2   1   2   1   2


I can now see there is 2 more restrictions, and two requirments.

Restriction 1. Once you leave origo in one direction S,W,E,N you can go on a straight line but never go back like +W -W that would not be the shorest path. 

Restricton 2.And **Exception*** last digit hold 4 values the searched number could be in the negative directon?. You must always take an extra step to find the number stored at the cross section node.

Requirment 1. Need an intitialisaton vector SE, SW, NE, NW.

Requirment 2. A structure to create the lookup table for the numbers.

So is it possible, well i will try implement it with a lookup table for squares, but the big benefits is probably using more nodes, platonic solids?

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#25445

Den fredagen den 18:e juli 2014 kl. 17:49:47 UTC+2 skrev jonas.t...@gmail.com:
> Den fredagen den 18:e juli 2014 kl. 14:43:11 UTC+2 skrev Ben Bacarisse:
> 
> > jonas.thornvall@gmail.com writes:
> 
> > 
> 
> > <snip>
> 
> > 
> 
> > > I do mean connecting just one shape Ben in such a way all outgoing
> 
> > 
> 
> > > nodes have individual names. There is no problem if the current corner
> 
> > 
> 
> > > connect to a corner using the same name, but all the outgoing paths
> 
> > 
> 
> > > should lead to unique named corner/crosspoint.
> 
> > 
> 
> > 
> 
> > 
> 
> > OK, I had a stab at it, but I don't know what you mean.
> 
> > 
> 
> > 
> 
> > 
> 
> > -- 
> 
> > 
> 
> > Ben.
> 
> 
> 
> I am not that mathematicly inclined so i do not have the sufficient language to communicate the problem. But i will try to program it for a square.
> 
> Given the square you can the Origo each corner/cross section have four nodes "those nodes around each corner could hold natural numbers *4*. 
> 
> 
> 
> But since it is a one way path leading from Origo to the individual "it seems a waste of space and time to use 4 digit we could had managed with just two? Because the paths out from square is oneway thus two pointing to the square itself? But we could store four  natural numbers centered around each "corner" cross section. 
> 
> 
> 
> I distinguish between cross section names and node names maybe that what people find weird? 
> 
> 
> 
> To find one of the four natural numbers stored around each corner/cross section you must take an extra step out.
> 
> 
> 
> 
> 
> So could i managed below with just 2 digits and still have unique optimal path leading out from each chosen square? 
> 
> 
> 
> 2    1    2     1    2    1 
> 
> 
> 
> 4    3    4     3    4    3
> 
> 
> 
> 2    1    2     1    2    1
> 
>              O
> 
> 4    3    4     3    4    3
> 
> 
> 
> 2    1    2     1    2    1 
> 
> 
> 
> 4    3    4     3    4    3
> 
> 
> 
> 
> 
> Admittedly i feel a bit dizzy about this, but can we chose an optimal path to find any of the  4 numbers stored around each of the cross sections using two digits?
> 
> 
> 
> 
> 
> 1   2   1   2   1   2    
> 
> 
> 
> 1   2   1   2   1   2 
> 
> 
> 
> 1   2   1   2   1   2
> 
>           O
> 
> 1   2   1   2   1   2
> 
> 
> 
> 1   2   1   2   1   2
> 
> 
> 
> 1   2   1   2   1   2
> 
> 
> 
> 
> 
> I can now see there is 2 more restrictions, and two requirments.
> 
> 
> 
> Restriction 1. Once you leave origo in one direction S,W,E,N you can go on a straight line but never go back like +W -W that would not be the shorest path. 
> 
> 
> 
> Restricton 2.And **Exception*** last digit hold 4 values the searched number could be in the negative directon?. You must always take an extra step to find the number stored at the cross section node.
> 
> 
> 
> Requirment 1. Need an intitialisaton vector SE, SW, NE, NW.
> 
> 
> 
> Requirment 2. A structure to create the lookup table for the numbers.
> 
> 
> 
> So is it possible, well i will try implement it with a lookup table for squares, but the big benefits is probably using more nodes, platonic solids?

Hello Ben you see to be quite knowledgeable into math and if you read this and the post before maybe you can understand my unconventional way of thought. I understand i could be way off. But I find these things very strange and annoying, and if someone could give it a thought and understand what i mean i would be greatful. 

Basicly there is two things making up the encoding cross section and "their names" for squares "2 binary digits" needed for finding each node and finally the sought natural number. 

The natural numbers are stored around each cross section (lookup table needed) and you can see above that only two binary digits needed to store for each node.

Well this is how the actual lookup table storing the naturals at the cross section could look like and you find them using the node table in previous post.

Well +1

34_|_35  6_|_7  10_|_11
33 | 36  5 | 8   9 | 12
30_|_31  2_|_3  14_|_15
29 | 32  1 | 4  13 | 16
26_|_27 22_|_23 18_|_19
25 | 28 21 | 24 17 | 20 

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#25447

jonas.thornvall@gmail.com writes:
<snip>
> Hello Ben you see to be quite knowledgeable into math and if you read
> this and the post before maybe you can understand my unconventional
> way of thought. I understand i could be way off. But I find these
> things very strange and annoying, and if someone could give it a
> thought and understand what i mean i would be greatful.

Sorry, I can't follow it at all.

<snip>
-- 
Ben.

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#25450

Den fredagen den 18:e juli 2014 kl. 21:00:24 UTC+2 skrev Ben Bacarisse:
> jonas.thornvall@gmail.com writes:
> 
> <snip>
> 
> > Hello Ben you see to be quite knowledgeable into math and if you read
> 
> > this and the post before maybe you can understand my unconventional
> 
> > way of thought. I understand i could be way off. But I find these
> 
> > things very strange and annoying, and if someone could give it a
> 
> > thought and understand what i mean i would be greatful.
> 
> 
> 
> Sorry, I can't follow it at all.
> 
> 
> 
> <snip>
> 
> -- 
> 
> Ben.

But if i program it?

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#25455

jonas.thornvall@gmail.com writes:

> Den fredagen den 18:e juli 2014 kl. 21:00:24 UTC+2 skrev Ben Bacarisse:
>> jonas.thornvall@gmail.com writes:
>> 
>> <snip>
>> > Hello Ben you see to be quite knowledgeable into math and if you read
>> > this and the post before maybe you can understand my unconventional
>> > way of thought. I understand i could be way off. But I find these
>> > things very strange and annoying, and if someone could give it a
>> > thought and understand what i mean i would be greatful.
>> 
>> Sorry, I can't follow it at all.
>
> But if i program it?

Most likely I will simply assume that any errors are intended
behaviour.  And if there are no errors, my input will be of no value.

-- 
Ben.

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#25476

On Friday, July 18, 2014 5:15:35 AM UTC-5, jonas.t...@gmail.com wrote:
> I was a bit tired tonight thinking about this, and very diffuse in my problem statement. I try be a bit more coherent below.
> 
> But I think i need some help to formulate the problem in a more coherent manner.
> 
> It is about how many corner/node names needed to create a collsion free network. Warning i am not that good formulate the actual problem.
> 
> So i may need some help formulate the problem in a more coherent manner.
> 
> I will start using the easiest case a square.
> 
> A square is a unique individual that use different name for each corner.
> 
> The arrangement of the corners is free, a square and its corner can never be revisited.
> 
> Now i want to build a oneway network out from a cental starting square. I push squares together, creating outward nodes from a central square that will be collision free. ***You only push together corners holding same name*** thus a interconnected corner/node is named 1,2,3,4,5... and so on.
> 
> To be collision free means that a corner can not point to two corners holding same name, but it can itself hold the same name as a corner it pointing to because it is a oneway path network.
>
> How many corner names needed to create a collision free network.
> 
> 1. Triangle
> 2. Tetrahedron
> 3. Square
> 4. Cube
> 
> And other polygons and platonic solids, is this group theory, computational complexity?
> 
> Maybe it is self evident but i just do not see it.

Perhaps you're asking about Euler Circuit's?
<http://en.wikipedia.org/wiki/Euler_circuit>

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#25479

Den lördagen den 19:e juli 2014 kl. 13:41:45 UTC+2 skrev Michael Haufe (TNO):
> On Friday, July 18, 2014 5:15:35 AM UTC-5, jonas.t...@gmail.com wrote:
> 
> > I was a bit tired tonight thinking about this, and very diffuse in my problem statement. I try be a bit more coherent below.
> 
> > 
> 
> > But I think i need some help to formulate the problem in a more coherent manner.
> 
> > 
> 
> > It is about how many corner/node names needed to create a collsion free network. Warning i am not that good formulate the actual problem.
> 
> > 
> 
> > So i may need some help formulate the problem in a more coherent manner.
> 
> > 
> 
> > I will start using the easiest case a square.
> 
> > 
> 
> > A square is a unique individual that use different name for each corner.
> 
> > 
> 
> > The arrangement of the corners is free, a square and its corner can never be revisited.
> 
> > 
> 
> > Now i want to build a oneway network out from a cental starting square. I push squares together, creating outward nodes from a central square that will be collision free. ***You only push together corners holding same name*** thus a interconnected corner/node is named 1,2,3,4,5... and so on.
> 
> > 
> 
> > To be collision free means that a corner can not point to two corners holding same name, but it can itself hold the same name as a corner it pointing to because it is a oneway path network.
> 
> >
> 
> > How many corner names needed to create a collision free network.
> 
> > 
> 
> > 1. Triangle
> 
> > 2. Tetrahedron
> 
> > 3. Square
> 
> > 4. Cube
> 
> > 
> 
> > And other polygons and platonic solids, is this group theory, computational complexity?
> 
> > 
> 
> > Maybe it is self evident but i just do not see it.
> 
> 
> 
> Perhaps you're asking about Euler Circuit's?
> 
> <http://en.wikipedia.org/wiki/Euler_circuit>

It is mainly about Venn diagram a node holding two values?
Which lead to compression of the natural numbers.

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