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Re: Number of needed nodes to create collison free network.

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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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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

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