Maps, theory discussion

[spoon]

Originally posted by tesco samoa:
i never play ancient... they just see the map right ?

You can figure out which planets are starting planets by checking their size and resource values.

[Loser]

I'm trying to figure what a tetrahedron map would look like...

One with a system at each point is pretty simple.

code:

---

  1

 /|\

2-|-3

 \|/

  4

---

So I add one more system between each, and ... well, it's complicated. To complicated for ASCII, or for me in ASCII, anyway. It starts like this.

code:

---

    1

   / \

  2---3

 / \ / \

4---5---6

 \ / \ /

  7---8

   \ / \

    9---A

---

Then things get complicated, because the following connections are needed in addition to these.

• 1-A
• 2-7
• 2-A
• 3-8
• 3-A
• 7-A

And that's just ten systems.

So, my coworkers now have another reason to think oddly of me, as I have spent the Last hout or two figuring out how to make an equilateral triangle out of rectangular pages of paper, and then scribbling on it.

The next possible tetrahedron will have twenty systems, and after that thirty-five. It only gets more complicated and less readable.

So... how're those cubes coming?

[edit: note that the verticies are connected to three other systems and all other systems are connected to six other systems. It will remian this way for tetrahedrons of any size.]

[ January 19, 2004, 17:37: Message edited by: Loser ]

[Spoo]

You can figure out which planets are starting planets by checking their size and resource values.

So what if you made a map with many planets that had the proper size and resource values to be possible homeworlds.

[Loser]

M'kay, twenty.

code:

---

      1

     / \

    2---3

   / \ / \

  4---5---6

 / \ / \ / \

7---8---9---A

 \ / \ / \ /

  B---C---D

 / \ / \ / \

E---F---G---H

     \ / \ / \

      I---J---K

---

Additional connections:

• 1-K
• 2-K
• 2-E
• 3-K
• 3-H
• 4-B
• 4-E
• 6-D
• 6-H
• E-J
• E-K
• F-J

Anyone want to check my work?

[ January 19, 2004, 17:56: Message edited by: Loser ]

[geoschmo]

I have a 54 system cube on paper. Doing it in the map editor would take some time.

Ascii code I guess would look like:

code:

---

            /---------------\

           /  /-----------\  \

          /  /  /-------\  \  \

         /  /  /  /-----F1-F2-F3-----\

        /  /  /  /  /---F4-F5-F6---\  \

       /  /  /  /  /  /-F7-F8-F9-\  \  \

 (D3)-A1-A2-A3-B1-B2-B3-C1-C2-C3-D1-D2-D3-(A1)

 (D6)-A4-A5-A6-B4-B5-B6-C4-C5-C6-D4-D5-D6-(A4)

 (D9)-A7-A8-A9-B7-B8-B9-C7-C8-C9-D7-D8-D9-(A7)

       \  \  \-E1-E2-E3-/  /  /  /  /  /

        \  \---E4-E5-E6---/  /  /  /  /

         \-----E7-E8-E9-----/  /  /  /

                \  \  \-------/  /  /

                 \  \-----------/  /

                  \---------------/

---

Geoschmo

54 systems, and no system is any more then 6 hops from any other system.

[ January 19, 2004, 18:16: Message edited by: geoschmo ]

[Loser]

And thirty-four (not thirty-five, I forgot that the one in the center of the stack doesn't count, though it could...)

code:

---

          1

         / \

        2---3

       / \ / \

      4---5---6

     / \ / \ / \

    7---8---9---A

   / \ / \ / \ / \

  B---C---D---E---F

   \ / \ / \ / \ /

    G---H---I---J

   / \ / \ / \ / \

  K---L---M---N---O

 / \ / \ / \ / \ / \

P---Q---R---S---T---U

         \ / \ / \ / \

          V---W---X---Y

---

Additional connections (ho-boy...):

• 1-Y
• 2-P
• 2-Y
• 3-U
• 3-Y
• 4-K
• 4-P
• 6-U
• 6-O
• 7-G
• 7-K
• A-J
• A-O
• P-X
• P-Y
• Q-W
• Q-X
• R-W

Whew, I'm doing something usless while at work.

Situation: normal.

[ January 19, 2004, 18:29: Message edited by: Loser ]

[Fyron]

[geoschmo]

I had another interesting idea for a map a while back. This one you have to just visualize because I don't know how to represent it on paper. But all the warp points in every system are in one spot. Say in the center sector. Then you can travel several systems accross the map in one turn. I did it once with a random generated map that I went back through and moved all teh warp points. It took a while, but the result was pretty cool, I thought anyway.

[tesco samoa]

People you are taking this to a really complex level.

The math is very simple. Please let me outline it here.

1.



where in the first step we made the change of summation variable , and in the second step, we made use of the fact that any sum over all terms is equivalent to a sum from 0 to .

Now natually you will if you want to minimize your starting location seperation as N approaches infinity in the following series



in other words, since you don't plan on creating an infinite amount (theorectical impossible except with hacking SEIV and changing the default player number by increasing it beyond the current level of 20) you really have the following formula -- which is an approximation that becomes more accurate with the larger the number of systems:




There is a difference in spread between Sprial arm Quadrants (when maximizing the number of threads) and the Torus Quadrants-- in additiona the Sprial Arm Quadrant will limit starting locations based on a number of factors.

For this we look at the Fourier thereom as applied to Duration and Bandwidths as Second Moments (using the normalized second moments of the squared magnitude:




where





As you can all see this explains my point in an elemantary model that is easy to read and follow.

[geoschmo]

sssssssssssssBOOM!

The sound of Geo's head exploding.