(Duell ?) Networks

[alan2here]

Google docs gives the option to draw an orginisation diagram, it shows hyrachy in an orginisation.

 

me     parent
son1   me
son2   me
son3   me

 

Drawing this gives you a box at the top entitled parent with a line going down to me and then branching out to 3 sons.

 

Moving on to another expample.

 

2n     n

0      0
2      1
4      2
6      3

 

The values in the top row are lables, the second column is increased by 1 each row. The first column is double the second column.

 

If we continue this chart up to n=40 and draw it according to the rules this is the result.

 

http://img253.imageshack.us/img253/7651/image1kq7.png

 

This allows you to see the seprate sequances that follow the rules [math]n_{p} = 2n_{p-1}[/math]

 

so 2, 4, 8... and sepratly 3, 6, 12... but not 4, 8, 16... this is already used in the 2, 4, 8... column.

 

 

f(n),  n

0      0
0      0
1      1
2      1
4      2
4      2
9      3
6      3

 

The second column is increased by 1 every 2 times. The first column alternates between two functions, the first is n^2 and the second 2n.

 

The effect is to prouce a chart like this one

 

http://img267.imageshack.us/img267/8169/image1ut0.png

 

http://img412.imageshack.us/img412/544/image1ar7.png

 

The chart has some problems. A box can't point in a circle at itself. It can't point up or more than one level down the tree therefore there are some links left out, it is also inconsistant about which way round a parent will show it's children. If you draw the diagram yourself you will see that a small number of simple rules can be used to unambiguously draw a correct diagram.

 

However you can still see the distictly seperate groups and the two functions propergating down.

 

Any comments and can I express the last diagrams equation using the same notation I would for sequences?

 

If you tell me your google docs name I will share the document with you.