(Duell ?) Networks

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.