Equal flow distribution to 3x3 grid

[syphex]

This may be more of a math problem; it arose out of my curiosity of manipulating LED matrices and reminds me of a traffic flow problem, but I am sure it can model a variety of applications. Its not a homework problem but would probably make a good one!

You have a 3x3 grid of points, each point must be provided with an equal amount of flow from one of the outer points. I thought you could "split" the lines from the outer point for 2, 4, 8 (flow in = flow out and the flow is being halved each time), but this only seems to work for a 2x4 configuration, since otherwise the paths to the source would be different and hence flow rate would be effected.

Is this possible? Any advice?

Thanks in advance any help is greatly appreciated.

 

[mfb]

"Flow" of what? What determines flow rate? How do you define "flow rate of a point"?

you could "split" the lines from the outer point for 2, 4, 8

What does that mean?

 

[syphex]

The flow from any arbitary point except for the middle must be distributed equally to the remaining 8 points. Water, electricity, it doesn't matter the point is it must be done geometrically. The actual flow rate doesn't matter, only the distribution.

As for the split.. I simply mean if you split a wire for example into two, and then those two into two, you get four, and then 8, and so on. Simple geometric progression there. But how can you link that to the other points when the distance to any point from an outer point varies by distance.

 

[mfb]

There is no well-defined "flow at a point", neither in electricity nor for water. You can consider flow through a surface, or along a pipe/wire.

As for the split.. I simply mean if you split a wire for example into two, and then those two into two, you get four, and then 8, and so on. Simple geometric progression there. But how can you link that to the other points when the distance to any point from an outer point varies by distance.

Distance does not matter for electricity.

You can split a line into 3 parts, and split all 3 parts into 3 parts each afterwards. I don't see the issue.