Equal flow distribution to 3x3 grid

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Discussion Overview

The discussion revolves around the problem of distributing flow equally to a 3x3 grid of points from outer sources. Participants explore the mathematical and geometric implications of this distribution, considering applications in LED matrices and traffic flow. The conversation touches on the definitions and mechanics of flow in various contexts, including electricity and water.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that the problem can be modeled as a geometric distribution of flow from outer points to a 3x3 grid, questioning how to achieve equal flow to all inner points.
  • Another participant asks for clarification on what is meant by "flow" and how flow rate is defined, indicating a need for more precise terminology.
  • A participant emphasizes that the flow from any outer point must be distributed equally to the inner points, regardless of the actual flow rate, focusing on the geometric aspect of the distribution.
  • One participant challenges the idea of defining "flow at a point," suggesting that flow should be considered through surfaces or along pipes/wires, and questions the relevance of distance in the context of electricity.
  • Another participant proposes that it is possible to split a line into multiple parts and distribute flow accordingly, indicating that they do not see a fundamental issue with the proposed method of distribution.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of flow, with some agreeing on the geometric distribution concept while others challenge the clarity and feasibility of the approach. The discussion remains unresolved regarding the best method to achieve equal flow distribution.

Contextual Notes

There are limitations in the definitions of flow and flow rate, as well as the assumptions about distance's impact on flow distribution. The discussion does not resolve these ambiguities.

syphex
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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.
 
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"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?
 
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.
 
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.
 

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