Re: [Phys-l] resistors

[John Denker <jsd@av8n.com>]

On 03/17/2008 08:40 AM, Dan MacIsaac wrote:

> check out
> http://xkcd.com/356/
>
> and hints for elegant solutions are welcome (no, I don't have one).

Hint:  Fourier transform.



Lurid details:   http://www.geocities.com/frooha/grid/grid.html

which cites 
  D. Atkinson and F.J. van Steenwijk.
  "Infinite resistive lattices."
  Am. Jour. Phys., 67 486-492 (1999).

BTW the Fourier idea is worth remembering, because it comes up 
fairly often.  Feynman uses it somewhere in volume II to calculate
the evenness of illumination at desk-height from an array of lights
at ceiling-height.

The take-home message is that Fourier methods are not limited to
waves.  Any sort of periodicity will do, even if not wave-like.
Remember Fourier's book was _Théorie Analytique de la Chaleur_
and heat conduction is famously too overdamped to be wave-like.