Copyright © 2001–2008 jsd I set up some spreadsheets to solve
Laplace’s equation, with more-or-less any boundary conditions
you want. The spreadsheet becomes, essentially, a 2D cellular
automaton that directly emulates the physics. This version
handles objects in a D=2 universe in rectangular coordinates. In
flatland, i.e. D=2, the Z direction simply does not exist. Alas
many people are unfamiliar with the laws of physics in flatland.
Therefore it might be better to think of this as a D=3 universe
in which all D=3 objects are infinitely tall and translationally
invariant along the Z axis. In this case, the Z direction
exists, but is uninteresting, and the essential physics is the
same as the D=2 case. (This is not the same as considering a
thin flat “D=2” object embedded in the D=3 universe!) In any
case, each cell represents an area dx∧dy in the XY plane. The
spreadsheet to handle this case can be found in reference 1.
Occupying a large area near the upper left of the spreadsheet is
a grid that I call the po