Two-dimensional Phenomena — a Glimpse of Reality
The real world is, happily, neither one-dimensional nor yet specially three-dimensional in general. This is good news, as one-dimensional models of reality tend to be trivial and the three-dimensional ones are mostly too large to fit on present-day computers. A quick calculation shows that a typical problem such as the ones we have looked at in chapter 4 requiring 99 nodes in one dimension will require 99 * 99 * 99 nodes in three dimensions. If one needs to store, say, ten items of information about each node, this will mean something like 10000000 items in all. It is easy to see that a reasonably complicated three-dimensional problem might require more capacity than is readily available on all but the very largest computers. The problems may also take an enormous length of time to iterate to convergence.
Unable to display preview. Download preview PDF.