Friday, February 10, 2006

At the beginning

I'm used to seeing titles on my blog posts. but this time I'm not getting them. Anyway...
The next part that's needed is some kind of space for things and events in the virtual world. Like time, space in a virtual world has to be finite and bounded, and discrete, rather than continuous. A computer can only handle a finite number of divisions. I'm going to call a unit of space a space cell.

While time requires only one number to describe it, space may require one, two, or three. One dimensional spaces, or linear spaces, aren't very interesting, except for introducing elementary concepts; such as the boundaries: X_MIN and X_MAX might as well be names their names. It's typical and conventient to set X_MIN as zero, but there is no particular reason it can't be some positive or negative whole number. The number of cells in the space is one more than the difference X_MAX - X_MIN, a common source of programming errors.

A two-dimensional space is more interesting. Here there are two coordinates, X and Y, and as well as X_MIN and X_MAX, the boundaries would be Y_MIN and Y_MAX. The size of the space would have to be the x-size times the y-size.
One of the simplext common games, tic-tac-toe, can be said to take place in a 3x3 space. Most more complicated and more interesting games, of course, take place in larger spaces.

A three-dimensional space is even more interesting, but these are much more difficult to represent on a computer screen. Various methods of representing them are possible, but I'm going to have to leave this as a more advanced topic.

Even higher dimensional spaces can be described mathematically, but I can only point to these as a direction of further research.

It's typical, but not always necessaty, to set up space as an array of some kind, and give each cell some kind of attribute. There's not much point to doing that if space is empty, or there is nothing in it, but before I discuss what is in space or what it is like, I want to discuss position.

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