On Game Design - Game Design Theory - page 29

Discrete Space Continuous Space

Position: X = 5, Y = 4 Position: X = 0.41644, Y = 3.98558

Figure 8 . Examples of discrete and continuous spaces.

Of course, inches themselves are discrete units of measurement that
we use to describe and record length, but in the Quake example the dis-
tance to the explosion is effectively continuous (even though the in-game
system probably has some kind of grid if you look at a small enough level
of detail). Because games always have to have an end condition, which is
necessarily discrete, no game is entirely continuous. The goal in soccer,
for instance, is a discrete space. Any game with continuous space is going
to have some discrete space at the end, if nowhere else, to provide the
condition that ends the game. An example of this would be the sport of
fencing, in which the first competitor to fall prey to three touches —get-
ting hit by the opponent's weapon—loses the match. A touch is defined
differently depending on the type of fencing, but usually there is a dis-
crete area on the body that is considered valid for touches. Judges watch
carefully to discern whether or not this discrete area has been hit by the
opponent's weapon.

Continuous and Discrete Time
Time itself, which is normally continuous, can also be divided into dis-
crete segments. Any game that is turn-based divides its game time into
discrete spaces that we call turns. It doesn't matter if you take two seconds
or two minutes to take your turn in chess; both have the same meaning
to the game. Alternatively, in a game based on continuous time—also
known as real time—such as Super Mario Brothers , it absolutely does
matter precisely when you decide to do something. Because monsters
are constantly moving onscreen, jumping right now results in a very dif-