This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin’s (1990) Map Algebra, the term “Map Calculus” is used

computational capacity of inexpensive computers and the development of advanced

distributed computing environments, known as “Grid computing”.

The growth of the processing power of modern computers is a well-known

phenomenon. Although Gordon Moore predicted the growth in the design complexity

of integrated circuits, his “law” became, in effect, the benchmark for the computing

industry and pushed forward the design of faster and faster computers (Brown &

Duguid, 2000). The emergence of inexpensive and powerful computing environments

enabled the development of “Supercomputer” scale machines from standard inexpensive

computers, in configurations such as Beowulf clusters (Bell & Gray, 2002). While this

classic supercomputing architecture is geared towards sustained peak performances, it is

less suitable for Map Calculus-enabled GIS, as it requires peaks of computing, followed

by period of minimal activity. This makes the emerging Grid computing (Foster,

Kesselman & Tuecke, 2001) a more attractive environment for its development. In Grid

computing architectures, a network of computers is configured in such a way that unused

or underutilised computing resources are available to those users who need them.

Another reason for the adequacy of Grid computing, is that it is based on the

distribution of computational problems across the network. As many geographical

problems are naturally divisible using a spatial decomposition, they are suitable for

distributed computational models. Although knowledge of, and experience with Grid

computing is in its early stages, experiences from projects like SETI@Home demonstrate

that extensive computations can be performed by distributing the load across the

network.

In the next section, a simple implementation of Map Calculus-enabled GIS is described,

to demonstrate the concepts and principles that were described above.

Demonstrating Map Calculus-enabled GIS

To demonstrate the feasibility of Map Calculus-enabled GIS, a basic prototype was

developed using Manifold System 5.0 (CDA International Ltd., 2001). This GIS package

was selected because it enables the use of Perl as a scripting language and, therefore, can

be enhanced quite easily using widely available Perl libraries. It is important to note that

Perl (Wall & Schwartz, 1991) is not a functional language, but rather an imperative one.

However, Perl has hybrid origins, and it was designed by borrowing from a wide range of

languages including Lisp (Wall, 1999). Therefore, it is capable of evaluating expressions