Since the time of Escher, computers have increasingly been used in the drawing and design of tessellations, of both mathematical and representational types. As such, although by no means an expert in this field (indeed, my knowledge is most limited) in the applications at least of computers to tessellation, it would be amiss of me not to give my thoughts and opinions on the subject.

As such, it is important to note that the above two aspects are essentially independent of each other. By far the simplest task for the computer is the actual drawing of an outline, as with say squares and triangles, to give the simplest examples, from which repetition is easily accomplished to form tessellations. In contrast, the design stage as regards the representational aspect appears to me to be most limited in extent. For example, an expert in computers (and in computer graphics), Craig S. Kaplan, uses his Escherisation method to compose examples, but these are noticeably lacking in quality when compared to Escher and his few successors of note. In addition, the method he uses is not a matter of what I would term as design, as he in effect takes an arbitrary shape and instructs the computer to adapt this into a tessellating shape. However, as it is still relatively early days with the computer, and so improvements in quality must be expected in due course. However, quite when, or indeed if this will occur is speculative. As such, the Holy Grail for a computer would be a realistic, �complete' animal, of which even further refinements would include different breeds if appropriate. If a program can be written to accomplish this, any need for human effort would be made redundant. However, such an ideal is far from even remotely being accomplished, indeed, if it ever will. An analogy perhaps can be drawn with that of a different field, music. Although it is possible to reduce musical notation to a mathematical analysis, and thereby with the potential to examine 'all possibilities', there appears to be no shortage of new music being composed, of whatever genre. A possible similar situation may also arise with tessellation � the variety of motifs, of differing poses, of differing symmetry systems may prove impractical to unite to a computer program.

In recent years various specific tessellation software packages have arisen, with those aimed at the representational type including Tessellmania! and TESS. However, these to me appear somewhat limited in their extent, as the degree of control when designing is absent. Put simply, when using �pencil and paper', this can be regarded as a direct extension of one's thoughts, with the implements of design under full control. In contrast, when using computer input devices, such as mice or graphics tablets, effectively these are thus additional implements that come between the designer and the drawing (of whatever medium). Quite simply, no device is yet (indeed if it ever will be) as manipulative or dextrous as a hand can be. Aside from tessellation art, there is no comparison in the degree of control of pencil drawings with the actual implement and the computer equivalent tool.

Other ways of designing include the use of general graphics programs that are not specifically aimed at tessellation, such as Adobe Photoshop. However, as with the discussion above, the same difficulties in matters of �dexterity' reoccur. Therefore, this appears more useful for the task of repeating the motifs (although I have yet to use this in this way) rather than their actual creation. Certainly, if the problem of �dexterity' can be overcome, then the various image-editing facilities offer possibilities that are simply impractical by the traditional media.

Perhaps the best use of computers at present is in the purely mechanical task of replicating and colouring the motifs. Essentially, the 'tedium factor' can thus be eradicated. Quite simply, this factor must be borne in mind, as if an inordinate number of motifs are contemplated, the tedium of continuous repetition, whether drawing the motifs and their colouring, as fatigue can set in, leading to an inferior quality of finish, no matter how dedicated one is to the task at hand. Using the computer in such a mechanical way has three distinct advantages over traditional media such as pen, paper and paint:

• Time. Quite simply, a single repeating motif, once designed, can be repeated ad infinitum, with the minimum of time expanded. Such a tool has obvious advantages in terms of time saved, negating such repetitive matters of that of necessity require a new drawing of the motif each time.
  
• More motifs. Considerably more motifs can be shown than otherwise would be the case. Simply by utilising the 'cut and paste' tool vast numbers of motifs can be shown (an example of this is in The Magic of M.C. Escher, utilising drawings No.66 and 130 (cover and endpaper), that would be impractical by the �old fashioned' method by hand.
  
• Colouration. This can be achieved considerably quicker using a 'paint fill' tool. Furthermore, variations of the colouring using more colours than the minimum thus become a practical proposition.

So, what can be drawn from this? Although in the modern age it may be thought that some degree of basic knowledge of computers would be highly desirable, if indeed not essential in undertaking representational tessellations, such matters are demonstrably not of necessity. Escher himself, for obvious reasons, never had access to a computer, and yet this did not hinder him in producing quality examples. Indeed, perhaps to give encouragement to people who believe this aid to be a necessary requirement, all the drawings here have been designed using the �old fashioned' pen and paper (and coloured using paints). Therefore, demonstrably, the field is still open to anyone who has the desire to attempt such things � a computer is thus not essential. In short, if one cannot design quality tessellations by 'pen and paper', a computer will confer no advantage - essentially, it is a matter of understanding tessellation matters, and is thus not simply a matter of the 'computer power' or software at one's disposal.