Upon my paper in the Bridges 2008 art exhibit, available at http://archive.bridgesmathart.org/2008/bridges2008-453.html, a total of five pictures was shown in the exhibit of the same bird motif tessellation, with a theme of using four colours to echo the four main elements of the bird, namely the head, body, wings, and tail, with the premise of a map colouring. These I show on the exhibit page following this. These also appear on the CD Rom that accompanied the book, of which I made reference to a discussion on aspects of colouration, involving one, two, three, and four colours. This is discussed on the colouration aspects page.
An aspect of tessellation that is given scant regard, indeed, if it is even considered at all, is that of what I term as systematic coloration of the motif. As a rule, the designer, upon completion of a tessellation then colours the motif very simply, with generally a single colour. As such, there is nothing wrong per se with this. Indeed, as a rule simplicity in colouration is preferred. However, such a simplistic approach can be said to be lacking in imagination, as more colours can be used, and thereby thus being of more interest.
As such, the first step in the process is noting that any motif can be divided into discrete areas. For example, to illustrate this point with two frequently found motifs:
(i) bird, with a head, body, wings and tail
(ii) fish, with a head, body, fins and tail
Note that for reasons of consistency the fins and wings of the respective creatures are regarded as of a single unit. Although it is indeed possible to have different colours for these elements, such instances have a somewhat jarring effect, and indeed thus lack consistency. Furthermore, of birds, I am unaware of any that in real-life have such a colouration scheme. Consequently, each can thus serve as a distinct region. As such, for any one motif, it is thus possible to colour this 'partitioned' motif in more than the simple one colour as discussed above. Below I show an example:
Instances of such multiple colouring with two or more colours can be seen in examples of tessellations, such as with a bird motif, with say the head, wing and tails of one colour, with the body of another. However, I have to say without exception, such instances are very much non-systematic in their nature – the artist simply colours in the above instance, in an arbitrary aesthetic way. As such, for a 'one-off' tessellation this is fine, but what about other combinations? An obvious question to ask is can such a ‘2-colouring' have other possibilities, such as the head of one colour, and body, wings and tail of another. What about introducing three, four or even more colours? As such, although arbitrary examples of these can be found by trial, such a process is to be regarded as unsatisfactory, as such a procedure is obviously lacking in thoroughness – by the very nature of such a arbitrary way of colouration, a more interesting coloration may be missed. Therefore, what is required is a more systematic approach to determine all possibilities in this field. So how best to approach this problem? As such, this is best undertaken in two distinct parts
(i) The calculating of the possibilities of colour combinations for individual motifs (Part 1)
(ii) The application to a tessellation. That chosen here is of a 4 x 4 bird motif block (Part 2)