Methods for the Seventeen Distinct Types of Two-Colour Frieze Patterns

installations:a souvenir shop, cafeteria, administration office, information center and cloakroom. The exhibition space is designed to simulate a modern museum setting. It presents the historic environment of an archaeological museum constructed in the form of a theatrical landscape of ruins and forests simulating the magic atmosphere of the Bedayano’sadoration of Diana, the goddess of nature. The indoctrination process is accomplished by linkingan academicpresentation to each sectionof the museum. The fictionaltext iswritten in an academic-scientific style,integrating an existing history of a city or an institution. It is on this basis that the Maybe Is Good Productions’simulated museumsare conceived. This project is a commentary on the mechanism by which the political-industrial aristocracycan mobilize a museum’s academicdisciplinesof art and science. These disciplinesbecome tools for fabricating a nation’scultural identity. Evidence of this phenomenon can be found in various national museums in Europe. Their policiesreflect the paradox of integrating archaeologicalfinds “acquired” during European countries’colonialpenods into politicalconcepts that glorify their own national heritages. Further examplesof the danger of the strange hybrid of art and history usurped by political organs is evident in the vulgar presentation of German identity by both the Nazi and the East German regimes in their museums. The members of Maybe Is Good Productions are Ira Marom, museum director, concept development and writer ; Hermann Verbeek, photographer for the Bedayano project;Juka Notio, art director; Andonis Michaelides,project realization. METHODS FOR THE SEVENTEENDISTINCT TYPES OF TWO-COLOURFRIEZE PATTERNS h e r Shaker Salman, School of Mathematics, University College of North Wales (Bangor), United Kingdom. Received 29June 1992.Accepted fmpublicution RogerF. Mulinu. A mathematician, like a painter or a poet, is a master of p a t t a s . -G. H. Hardy Over the last severalyears I have used computer graphics to generate, study and analyse more than 400 one-and twe dimensional repeat patterns. These patterns offer a rich source for exploitation F i g .4. h e r Shaker Salman,diagram showing the stages of the technique. Frieze + colour n pattern Copy in one direction Create a template file Fig.5. h e r Shaker Salman, examplesof twocolourfrieze patterns and their algorithms. (a)Pla1[21: u=TCTTC?H.(b)Pmm2[2]z: U=TC~TCIHTTCVATC-~R by artistsand are alsoof interest to architects , mathematiciansand researchers in multicultural studies.Graphic facilities on microcomputers are a well-known tool for the operations needed to explore colour symmetry patterns. The facilitiesto construct rectangular shapes accurately,to handle them, and to do such operations as move, rotate, reflect horizontally and vertically, copy, colour, etc. are easily understood and suited to the user in the context of the classical method. Computer graphicsis a particularlyenjoyableway to create these patterns. The major goal of my work in this area has been to develop a formalism to construct simple methods for the generation of the 17types of colour frieze patterns . The algorithms are suited for use with interactive computergraphicssoftware that provides the facilitiesneeded. Once students became familiarwith these methods, they can not only create sets of attractivecolour patterns, but also analysepatterns from different books. An additional goal of my work is to (1) perform symmetry analysis on the patterns and class@ them according to their symmetrygroups and (2) extract numerical data for the efficientgeneration of the patterns based on the analysis. The technique of creating twocolour frieze patterns is as follows: First, create a template tile T, which is a generating region for the unit tile. We will suppose the template tile to be a rectangle, although this is not essential. Second, obtain a unit tile U by combining the number of Ts needed to p r e duce the desired type of unit after having applied the required actions to them. An action applied to T can be any one of the following: 1. Colour with two colours. Sometimes the whole of the tile is coloured and sometimes only the interior of the pattern. (In this paper black and white are used to represent any two different colours.) 2. Colour by switching the two initial colours. 3. Reflect horizontally. 4. Reflectvertically. 5. Rotate through 180degrees. U in one dimension. of the technique. Figure 5 shows examples of two-colourfrieze patterns...