Examples

EXAMPLES

Figure 8.

Figure 9.

Figure 10.

Figure 8b displays a sequence of nine 10x11 Lunda-designs generated by introducing, step by step, more horizontal mirrors along the principal diagonal (Figure 8a). Figure 9b shows what happens if we introduce the mirrors in pairs (Figure 9a). This time, the resulting Lunda-designs have a two-colour symmetry: a half-turn about the centre interchanges white and black. This also happens with the Lunda-designs in Figure 10.

Figure 11.

In Figure 11a shows a sequence of three mirror designs, of which the second and third generate the same Lunda-design (Figure 11b). These Lunda-designs admit vertical and horizontal reflections. The first preserves the colors, where as the second reverses black and white.

Figure 12.

Figure 12a displays three mirrors designs with two-fold rotational symmetry. The Lunda-design generated by the first is also invariant under a half-turn about its centre. In the second and third cases, a half-turn around the respective centres reverses the colours.

Figure 13.

The symmetrical mirror designs in Figure 13a generate Lunda-designs with horizontal and vertical reflections which interchange black and white. (Many) Lunda-designs seem to me - and to colleagues and students to whom I have shown them - aesthetically appealing. Where do possible reasons for this lie? What do all these Lunda-designs have in common? Which characteristics? Do they possess specific symmetries?

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