By John George Williams

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Extra resources for A field guide to the butterflies of africa

Sample text

Once more we have, in agreement with Corollary 2, that one returns to A from below on the right hand side. Conversely, if we traverse the mirror lines design, starting in A, going downwards to the left, one returns to A once again from below on the left hand side, in agreement with Corollary 2. Let us now eliminate horizontally the crossing A and traverse the mi rror lines design from X (see Figure 1. 32b) onwards in the indicated direct ion (••» . As the initial mirror lines design was monolinear, at a given moment one traverses the arc below A, from the right to the left.

_. _. - . -. -. -. _. _. - . 2 Figure 2. 4 General sy mme try lu'ope rties Searching for the common characteristics of Lunda-designs (of dimensions mxn), the following symmetry properties were observed and proven: (i) In each row there are as many black as white un it squares; (ii) In each column there are as many black as white unit squares; (iii) Of the two border unit squares of any grid point in the first or last row, or in the first or last column, one is always white and the other black (see Figure 2.

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 li e? What do all these Lundadesigns have in common? Wh ich characteri stics? Do they possess specific symmetries? -. _. -. -. -. -. -. -. -. -. _. _. _. -. -. -. -. _. -. _. _. _. -. -. -. _. -. _. -. _. -. -. -. _. _. -. _. -. _. _. _. _. _. -. -. _. _. -. -. _. -. -. _. -. -. _. _. -. -. -. -. -. _. -. -. -. -. -. -. -. -. -. - . _. -. _. _.

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