Line Art (2)
A simple line figure can be changed, by repetition, into unexpected pieces of art. The way the repetitions are carried out determines what the whole pattern will look like; small variations most often have large consequences. "One step aside" and "one step down" is quite obvious on checkered paper (little squares!). The pattern showing up has a square lattice making it somewhat serious and monotonous (see for instance the figures 2, 5 and 6c in Line Art (1)). It is much more exciting to have the basic pattern more or less decide for itself how it must be repeated. Take for instance a simple pattern (7a). Repetition according to a square lattice gives figure 7b.
7. Repetition
8. Mat (image 0883)
Apart from a competing pattern showing up (a kind of a four-leaved clover), the new pattern can be called quite boring. Figure 7c shows a more playful way of repeating. Free style continuation yields an intriguing pattern (8).
At a closer look, figure 8 has not a regular lattice (in a more strict sense). The way a basic pattern has been repeated can be made visible by connecting the centres by lines; the repetition itself becomes a (basic) pattern. The repetition pattern of figure 7c is given in figure 9a, that of figure 8 in figure 9b (here, one square represents nine "little stars"). The way of repetition can now be influenced directly by changing the repetition pattern. In figure 10, a different arrangement of the squares has been chosen. "Translating" this back into the original little stars, the pattern of figure 11 arises.
Repetition pattern
9. Repetition pattern
Different repetition pattern
10. Different repetition pattern (Varia 5 image 0166)
Doesn't work!
11. Doesn't work!
Compared to figure 8, this "does not work" in my opinion! The better the basic pattern is able to fill up the room between the squares, the more elegant the resulting pattern will become.

Here are some more examples (12, 13, 14, 15).
12. Caged (Squares 4 image 0904; to see an animation, click here)
13. Dumb-bells (Varia 9 image 0313)
14. Mask (image 0881)
15. Baron (image 0889)
By this, the number of possible repetition patterns is by far not exhausted of course. In fact, the number of variations can be as large as in the original patterns. Here is yet another example (16, 17). (By the way, the computer screen is not really capable of representating the patterns accurately!)
Yet another repetition pattern
16. Yet another repetition pattern
Four-pointed star
17. Four-pointed star (compare image 0885)
If the variation of repetition patterns can be as large as of "normal" patterns, why not turn it upside down? First make a repetition pattern that looks good, and then look for a basic pattern that fits. The last example was created in this manner (18, 19).
18. Waves (Varia 8 image 0293)
19. Clew (image 0888)

back top next

All drawings and figures, copyright © 1978-2010, Zef Damen, The Netherlands.
Personal use only, commercial use prohibited.

Nederlandse versie Nederlandse versie Last updated: 12-January-2010

Since 1-February-2005