Fig. 11  A logo exemplifying repetition of identical elements in a symmetric pattern

Second, this line of repetition can be either an undirected line or a directed vector with one end being a "start" and the other, "finish."  This depends on whether the repeated objects are exact copies of each other or they undergo some transformation along the way.  The case of plain repetition, as if it were in reward for its simplicity, often implies symmetry and uses curved lines for placing objects (Fig. 11).

If, on the other hand, repeated objects present a trend of development, be it in their color, form, etc., the vector they form usually does not fit quite well into a symmetric composition and seldom uses curved paths.  One example of such developing repetition you've already seen in the sample project of Part I; another example, shown on Fig. 12, is interesting in how its balance is preserved by deliberate deviations from symmetry in both the shape of the repeated "leaves" and in their positioning.

Fig. 12  An example of developing repetition with broken symmetry

How many objects should we use in a repetition?  The above examples suggest that the most popular number is three, and it can be justified.  Indeed, a pair of objects is not enough---they will most probably be perceived as an implication of either symmetry or contrast; the least number of steps that makes a stairway is three.  The nature of logos endorses simplicity, that's why three-member repetitions are so popular.  Another approach may be to equate the number of elements to the number of letters in the logo's text, as in the logo of Digital Equipment Corp. A few words should be added about symmetry which is, in fact, just a special case of repetition---the case where a couple of identical objects are mirrored around an axis or a central point.  A symmetric arrangement is one of the most engaging and pleasing for human perception.  Symmetry reveals the beauty of a purely abstract form, and it's not accidental that the most perfect real-world creations such as the human body are nearly symmetric. However, one thing is true about symmetry as it is true about simple proportions that we discussed above: It must not be too obvious.  A composition where every detail is in symmetry tends to be too stable and, as a result, boring.  Here, as in many other cases, contrast may come to help---namely, an articulate contrast between symmetry and asymmetry will greatly dramatize the scene.  For instance, if you have to make a logo for a company whose title is already symmetric (see Fig. 8), it's a good idea to restrain this symmetry by using a forcibly asymmetric visual and even asymmetric letters.