When iconicity stands in the way of abbreviation: No Zipfian effect for figurative signals

Zipf's law of abbreviation, relating more frequent signals to shorter signal lengths, applies to sounds in a variety of communication systems, both human and non-human. It also applies to writing systems: more frequent words tend to be encoded by less complex graphemes, even when grapheme complexity is decoupled from word length. This study documents an exception to this law of abbreviation. Observing European heraldic motifs, whose frequency of use was documented for the whole continent and over two large corpora (total N = 25115), one medieval, one early modern, we found that they do not obey a robust law of abbreviation. In our early modern corpus, motif complexity and motif frequency are positively, not negatively, correlated, a result driven by iconic motifs. In both our corpora, iconic motifs tend to be more frequent when more complex. They grew in popularity after the invention of printing. Our results suggest that lacking iconicity may be a precondition for a graphic code to exhibit Zipf's Law of Abbreviation.