Efficiency for identifying letters and words as a function of their complexity.

<p>Efficiency is nearly inversely proportional to complexity over a nearly hundred-fold range. The horizontal scale is the perimetric complexity (perimeter squared over ink area) of the letter or word. Each<b>+</b>is efficiency for identifying one of 26 words of a given length (1 to 17) in Courier <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064803#pone.0064803-Pelli1" target="_blank">[24]</a>. Each Courier letter has a complexity of 100 (averaging a-z), and the complexity of a word is proportional to its length. Each △ is efficiency for identifying one letter of one of 14 traditional fonts and alphabets by native or highly trained readers, in order of increasing complexity <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064803#pone.0064803-Pelli2" target="_blank">[25]</a>: <i>Braille, bold Helvetica, bold Bookman, Sloan, Helvetica, Hebrew, Devanagari, Courier, Armenian, Bookman, Arabic, uppercase Bookman, Chinese, Künstler</i>. The outlying □ is efficiency for a letter in an untraditional alphabet: <i>4×4 random checkerboards</i>, after extended training <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064803#pone.0064803-Pelli2" target="_blank">[25]</a>. The outlying ○ is efficiency for identifying the location of a disk. (See ‘Experiment 5. Identifying disks’ at the end of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0064803#s3" target="_blank">Materials and Methods</a>.) A disk has the lowest possible perimetric complexity <i>K</i> = 4<i>π</i> = 12.6. A linear regression of log efficiency vs. log complexity for the traditional letters (13 fonts and alphabets) and words (13 lengths), excluding the untraditional alphabet and disk, has a slope of −0.92 and <i>R</i>² = 0.99. The regression line and its equation are shown.