a design involving lines of water, such as embroidered on a huipilli (see attestations)
Perhaps another similar term to atlacuilolli arises in the personal name Tlacuilolatl, which appears in the Matrícula de Huexotzinco. See:
https://aztecglyphs.wired-humanities.org/content/tlacuilolatl-mh779v (SW)
A. Wimmer, in the Gran Diccionario Náhuatl, points to a reference to atlacuilolli designs on a huipilli (blouse) and a cueitl (skirt) that appears in the Codex Matritense. This is explained in the GDN as being decorated with lines of water ("décoré de lignes d'eau"). Also, as Stephanie Wood notes in the Visual Lexicon of Aztec Hieroglyphs, the vast majority of Nahuatl hieroglyphs for water (atl) shows lines of current.
The keywording team of the Digital Florentine Codex give atlahcuilolli and amalacayoh as keywords for the sketch of aoztotl (a cavern with swirling water) in Book 11, folio 245 verso. Swirling water appears in a great many Nahuatl hieroglyphs, which is a feature that is tagged in the database of the Visual Lexicon of Aztec Hieroglyphs.
Marc Thouvenot identifies the verb icuiloa (or ihcuiloa, with the glottal stop), which means to paint, write, or print, as having a root of -cuil-. He notes how it also appears in tlacuiloliztli (writing), tlacuilo (writer), and cuicuiltic (mottled). He goes on to show various uses of icuiloa that take it beyond the simple definitions just given, resulting in something like the action of creating a design (e.g., on leather, ceramics, sculpture, or in textiles). It can also be something like the action of decorating (e.g., to put a flower on a cup of atole). He associates icuiloa and tlacuilolli with "cultural artifacts," such as arts and crafts or examples of writing and painting, but cuicuiltic with effects created by "nature." This short summary barely does his article justice; it is worth reading the entire piece. How Thouvenot's study might connect with the concept of bent or curved mentioned by Prem (1974: 555, 682) raises an interesting question. Perhaps the bent or curved lines of writing, painting, carving, embroidery, and so on, fall with in the realm of expressions of -cuil-. See Marc Thouvenot, "Imágenes y escritura entre los nahuas del inicio del XVI," Estudios de Cultural Náhuatl 41 (2010).
Besides referring to writing (whether alphabetic or hieroglyphic) made on paper or on other media as mentioned by Thouvenot (above), tlacuilolli (a root of atlacuilolli) might also refer to designs created on land, perhaps as a part of agriculture or land tenure documents.
See these examples from the Visual Lexicon of Aztec Hieroglyphs, all found in the Matrícula de Huexotzinco:
https://aztecglyphs.wired-humanities.org/content/cuemicuilo-mh514r
https://aztecglyphs.wired-humanities.org/content/mocuemicuilo-mh521v
https://aztecglyphs.wired-humanities.org/content/cuencuech-mh714r
https://aztecglyphs.wired-humanities.org/content/cuentlacuilol-mh664r
(SW)