The Afrikaans common name for Avonia albissima is gansmis (goose droppings). Seen close-up, the brown bract tips clutching the pliant cylinder stems appear like imbricate dirty fingernails. The slightly sickle-shaped brown markings are more prevalent on the upper stem parts.
The cluster in picture shows mature and young, round-tipped developing stems as well as some broken remains of past branches. Branching takes place low down.
The solitary (or groups up to three) stem-tip flowers are purple-stalked, cup-shaped, about as wide as the stem and white in colour; the pointed petal tips erect (Frandsen, 2017; iNaturalist).