This is a single-row mosaic pattern, worked flat without breaking the yarn. Helena Asmus Lim has a highly-detailed explanation of the technique here, but you should be able to work this pattern from the pattern instructions alone.

The pattern is inspired by traditional basketry of the Eastern Band of Cherokee. See their work here.

Gauge:
19 sts and 18 rows in 4” in single-row mosaic
18 sts and 17 rows in 10cm in single-row mosaic

Materials:
Sport weight(5-ply/fine/category 2) cotton
65y/60m MC
55y/50m CC
Crochet hook, size F/3.75mm
One locking or split ring stitch marker
Scissors & yarn needle for finishing

You may choose to use aran-weight crafting cotton like Lily Sugar ‘n Cream or DROPS Paris, but you will need a larger hook and more yarn, and your finished dishcloth will be oversized.