"natural marking found on some stones in the form of branching shrubs, trees, or mosses," 1745, from Greek dendrites "of or pertaining to a tree," from dendron "tree," from PIE *der-drew-, from root *deru- "to be firm, solid, steadfast," also forming words for "wood, tree."
Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).
In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.
<a href="https://www.etymonline.com/word/dendritic">Etymology of dendritic by etymonline</a>
Harper, D. (n.d.). Etymology of dendritic. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/dendritic