'chaotically-partitioned' is a compound formed from 'chaotic' + the past-participle form of 'partition'. 'Chaotic' traces to Greek 'khaos' (χάος) meaning 'vast void' or 'gap', later meaning 'confusion or disorder'. 'Partition' comes from Latin 'partire'/'partitio' (via Old French/Medieval Latin) related to 'pars/part-' meaning 'part'.

'chaotic' comes from Greek 'khaos' → Latin/Old French 'chaos' → Middle English 'chaos' and developed the adjective 'chaotic'. 'Partition' developed from Latin 'partitio' → Old French 'particion' → Middle English 'partition'. The compound usage (adverb + past participle) is a modern English formation used to describe how something was partitioned.

Originally 'khaos' referred to a vast void; over time it shifted toward the sense of 'confusion or disorder'. 'Partition' originally meant 'a dividing into parts' and has retained the core meaning; together the compound now specifically conveys 'divided in a disorderly way.'