Used to describe actions, decisions, or participation that are left to one's own will or discretion, not compulsory. Often used in formal or written contexts.
Participation in this training is voluntary.
Enrollment in the insurance is optional, but recommended.
自発的 means 'spontaneous, voluntary' with a nuance of arising from one's own initiative, while 随意的 emphasizes the absence of compulsion or obligation.
Formed from 随意 (voluntary, optional) + 的 (adjectival suffix). The exact historical derivation is uncertain, but the word follows a common pattern for creating adjectival nouns in modern Japanese.