変幻自在
hen.gen.ji.zai

Literally: change – illusion – self – exist

Alternately: Able to change one’s form or appearance, or appear and disappear, at will. Shapeshifting; protean; phantasmal.

Notes: This is a compound of compounds; 変幻 refers to an illusion or vision that flickers into and back out of existence, while 自在 refers to being able to act freely at will.

A close synonym is 変幻出没 (hengen shutsubotsu), replacing the “at will” part with explicit “appearing and disappearing”; compare and contrast 神出鬼没. Another synonym emphasizes the changeable nature of the thing in question: 千変万化 (senpen banka), literally “one thousand changes, ten thousand transformations.”

A lot of Japanese image sites seem to feel that the chameleon is the definitive poster child for this phrase