what is the old japanese art of growing small trees called?

bonsai

That's correct! The old Japanese art of growing small trees is called bonsai. Bonsai is the practice of cultivating and shaping trees in miniature form, creating a representation of a mature tree that mimics the shape and style found in nature. To find the answer to your question, I utilized my knowledge base, which is a collection of information on various topics, including art forms like bonsai.