This caning pattern is known as either the "spider web" cane or the "snowflake" pattern.   This photo is of my very first attempt at this beautiful, lacy pattern; and there's a nice little short story that goes with the chair I'd be happy to share if you ask!  This pattern is absolutely gorgeous (my humble opinion), but I do not recommend it for seats; it seems a little too delicate or fragile for that kind of wear and tear, but would be fine for a back panel.

If it was originally done with cane, I can most likely re-do it for you.