Luwian hieroglyphics — also called Anatolian hieroglyphics or (incorrectly) Hittite hieroglyphics — do not seem to be stylistically related to any other language, so it is likely this writing system was invented by the Luwians, although they pretty certainly knew of writing, given the Hittite cuneiform in the same region.
There is some evidence that although Luwian hieroglphyics are used to write the Luwian language, the writing system was influenced by the Hittite language. For example, some of the syllabic characters have pronunciation similar to the Hittite word for the object they look like, instead of from the Luwian word for the object they look like. (It would be as if English were written with a syllabary that has a symbol that looked like a bull, but that symbol was pronounced “toh” like the first sound in Spanish “torro” instead of “buh” like the English “bull”.) This is sort of backwards from the relationship of Proto-Sinaitic to Egyptian hieratic.
Luwian hieroglyphics were frequently written boustrophedonically — left-to-right on one line, then right-to-left on the next line. It is easy to see which direction you are supposed to go because the characters always “face into” the direction of reading. For example, if there is a donkey facing left, the reading direction is left-to-right. If there is a bull facing right, the reading direction is right-to-left.
Luwian hieroglypics look “jumbled” to me, with each line of text having two or three glyphs stacked one-on-top of each other, except that “stacked” implies more order than they really have: