Twinkle and shimmer are different in DMX. When a LOR controller is operating on a LOR network, a shimmer or twinkle is a single command that the controller then interprets and generates the shimmer or twinkle. A DMX network only understands a single command - the current level. Therefore, in order to send a shimmer, the show computer or director must send a command for whatever level, followed by an off command, and repeat very quickly. A DMX network sends each channel command about 45 times per second.
I see Ebuechner answered most of this too.