You may have what's called a "stumped" ceiling, and the tools for various desings can sometimes be found at major lumberyards, but you can also achieve re-creation of this pattern with a little trial & error and sometimes some help from simple items you may have in a kitchen "junk" drawer.
The material used to make the pattern can be drywall mud, usually watered down a little (to about the consistency of pancake batter or slightly thicker). Use a scrap of drywall or something similar as a test surface & try duplicating the pattern using whatever you think might seem right; paint brush, wallpaper pasting brush, sponge, bottle brush, wire whisk, spaghetti spoon, etc. Wipe errors away while wet with a sponge & try again until you find the tool that gives you the right effect. Once you have the method down, apply it to the ceiling.
Have fun trying different approaches; it's a very forgiving medium, and can be scraped off easily while wet to try again. Good luck!