Updated : 2021
You can create instant splatter background in Adobe Illustrator by using symbols.
The advantage of symbols is that the background can be changed in seconds from a background of spots and dots to a splattered background of stars or cube or any other paths. The key thing is to use the Illustrator static symbol and not the dynamic symbol as the application will keep the symbol for the background live and editable at all stages.
To create the background, you can start with a single symbol and then spray that and then use that as a new static symbol and then spray the new symbol and the combination will rapidly create 100s of artworks all across the image / artboard
create a path such as a circle (a small path compared to the size of the artboard)
set the fill color and set the stroke to none
drag to the symbols panel
save as static
OK
OK, now you have your first symbol and so you need to apply that across the image. Go to the symbol sprayer tool in the toolbar and spray the design with numerous spots or dots / paths through it is probably best to keep them together.
Go to the other symbol sprayer tools and hold down the alt / option and re-size (shrink) the paths to create large and small symbols / paths
select the symbol in the panel
go to the symbol sprayer tool
apply and spray multiple times close together
use the alt / option to decrease the size of some of the symbol instances
select all the symbols sprayed and place that in the symbols panel (again, static)
You can now apply the symbols group and spray that over the document / artboard. You can re-size those using the sizer tool. You can also rotate the groups using the spinner tool
select the new symbol
apply the symbols across the artboard
fill the entire document
go to the sizer tool and hold alt / option to resize some groups
go to the spinner tool and rotate the paths (in the same group as the symbol sprayer tool)
You can then repeat this a number of times but you will have 100s of spots / paths / dots / stars (depending on the initial default path)
You can alter the entire splatter spray design in Adobe Illustrator simply by double clicking the original source symbol in the panel and editing that (such as changing the color or the path etc) and exiting out of the symbol edit.
You can then create a splatter filled document with stars instead of spots and dots etc. You could create an initial spot symbol with multiple colorful paths such as a red star and green star etc.