For some reason the desmos engine doesn't do mod(x,3)=0, perhaps it's graphing an infinately small point. If you allow the value of the modular function to be less than a small number, say, mod(x,3)<0.01, then you will see the points you expect.
Verbatim is defined as an exact repetition without changing the words. An example of verbatim is when you quote someone exactly without changing anything. word for word; in exactly the same words. Origin of verbatim.
1 Direct Speech and Indirect Speech.  2 While direct speech purports to give a verbatim rendition of the words that were spoken, indirect speech is more variable in claiming to represent a faithful report of the content or content and form of the words that were spoken. Direct Speech and Indirect Speech.  2 While direct speech purports to give a verbatim rendition of the words that were spoken, indirect speech is more variable in claiming to represent a faithful report of the content or content and form of the words that were spoken.