TazeTSchnitzel has released PictoSwap, a SwapNote clone for the 3DS, it is quite new and at the moment has its flaws, such as a slight slowness, apart from that, it seems to work quite well, take note though, that this isn’t a native 3DS homebrew, it is a web browser application dedicated to the 3DS, here is a quote from the source:
What’s this? PictoSwap is a web app intended to be used in the Nintendo 3DS Browser. It’s essentially a clone of Nintendo Letter Box (or “Swapnote” in the US), which let you scribble little drawings and send them to other 3DS users. Unfortunately, Nintendo suddenly stopped the “SpotPass” feature of the app in 2013, due to abuse of the service. Hence I decided to clone it. Where does the name come from? I posted a thread on reddit’s /r/3DS subreddit to try and find a name. I liked /u/TengenToppa’s “PictoPass” suggestion, and changed it slightly to “PictoSwap”. The suggestion was, presumably, a reference to note passing and PictoChat (a feature on the original Nintendo DS).
Here is a video of it in action: Visit this link on your 3DS browser: