Scott Haley mentioned my old Hellduino post on Facebook: a simple project that used an oscillator powered by an Arduino to send Hellschreiber, a kind of simple fax mode invented by Rudolf Hell in the 1920s. I did this mainly as a simple test, inspired by Steve Weber, KD1JV's "temp2morse" project. But unfortunately, that page seems to be gone, so the schematic isn't available. It's not a huge deal: almost any Colpitt's oscillator would do in its place, with the main power rail being powered by a digital output on the Arduino, but I thought I'd see if I could find one suitable. I've built this low power oscillator documented by Hans Summers before, it's probably overkill (it's meant to drive a 50ohm antenna, and actually radiate some single digits worth of milliwatts). K7MTG's HF Thermometer project was the inspiration for Steve's, so is probably a good place to start. If you look at his schematic, you'll see it has no antenna, and no power amplifier. It is actually a bit more sophisticated than my first test circuit was: L1 and C3 form a tuned circuit, which probably makes the waveform a bit more sine-like (if you look at my video, you'll see the waveform isn't ideal). To convert this circuit to send Hellschreiber is just a question of software, since Hellschreiber is (like Morse) just sending dots at the right time.
Addendum: Jeff Kellem was nice enough to do some heavy lifting and find a copy of the original schematic for Weber's temp2morse project: