Magic Printer Cartridge Paintbrush
spritesmods.com
spritesmods.com
They are shift registers, and the data fed to each nozzle is essentially a serial data stream, but multiple lanes are used to increase the bandwidth and allow higher printhead speeds.
The signals are not all that different from those used for driving LCDs and EPDs[1], if you step back to a higher level of abstraction and look at how they all "print" information --- there's clocks, serial data inputs, and latch signals.
This is a resistive heater "bubblejet" type printhead, the other major inkjet technology is piezoelectric which is widely encountered in Epson printers and also the majority of industrial ones due to their better robustness and ability to handle a wide range of inks. The piezoelectric heads use an even higher driving voltage (~40V) and are usually driven with a trapezoidal waveform, which can be timed with the firing pulse to obtain different drop sizes.
[1] Trademark "eInk", he also has another page on driving those: http://spritesmods.com/?art=einkdisplay