Doable but expensive. A wifi version would need at least:
wifi chip plus antenna - $30
microcontroller + associated bits - $8-15 or so
stepper motor drivers (you need two) - $8 or so
stepper motors - $6 min
printhead and ink - $12, replaceable
Battery and charging circuitry
And that's not counting manufacturing and profit. Would you pay $70+ for printed toilet paper? If a couple people would, I'm willing to design the device, sell a couple, and open source it.
Speed is traded off for resolution. The thicker the paper, the more it would absorb the ink, and the less would rub off. I would not recommend this for thin (2 layer) paper.
If you are actually interested in doing this, I'd be up for doing the project. I actually have the motors, motor drivers, microcontroller, and inkjet cartridge full of red ink already. I also have a 3d printer for mechanical prototyping, and a good supply of toilet paper. If you are interested in working on this with me, email me at kliment.yanev at gmail.
wifi chip plus antenna - $30
microcontroller + associated bits - $8-15 or so
stepper motor drivers (you need two) - $8 or so
stepper motors - $6 min
printhead and ink - $12, replaceable
Battery and charging circuitry
And that's not counting manufacturing and profit. Would you pay $70+ for printed toilet paper? If a couple people would, I'm willing to design the device, sell a couple, and open source it.