The Entanglograph is yet another Etch-a-Sketch related idea. It consists of two devices which are entangled, in the quantum sense, with simulated action-at-a-distance ensuring that their displays are kept in sync.
Draw on one device, it appears on the other also. And vice versa.
Internally, each 'Sketch contains encoders, stepper motors, SIM card and battery. The infallible cellular network is a likely candidate for data synchronisation. Encoders will need to be absolute to reduce the risk of desyncing.
An on-board accelerometer detects the shaking motion needed to erase the display, which triggers a matching agitation in the paired device. There are a few ways of implementing this, the most boring being a wiper and scoop which redistributes the aluminium powder onto the screen, the most exciting being a series of internal solenoids and weights which jolt the device around substantially. Either way, shaking the device must ensure that both screens are cleared before further drawing takes place.