Do LCD's or Plasmas have a circuit for each pixel or they are lit in an array fashion?
There is a grid, with transistors at the intersections:

https://en.wikipedia.org/wiki/Thin-film-transistor_liquid-crystal_display#Construction

There's a grid, and the grid is "strobed" at high speed by the display driver circuitry which activates one row at a time while driving pixel voltage values for that row on the columns. The transistor ensures that this doesn't affect other rows, and the inherent capacitance of the system holds the voltage there for a few miliseconds until the next display refresh.

In your example, you don't drive both pixels at the same time, but one after another, and they stay at the value they were set at for a while.