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Logic Displays are the blinky lights in the rectangular openings of R2-D2's dome (2 front, 1 rear) that separate dead droids from the living.
Original trilogy logic displays used bundles of fiber-optic cables which were routed from the exterior of the dome to an illuminated 'color wheel'. As the wheel rotated each strand of fiber-optic cable would transition between colors, giving a satisfying organic appearance that's not immediately identifiable to the viewer. These are not simple LEDs that blink or fade on and off; they're something that comes from a galaxy far far away. They were developed by John Stears between 1975 and 1976 during Star Wars pre-production.
The RSeries Logic Engine combines Arduino, RGB LEDs and fiber-optics to accurately emulate the color-wheel logic display patterns seen in the original Star Wars trilogy. This is arguably the most screen-accurate logic display system since Return of The Jedi.
At its heart is a microcontroller board which runs a series of LEDs. These RGB LEDs cross-fade between set colors. For example the Front logic LEDs typically fade from black to blue to white and back again. As it arrives at each "key" color, that LED is paused for a random length of time - this creates constantly evolving color patterns that appear almost random at first glance.
Fiber-optic cable is used to route the light from each LED to specific 'pixels' on the logic bezel, which is what is finally seen on your droid. So we end up with displays that look identical to the Origintal Trilogy R2, but we have individual pixel control, so can perform some fancy display sequences.
See a quick demo on YouTube:
The Logic Engine is supplied as DIY kits that are prepared exclusively for members of the R2 Builders Club. Look in the 'Other Parts' forum on Astromech.net to check current availability.