This is my attempt at a 4×4×4 LED Cube. It is completely controlled by an AVR Atmega microcontroller. I have a few simple animations so far, they can be selected via a switch on the board.

The LEDs are in a grid such that all the anodes of a horizontal plane are connected, and all the cathodes of a vertical column are connected. To turn on an LED, the uC sets the column pin to +5v, and the row pin to ground. It then goes row by row turning on each column that should be lit for that row. This is done fast enough that there is no visible flicker, and all the LEDs will appear to be on at the same time.

The source code is available from my SVN server: http://www.LlamaByte.com/svn/LED_Cube/

And, for your enjoyment, a quick video: