Adafruit 12 ultra bright smart LED NeoPixels are arranged in a circle with 1.5 inches (37 mm) outer diameter. The rings are 'chainable' - connect the output pin of one to the input pin of another. Use only one microcontroller pin to control as many as you can chain together. Each LED is addressable as the driver chip is inside the LED. Each one has 18 mA constant current drive so the colour will be very consistent even if the voltage varies, and no external choke resistors are required making the design slim. Power the whole thing with 5V DC and you're ready to rock.
There is a single data line with a very timing-specific protocol. Since the protocol is very sensitive to timing, it requires a real-time microcontroller such as an AVR, Arduino, PIC, mbed, etc. It cannot be used with a Linux-based microcomputer or interpreted microcontroller such as the netduino or Basic Stamp. Our wonderfully-written Neopixel library for Arduino supports these pixels. As it requires hand-tuned assembly it is only for AVR cores but others may have ported this chip driver code so please google around. An 8 MHz or faster processor is required.