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Each block is going to be one dot. He's looking for a simple directional light bar. I'd just use a simple micro controller and whatever driver circuit for the LED modules. The modules say they run directly off 12 volts so I'm not even sure they need a full driver or just a simple transistor switch. Keep in mind RobXr1 that if this is for a vehicle in the United states that the only colour you can use is yellow, red blue or green are not allowed for civilian use. I recommend a micro controller to sequence the LED's because the pattern you're looking for would be needlessly difficult to do in discrete logic.
Rob, as long as you're comfortable with technical terminology and aren't afraid to read micro controllers are relatively easy to start with. There two schools of thought around here primarily, AVR's and PIC's. There are more PIC users here (I use AVR's) but either one has good support. There are free basic compilers for both AVR and PIC lines and for someone new to micro controllers as long as you can get the software installed and read a few instructions you'll be blinking LED's in no time. You would have to make a transistor driver for the LED modules as well micro controller only put out a little bit of current, so you need to determine the current they draw when they're on.
For that particuar animation the scrolling string a micro controller would be the easiest sollution. You could have 1 LED on at a time scrolling left or right with simpler digital logic like a 555 and a shift register, but a micro controller and driving circuit give you more flexibility and an overall simpler setup.
Programmers for micro controllers are relativly cheap. Bellow is some starting reading, give it some thought.
Colin. I thought his post had been clear the animation made sense to me.
He wants to light up a string of LED's going from left to right until they're all lit. And then turn them off one at a time from left to right until they're all off. It will give the appearance of a moving line. All the ambulances around here have turn signals that do this. I'm going to guess that he of also wants to be able to go from right to left as either a turn signal or caution indicator. You'd have a hard time replicating that pattern using discrete logic. You could get something like it easily, but not that particular pattern.