The design went through many stages. First and foremost I knew I could use a 555 timer to create a basic clock signal that could turn the light on and off. By manipulating these signals, inverting them, and counting them, I found a way that I could create 4 different clock signals that would create a nice looking flash pattern. The patter would look as follows:

[ 1 2 ] [ 4 3 ]

These are the arrangements of the 4 segments of LEDs I would create. They would then flash in the following pattern (* is on, and _ is off), each group represents how the bar would look at a frozen point in successive time:

Time 1 Time 2 Time 3 Time 4 Time 5 Time 6 etc etc. [ * _ ] [ * * ] [ _ * ] [ _ _ ] [ * _ ] [ * * ] [ * _ ] [ _ _ ] [ _ * ] [ * * ] [ * _ ] [ _ _ ]

This pattern would give a circular flash look to the LEDs

This idea was amazing in theory. Unfortunately, and after spending a good amount of money on parts from Digi-Key I found that there were some significant problems with this design.