LEDs come with different beam angles. That is how much the light spreads out as it leaves the chips. If they have a diffusion lens that also makes a difference.
I have seen LEDs so small that they were not much larger then a grain of sand. Do not know where to source them. Check places like digikey mouser and newark to see what is out there. Maybe order a few different types to see which you want to use.
There have been several threads about powering LEDs over the last year. Maybe search for and read a few of them.
That still leaves you the logic to control the LEDs. You could go with logic chips but in the end it will be easier to program a micro controller to sequence the display. With the microcontroller you could have the pendulum move slower at the ends of its swing. You could also fade one position out while fading the next in.