Why this arrangement of thingys in this light-induced fusion reactor? Here is a photo from inside a light-induced fusion reactor at the National Ignition Facility, California.

 Image source: Wikipedia
I'm not sure what those thingys all around it are but I assume they emit light.
Why are they in this particular (non-regular) arrangement?
 A: The holes in the wall must be ports where laser beams enter the chamber. I can't give any details about this arrangement, but it is as symmetrical as possible. 
The fuel for this kind of reactor is a glass sphere filled with water. The water is made with heavy isotopes of H that fuse if compressed and heated to insane temperatures. This is done by hitting it from all sides with very powerful laser pulses. It takes very careful alignment and timing. 
The pulses vaporize the outer layer of glass. The vapor flies away at high speed. This is like a rocket, where gas leaving at high speed propels the rocket upward. But here, gas flies away from the entire surface. The surface is forced inward, crushing the sphere to high density. If the beams did not arrive all at the same time and from all directions, the sphere would just be kicked to the side. 
A: 
I'm not sure what those thingys all around it are but I assume they
  emit light.

Actually only a few of them do, near where the person is. The rest, most of the larger ones especially, are for diagnostic instruments. Lots of very expensive cameras basically. This device is purely experimental, so it has to be super-instrumented, and that's most of what you're looking at.
The reason for the actual laser ports being at the end is due to the way NIF works. It does not shine the laser on the fuel directly, instead, it aims the light onto the inner side of a metal cylinder. To get the light inside, it shines it through either end of the cylinder, which is why the only ports are at two "ends" of the device, at the top and bottom of the chamber. See the second image here. They cover about 35 degrees down from the top and bottom, look for the grey-blue bits at the end of the red beamlines in this image.
NIF was designed to allow the beams to be moved around, and some of the other holes are beam ports for this purpose, but during construction, they basically gave up on this and I'm not sure if the design as-built actually allows this.
