Just another arc reactor prop, along with the dozens of others already made and showcased on this site.
This particular one stands out though, with it's central infinity mirror core.
This whole project cost me less than $5, but mostly because most of materials I used were scraps, some hard to come by.
I will included info on parts you can substitute for them.

Step 1: Parts

For this instructable, you'll need:

-Lights ; I pulled a several white LEDs (5mm) out of an 24-LED light that cost me $3 AUD.
I used a total of 16 LEDs.
I suppose small incandescent bulbs may be used, but these are less efficient, and usually give off a yellowish light (For a steampunk arc reactor, maybe?)

-Ring - I cut up a section of clear piping (origin unknown) and joined the ends with a hot glue gun.
Alternatives include: -Umbrella table ring (http://www.patiofurnituresupplies.com/table-umbrella-hole-ring-p-248.html? osCsid=9de221b0bfeda4be25cd9d5a2cfec222 )
   - Hot glue gun molded ring (https://www.instructables.com/id/Build-an-Arc-Reactor-with-Basic-Tools-and-Skills/ )
   - Acrylic cut into a ring shape (sanded and coloured in with high lighter to diffuse and colour light)

Coils - I found wire from an old toroid, found in a computer ATX supply. Not sure what guage, but it doesn't really matter.

Outer casing - I used steel from an old cookie tin. Soda cans are a bit soft for my liking, but still usable. Otherwise, any other reasonable thickness sheet metal should work.

Mirror - Find a reasonable sized mirror, I found a perfect circle mirror in this comb-mirror set. (My sister's). Actually, the size of the whole prop was based around the mirror. If you don't have a mirror, you could use the shiny side of aluminium (I'm Australian) foil to a decent-poor affect.

One way mirror/tinted glass - Sound hard to come by? I used the lens from these sunglasses. Not many other alternatives I can think of, other than proper tinted glass or the sticky film you can buy somewhere to tint glass...

Power - I used an old mobile phone battery (li ion) Light weight, small, pretty good capacity. You could use AAA batteries (3, or less with a joule thief) or any other smallish rechargeble battery.

Electronics - A switch, or just 2 pieces of wire you can twist together to turn the thing on.
   2 silicone diodes (standard ones, 1N4001, etc. Don't use signal diodes though; I'll explain why later.)

General - Solder, tape, glue, hook up wire, switch, common sense, etc.

Step 2: The Infinity Mirror

The number of LEDs used is not critical, I used 6.
Arrange them on a strip of cardboard, as long as your mirror's circumference.
Colour the cardboard now with black marker, paint, etc.
Join the ends up

Then, take your sunglass eyepiece, and place it on top of the cardboard ring.
Make sure the side that you would normally look into is away from the LEDs.

Finish off by gluing/taping the mirror on the back
(Reflective side to the LEDs)

Step 3: The Light Ring

Take your plastic tube, ring, or whatever, and divide it into how many sections you want. Put a small mark on each.
I chose 10, to make it *slightly* more movie accurate.
Connect the ends together (if you're using the plastic pipe)

Take your wire, and wrap an even length around each of the markings you made earlier.
Make sure each 'winding' is sufficiently spaced apart to allow light through.

Now, the LEDs:
Flip the ring over, and fix as many LEDs you want/can to each space in between the windings (one for each is fine).
Wire it all up (I'll assume you have basic knowledge of electronics; see the basic schematics)
The 2 diodes in series drop the voltage to around the forward voltage of the LEDs
I didn't really want to have to sit and wire a resistor to every single LED
That, and I don't have enough resistors....everything I make is out of scrap/spares, including this prop.
The only 2 electronic stores I know that are close by are Altronics and Jaycar, and I only got there if I need stuff like MOSFETs and higher quality parts.

Step 4: Metal Case

Take a strip of metal, plastic, even cardboard if you're kinda stuck, and wrap it around the ring.
Make sure it fits tightly, and glue it together.
If you're using metal, a blind rivet is used.

I used a 22.5cm x 3 cm strip of steel from a cookie tin, sanded down and sprayed with WD-40 to protect it from rust. Sorta.
Any ideas on how to make steel rustproof cheaply would be greatly appreciated.
I drilled a hole through the ends, and connected it together, making sure the light ring would fit inside tightly.

Step 5: Putting Everything Together

Wire everything up, along with the phone battery (See the basic schematics)
Include the switch and diodes in series with the phone battery as well.

Slide the infinity mirror into the case, making sure it is the right way up, and glue it in.
Same for the battery and switch
Hot glue works pretty good for holding the wires down once they're all soldered.
Or twisted and taped, like I used to do when I was 10 and didn't have a soldering iron.

Switch on, and admire your work.