Hello Scott, welcome to the club!
The "Angles Mirror" looks the least complicated, at least technically. The nearly 500 servos will still run about $1000, plus the supporting processors and programming effort.
The full size mirror has 30 servos across at the base, by my count. A more modest project having a base of 10 servos would run about $100 for the motors, more suited to a first effort IMHO. A 15 servos base, half the width of the original, would contain 120 motors at a cost of around $240, perhaps a good balance of cost and visual impact.
Probably several Arduino Mega clones would be needed to provide all the IO pins required. A Raspberry Pi with a video camera and running OpenCV software could provide the real time pixelated image needed to set the servo patterns.
I'll need to research this some more but it definitely seems doable - and possibly more satisfying than the LED cubes that I've been seeing on eBay lately...
"Twisted Strips" is also pretty cool, and even simpler to implement with about 40 servos:http://www.bitforms.com/rozin/twisted-strips