When I first saw the nanoleaf light panels, I instantly knew that I need to have them on my wall. But after I checked their price, I thought that it would be neat to try make something similar myself. Using arduino nano and a bunch of WS2812 led strips I was able to make a light panel that looks pretty much the same as the commercial nanoleaf. I made my panels a bit smaller than original, but scaling them up shouldn't be a problem. Original plan was to have interlocking connectors on each panel, but bolting the panels together with M4 bolts proved to be way simpler approach. It's difficult to take good pictures of the lights, as the camera makes the colors look less uniform as it is in reality.
The diffuser sheet can be made from ordinary white paper, I made mine from slightly better quality textured "cloudpaper" which gives a slightly better look. The paper is kept in place with a snap-fit cover. Each panel has 6 leds, two in each corner. Leds are powered directly from the nano which is powered from usb, the current draw is surprisingly low and connecting 10 or more panels in series is not a problem as long as no white light is displayed at full brightness. I was planning to add a bluetooth module to control the lights, but decided to leave it as it is, because I would still mostly display "slowly changing rainbow" effect on the panels. I powered the panels directly from the usb port of my laptop, so the panels are only on when the computer is. Mounting the panels to the wall is as simple as drilling holes through the back of the panels and driving nails through them.
I included two example codes which work with Adafruit_NeoPixel and FastLED libraries to get you started. The leds are cut from a led strip which has 60leds/m. I used WS2812 leds, but other kinds of leds could be used. The wiring is done so that the leds are in series just like they were on the original strip, and the whole panel can be controlled like it would be one strip of leds. Only three connections are needed for the arduino: data wire to pin 6, and power leads to +5v and GND. I also desoldered the red power indicator led so it wouldn't interfere the colors.
Protip: White nail polish works well on hiding all the black wires + arduino board.
All honor to the original nanoleaf product, you should really go check their lights out as they are awesome.