Here's a little item you can make that will blow the minds of your friends in several ways:
First, it's a Rubik's Cube that appears to be floating in space. Next, as you move around it, the Rubik's Cube rotates in mid air, always following you - left, right, up, down - no matter which direction you move, the cube moves with you - watch the video to see what I mean. Finally, when your friends manage to discover how your possessed Rubik's Cube works, it will really blow their minds! The video at the end of this Instructable exposes how the illusion works.
I got the idea for this piece of visual deception from various items I've been familiar with for quite a while. If you do a search on "Hollow Face Illusion", "Hollow Mask Illusion" or "Gathering for Gardner Dragon" you'll see some of the inspirations for my Rubik's Cube. The success of these illusions is dependent on how our brains process the information sent by our eyes - the brain relies on familiar references to tell us what we're seeing, so we can be deceived when something looks like a familiar object but actually isn't. It occurred to me that a Rubik's Cube is a very familiar object that ought to be able to trigger the same response, so I tried constructing a Rubik's Cube version of the illusion and discovered that it works beautifully. I did a pretty thorough search and - to my knowledge - this is a first; I've not encountered anyone else who has applied this illusion to a Rubik's Cube. It's hard for me to believe that someone else hasn't already done this, but if they have I was not able to find any reference to it. If someone else out there has, please accept my apologies, but I believe as I write this that it's a brand new application of the Hollow Mask Illusion.
First, I'd like to offer a little explanation of the Hollow Mask Illusion and how it applies to my Rubik's Cube Illusion. The Hollow Mask Illusion works because we are familiar with what a human face should look like. When we encounter the inside of a mask of the human face - if certain visual cues and lighting are right - our brains tend to interpret what we're seeing as the outside of the mask rather than the inside, as we are not accustomed to seeing a face as if we were looking at it from the inside. Then, when we move - or the mask moves - so that our perspective changes, the face appears to be following us. As long as our (or the mask's) range of motion is constrained to an area where no edge line of the mask interferes with the illusion it will persist - and can be quite unnerving! The moment we move outside these constraints the illusion breaks down, our brains get busy recalibrating the information we're receiving and we experience a flash of confusion until our brains can figure it all out.
The same applies to my Rubik's Cube. An observer will believe they are looking at three of the outer faces of a normal Rubik's Cube because that's what they are familiar with seeing. What they are actually looking at, however, is three faces of a Rubik's Cube as if they were inside the cube looking out - instead of the point where the three faces meet being nearest them, it is the point farthest from them. Then, when they move to the left, for instance, the brain expects the point where the faces join to move to the right, because that's normally what happens. However, since the entire object is inverted, the point where the faces join appears to move to the left - the same direction the viewer is moving - creating the illusion that the cube is rotating in mid air to follow the viewer's movement.
Two factors can either enhance or detract from the illusion - lighting and perspective. Since the object is actually inverted, normal lighting can cast shadows that will throw dissonance into the illusion. For that reason it is best to either have lighting coming from a bit below the object (because it normally comes from above) or strong enough to wash out most shadowing. This is not a big problem in the Rubik's Cube version as there are only three flat faces so there is little in the way of shadow. Soft light shining directly into the cube without casting too dark of a shadow behind it will work best.
The second factor is perspective, and this turned out to be the tough nut to crack. Perspective is how our brain perceives distances. It knows that the farther away from us a regularly shaped object is, the smaller it will appear to be. And since a Rubik's Cube is very regular in shape, there should be a strong sense that the outer edges of the Rubik's Cube get smaller as they recede from us. But if you were to make this cube of three square faces you'd discover that because the edges are inverted, the ones that should be appearing to get smaller because they are farther away actually are getting larger because they are actually closer. This can really mess with our brains - as well as the illusion.
I lost count of how many iterations I went through trying to solve the perspective problem. I suppose if I owned some decent CAD software it might have made it much easier...but I don't. Calculations I thought would work didn't and it all wound up boiling down to trial and error. The pictures I've provided are the end result of way too many long nights creating prototypes, discovering that they didn't satisfactorily solve the perspective problem, tossing them out and starting all over from scratch. But the good news is that the final result works quite well...and I'll never have to go through that exercise in frustration again!
I'm going to describe three methods of making your own cube - the Quick and Dirty Version, the Lucky Scavenger Version, and the From Scratch Version. Each will be pretty much it's own process, so each "step" of my Instructable is actually one of the three versions of my possessed cube. The actual construction steps are broken down within each version.
Step 1: The Quick and Dirty Version
You can make this version in only a few minutes just to see the effect and decide if you want to make a more substantial version, This cube will not hold up for very long, as even a thicker paper will begin to curl after a short while and that will mess up the illusion.
To make this version, simply:
A. Print out the Rubik's Cube faces in Figure 1. Size the image so that the edges that join at 90 degrees are about three inches long. If you have thicker paper and your printer will accept it, use that. You'll notice that I used yellow paper - that's because I didn't have any white card stock laying around, but I did have yellow.
B. Cut carefully along the outer edges of the faces and the tab. Make a clean, sharp fold (a ruler held firmly down along the fold line will help) down the center of the black areas between each face so that you are folding the colored faces toward each other as in Figure 2. Fold the tab along the third face in the same fashion.
C. Fold the red and yellow sides up so they are at 90 degrees to the blue face. Fold the tab behind the yellow face and tape or glue it in place (Figure 3).
D. Print out the image for the cube arm (Figure 4) and cut it out and fold it along each line as in Figure 5. Now fold it together to make a triangular tube. The fourth section is used as a tab which should overlap and be glued or taped to the first section. Slit each of the three edges down to the mark and fold the three resulting tabs away from the tube. Attach the tabs on one end to the center back of the cube (Figure 6). The tabs on the other end can be spread out and taped or glued to the surface on which you want to mount your cube. That's it!
NOTE: The arm can be made as short or as long as you like depending on where and how you want to display your cube. The longer the arm, the more the cube will appear to be floating in mid air. But a longer arm reduces the range of motion the viewer has before revealing the presence of the arm. The shorter the arm, the greater the viewer's range of motion - but the weaker the mid air illusion will be.
Step 2: The Lucky Scavenger Version
IF you are lucky enough to happen upon a plastic container of some sort with a roughly 3" square base you can save yourself a lot of detail work. I was hoping to make mine this way, but after tearing the house apart and rummaging through several dollar stores I was unable to find an appropriate container. I didn't think it would be difficult, but it was.
If you do happen to be lucky enough, here's how to proceed:
A. Cut the height of the container down to the same size as the base (Figure 7). Then cut two adjacent sides off the resulting piece and you have your basic semi-cube form for the illusion (Figure 8).
B. Size and print Figure 9 so that the faces (including the black edges) are a bit smaller than the inner faces of your cube base.
C. Cut out each face, spray the backs with adhesive (Figure 10) and carefully apply the faces to the inside faces of the semi-cube.
D. Once the faces have been applied it will become apparent that the outer edges are not 90 degrees and you'll have to cut or sand the edges of your semi-cube down so that they'll be flush with the images you glued to them. Use whatever method you used to cut the container to make the cuts. I have a mini table saw I used (lower the blade height to just high enough to cut the plastic - this will keep the plastic from cracking as you cut), but there are a variety of ways to cut plastic - the important part is that you want the edges to be straight and clean.
E. Use a black Sharpie or a small paintbrush and flat black paint to run along the outer edges of each face to cover the thickness of the paper and the underlying plastic. You can also run the Sharpie or brush along the inner angles to help them disappear (Figure 11).
F. Use leftovers from the original container or some other available strips of rigid plastic to make the arm for the back of the piece. I used epoxy to glue three pieces together for the arm as in Figure 12. Glue the arm to the back of the semi-cube as in Figure 13 and you're done.
NOTES: A black or transparent container will work best. If you want a really convincing product, don't settle for "good enough" - the surfaces must be truly flat and the inside corners must be truly square for the illusion to work well - rounded inner corners just will not do. The outer edges must blend into the black of the faces, so if your piece is transparent, you really need to paint the edges flat black (best choice) or go over them with a black Sharpie so they will not be noticeable.
Step 3: The From Scratch Version
I couldn't find an appropriate container so I had to go this route. Fortunately, I had a whole pile of extra plastic CD cases made of very thin and rigid transparent plastic (Figure 14).
A. I cut three 3 1/2" squares out of the CD cases. Using the table of my miter saw for a precise 90 degrees, I used epoxy glue to glue two of the squares together at 90 degrees. - I put a layer of wax paper between the squares and the table so I wouldn't glue the squares to my miter table. Once that joint was dry, I epoxied the third square to the first two in the same fashion (Figure 15). I made my semi-cube 3 1/2 inches, planning to cut it down to the exact size once I had applied the Rubik's Cube faces.
B. Return to part B in the Lucky Scavenger Version (Step 2) and proceed from there.
Thoughts on displaying your Possessed Cube: The paper cube is easy - fold the tabs on the far end of the arm outward and tape them to whatever surface you want. Use your imagination for the plastic version. If I had made the arm for my cube in the video just a tiny bit wider it would have slipped right over the on/off knob on my pole lamp. But I had to find a short cylinder that would fit inside the arm and use a rubber band to attach the cylinder to the knob. A peg that fits inside the arm works fine - that's what I used for the cube in the picture frame - just painted a piece of plywood, drilled a hole in the center to hold the peg and mounted the plywood inside the frame. Then I just slipped the arm over the peg. You could also drill a small hole in one face of the arm near the end and hang it on a wall with a hook or angled nail. Like I said, use your imagination!
For maximum effect, the cube should be placed somewhere that will limit the viewer's ability to move around it and discover how it's done. An excellent place would be to hang the cube on a wall at the end of a narrow hallway. You could put a frame around it as I did for one picture and the cube will float out of the frame. Or you could hang it inside an empty cabinet so that when someone opens the cabinet door, there the cube is, floating in front of them and moving wherever they move - freaky! Another idea would be to make a miniature version of the cube - say, about 1 inch on each face. Use a thin stick for the arm, hold the stick between the middle two fingers of your hand, and show it to the viewer, palm held flat and fingers together. As you move the palm of your hand around a bit, it will make the cube appear to dance in mid air over the palm of your hand. The video in this step shows how the illusion suddenly collapses when the viewing position goes beyond having all three faces in view.
And finally, if you want to really pop the effect once you've made your own Possessed Rubik's Cube, close one eye and move around it - you'll find it nearly impossible to shake the illusion! This is because it is our binocular vision that allows our brain to see perspective and judge distance. Since perspective is the biggest hurdle to overcome in this illusion, depriving our brain of the ability to establish perspective by closing one eye makes it that much easier to deceive our senses.
Thanks for taking the time to view my Instructable. I hope you're able to blow the minds of a few friends with your own version, and...
Runner Up in the