How Hidden 3-D pictures work

by Kevin J. North

Here's how Hidden 3-D Pictures work. It relates to depth perception, part of the field of psychology.

There are many ways in which we perceive depth, but there are two at work here, binocular disparity and convergence. Binocular disparity is the result of the brain receiving two slightly different views of an object, because our eyes are separated by a short distance. Our brain combines these two views into one, and interprets depth. Convergence refers to the rotation of our eyes as we focus on a nearby object. The more our eyes are turned inward, the closer we interpret the object we are looking at to be.

Normally, when we look at a piece of paper, or a flat computer screen, our eyes receive basically the same image, therefore we interpret it as being flat. We can use convergence to determine how far away the paper/monitor is (or, you can look at objects in the vicinity and use those for other depth clues, but let's ignore that for now).

Let's take this row of circles below. Normally, our when our eyes combine the image, our brain will match the correct object from each eye's view to form what we see. Simply, it works like this:

```   left      1      2      3      4      5      6      7      8
PICTURE      o      o      o      o      o      o      o      o
right      1      2      3      4      5      6      7      8
```
The "left" and "right" stand for each eye, and the numbers refer to the object number that we are looking at. For example, for object 4, each eye has a view of object 4, which is put together to form what we see. This may seem extremely simple, and it is. Our brain would normally not want to combine object 2 of the left eye with object 6 of the right eye, for example.

Now for the trick. Unlike a sentence of words, which you are reading now, notice that the picture contains identical, evenly spaced circles. What if we forcibly diverged our eyes so that we interpreted two adjacent circles, as being the same object? In other words, what if we looked at the picture and saw it like this:

```   left      2      3      4      5      6      7      8      9
PICTURE      o      o      o      o      o      o      o      o
right      1      2      3      4      5      6      7      8
```
Take object 3, for example. The left and the right eye are NOT looking at the same object, but our brain is going to interpret them as such. What will be the result? Pretend we are staring directly at the object. If the left eye looks directly at what it thinks is object 3, and the right eye does the same, and they are interpeted as the same object, then the eyes are now diverged more than they normally would be if they were looking at what really was the same object. Therefore, by the convergence rule described earlier, it seems like this virtual object is farther away.

Note that each circle now becomes a view for two different objects. This is why there should be a long line of the same pattern. Note also that there are now 9 objects instead of 8, with two of the objects only having a view from one of the eyes.

Because the space between the objects causes our eyes to diverge, it's only natural that the greater the distance between objects, the farther away it seems like they are. By varying the spacing, we can create a 3-d image. For example, if you diverge your eyes when looking at the stars below, each row will look like it is a different distance away:

``` *       *       *       *       *       *       *       *       *       *
*      *      *      *      *      *      *      *      *      *      *
*     *     *     *     *     *     *     *     *     *     *     *     *
*      *      *      *      *      *      *      *      *      *      *
*       *       *       *       *       *       *       *       *       *
```
It's interesting that the stars appear lined up in some columns, but not in others. The only way a column could possibly be straight in one but bent in another and still be interpreted by our brain as being the same column is if the stars were of varying depth (because if an object is not flat, each eye will see a slightly different view). Therefore we see a 3-d starfield!

The "hidden" object idea is just a variation of everything described so far. We create a 3-d image using stars, characters, or whatever by varying the distance that we perceive them to be. To create a raised, flat box above another plane, we might use a uniformly-spaced starfield, except in the vicinity of where we want the box to be, at which place we will place the stars slightly closer together in order to make them appear closer. As our brain looks at the nearer stars, they will appear to be in a box-like area, and we will see a box. Example:

```*        *        *        *        *        *        *        *
*        *        *        *        *        *        *        *
*        *        *       *       *       *        *        *
*        *        *       *       *       *        *        *
*        *        *       *       *       *        *        *
*        *        *        *        *        *        *        *
*        *        *        *        *        *        *        *
```
In the hidden image above, I've deliberately placed the stars in columns so you can see where the stars get closer together. In a "real" hidden image, the stars will be staggered or a more complicated pattern will be used so that it is almost impossible to figure out what the hidden object is, like this:
```lKJCLO\$H#fdMlKJCLO\$H#fdMlKJCLO\$H#fdMlKJCLO\$H#fdMlKJCLO\$H#fdMlKJCLO\$H#fdMlKJ
dMgkDcGonh\@dMgkDcGo\@dMgkDcGo\@dMgkDcGo\@dMgkDcGo\@dMgkDcGDko\@dMgkDcGDko\
nh\@NmbX!/BFnh\@Nm!/BFnh\@Nm!/BFnh\@Nm!/BFnh\@Nm!/BFnh\@Nm!/B\hFnh\@Nm!/B\h
!/BFj:lKJCLO!/BFlKJCLO!/BFlKJCLO!/BFlKJCLO!/BFlKJCLO!/BFlKJCLO!!X/BFlKJCLO!
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DcGonh\@NmbXDonh\@NmbXDonh\NmbXDognh\NmbXDogh\NmbX!Dogh\NmbX!Dogh\f#NmbX!Do
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#fdMgkDcGonh#MgkDcGonh#MkDcGMonh#MkDcGMonh#MkDcGMon#MkDccGMon#MkDcCJcGMon#M
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\@NmbX!/BFj:\@NmbX!/BFj:\@NmbX!/BFj:\@NmbX!/BFj:\@NmbX!/BFj:\@NmbX!/BFj:\@N
```
Can you figure it out? Have fun!