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The Transparent Box Illusion: Construction of Three Dimensional Form I

Updated: Jun 10, 2020

This is the first of a series of posts looking at how the eye constructs three dimensional form. If you enjoy this post, please consider looking at the companion article The Hexagon: Construction of Three Dimensional Form II.

While looking at the following paper collage transparent box illusion:

I got an idea. What if I made small changes in the collage? What would happen to my perception of three dimensional form? I tested this by making a number of collages that were slightly different than the one above. Below are two collages that I found especially interesting. Try staring at each one for awhile. Take your time. These probably feel pretty 'wrong' to you! You might even find them hard to look at. Something is extremely dissonant in each collage.

We will circle back in a bit to look at what specifically is so very wrong about these images and why. What I will say at this point is that most of the elements of the collage were not changed- and yet the three dimensional transparent box illusion is rendered extremely unstable, if you can see it at all.

Let's look more closely at the transparent box illusion to make sure you and I are noticing the same things. Here's a different example:

There are really two illusions you can find. The first is a box:

Standard Illusion Box

And the second illusion looks like the snout of an animal pointing out of the page, up and over your right shoulder:

Standard Illusion Snout

Here they are together:

Box Standard Illusion Snout

With this in mind, let's go back to the original transparent box illusion. You can probably now flip back and forth between the box and the snout. You may find that you favor one over the other. Spend a moment doing this:

Why are there two solutions to this problem? What is the ambiguity?

It is the direction of the incoming light. The light is coming from above and to the left. But is the light coming from in front of the page or behind it?

You can't tell. That's the ambiguity.

Imagine the light is coming from in front of the page. When you do this you will see the box. Now, imagine the light is coming from behind the page. When you do this you will see the snout. Don't take my word for it. Take a moment to convince yourself of this.

There is not enough information in the collage to choose between these two directions of light. The eye struggles with this, and the mind comes to a conclusion. Then, the illusion pops into view according to the imagined direction of the source of the light. Practice flipping back and forth between the box and the snout and notice how the direction of the incident light changes from in front of the page to behind it.

It is apparent that identification of the direction of incident light in all three dimensions is crucial to development of the illusion of three dimensional form.

The essential role of the direction of incident light becomes more clear in the next several examples, when I change things around a little bit.

In the example below, I reversed the luminosity of two elements. This left five of the seven the same as before. Together these five (in gray below) tell a consistent story about the direction of incident light.

The unchanged elements are in gray; the inverted elements are in red.

This is what the illusion now looks like:

Notice how you can still find the box and snout. But notice also how unstable the illusion has become. Every time you see the box, something seems to cause you to bounce off of that illusion and see the snout. As soon as you see the snout, something causes you to bounce off of that and see the box.

The luminosity of five of the seven pieces of the collage are correctly ordered to create a powerful three dimensional illusion. But if we are to see the image as a solid three dimensional object, one portion- in isolation- must be illuminated from a completely different direction. That’s a real problem for the eye, because it never happens. The simple act of inverting one element of the transparent box illusion places light- the most fundamental truth that defines our visual world- in conflict with the existence of a solid object. The eye chooses to believe the light, and rejects the existence of a three dimensional object. Here is the key point: As a result of a focal inconsistency in the direction of incident light, the illusion of the third dimension of the entire object is lost.

This tells me that the illusion of the third dimension of an entire object can be broken apart by an inconsistent element hidden within only part of the object.

Next I took the idea a little further, by mixing up the luminosities of three of the seven pieces of the collage, leaving the other four correctly ordered. I called this a scramble.

First, luminosities of all components, both red and gray, are correctly ordered:

Now the three in red are scrambled. The other four pieces, in gray, remain correctly ordered:

Resulting in the collage below. Take your time with this image:

Why is the destruction of three dimensional form so profound in this case?

Again, it has to do with the direction of incident light. Examine the illusion above and try to assign a direction to the light. You will find that this is impossible. In spite of the fact that four elements of the collage are correctly ordered to create a three dimensional illusion, no third dimension can be perceived.

Below, the standard illusion, the inversion, and the scramble are shown:

Standard illusion



Note that only in the first example, the standard illusion, is the direction of the light identifiable. And only in the first example is the three dimensional form easy to see and relatively stable. Together, these examples demonstrate that identifying the direction of incoming light that is consistent throughout the object is crucial to the generation of three dimensional form. Three dimensional form of the entire object can be destroyed by inconsistency in only a portion of the object. The correct order of luminosities represents a key, a solution to a problem. When the key fits, three dimensional form is unlocked. Focal inconsistencies in the key will destabilize or destroy the whole form. This is true whether the object is opaque or semi transparent.

This takes me back to the challenge of creating three dimensional form when I draw the figure. The figure is just form upon form upon form. I successfully generate the third dimension when the luminosity of each point relates correctly to its neighbor, down to the level of detail achievable with the medium I am working in, and what my eye can perceive. As long has there are no inversions or scrambles, then the key is unlocked to three-dimensional form. The relative values do not need to be exactly perfect, but the order of luminosity must be. When this happens, the shoulder looks round, and the three dimensional contours of the hand or buttocks can be seen.

When luminosity relationships are correctly ordered, the illusion of third dimension is profound. When they are disrupted, the illusion of the third dimension is usually lost. However, other effects can be created. In the collage below, the direction of incident light is carefully disrupted to create perception of flickering transparencies. These are easiest to see if you back away from your computer and close one eye. The creation of these complex illusions is discussed in more detail in the companion post The Hexagon and the Construction of Three Dimensional Form.


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