Created on 18 June 1997.

# The Necker Cube

• Your browser does not appear to be capable of running Java applets.

## Introduction

In 1832, a Swiss crystallographer named Necker published pictures of an unusual cube that appeared to assume different orientations as one continued to look at it. This widely known illusion is reproduced here. The interactive demo applet will also animate the spinning of the cube, producing a similar but even stronger effect.

The effect works because the drawing of the cube (an orthographic projection) carefully eliminates all depth cues. In attempting to fit the expected model of a cube to the picture, our brain must resolve the ambiguity as to which corner of the cube is closer. Different people resolve this ambiguity in different ways, and individuals resolve it differently at different times.

## The interactive demonstration

In its default configuration the applet window shows what appears to be a tilted rectangle divided in the middle by two parallel lines. This is in fact a drawing of the Necker cube from a perspective that looks directly down on its top front edge. The fact that it appears initially to be a simple two dimensional drawing will be discussed further below.

The Angle slider controls the angle from which the cube is viewed. You should begin by rotating the cube using the Angle slider until it looks more cube-like, then practice for a few moments viewing it in each orientation. If you have trouble doing this, then direct your attention toward the two vertices closest to the center of the image. Pick one and try to picture a cube for which this is the closer of the two vertices. Once you have accomplished this, do the same for the other vertex. Practice switching back and forth a couple of times.

The Start motor button acts as a toggle for the automatic spinning of the cube. Once you engage it you should have the clear impression that the cube is spinning in one direction or the other about a vertical axis. Depending on which orientation you choose when you first glance at the cube, it will appear to spin either from left to right or from right to left. If you have trouble seeing both directions, try looking away for a second or two. You may have to repeat this several times before you will achieve an apparent reversal of direction.

The Angle slider controls the angle of rotation about the vertical axis. This is the value that is incremented automatically when the motor is turned on. The Tilt slider controls the angle by which the cube is rotated about the other two axes and it remains the same as the cube spins. It is set to an interesting default value, but you may want to investigate if and how your perception changes as you adjust it. In particular, when it is at either extreme you will see at most two faces at a time.

The two sets of radio buttons to the right of the motor button provide a number of ways of strengthening and weakening the illusion. The first set allows you to select either a side view of the cube, a top view, or both displayed side by side. You should observe that the ambiguity evident in the side view disappears when the cube is viewed from the top. When the two are displayed side by side, does the top view help you disambiguate the side view?

The cube can be rendered either as a wire frame or with flat-shaded faces (with back faces removed). Selecting the shaded mode removes the ambiguity from the side view by providing depth cues in the form of both shading and occlusion. What is somewhat more surprising is that when the shaded cube is overlaid by the wire frame (by selecing the Both option in the right-most set of radio buttons), much of the ambiguity returns in spite of the shading depth cues. Clearly the visual system is more strongly influenced by edges than by shading.

The only other control is the Speed slider which, predictably, controls the speed at which the cube rotates. It has only a minimal effect on the illusory nature of the image, but you may find that it strengthens or weakens it.

As for all demo applets, the Dismiss button at the bottom of the applet window will remove the window from the screen. Selecting the APPLET link at the top of this page will then return it to the screen just as you left it, with the exception that the "motor" will be turned off when the window is dismissed and not restored when it is returned.

## Discussion

This illusion is one of several in this collection in which there is an ambiguity to be resolved by the visual system. In this case, there are no depth cues on which to base a choice of orientation for the cube. Your visual system must at some level choose which of the two interior vertices appears closer.

It is interesting to consider that the image shown is not really three dimensional but is nevertheless interpreted as a two dimensional projection of a three dimensional object. This impression is extremely strong in spite of the distinct lack of evidence, such as occlusion or foreshortening, that would suggest a three dimensional scene as opposed to a structured two dimensional arrangement of lines. With a rotation angle of zero, it does in fact look like a two dimensional pattern, but with only a small increment of rotation it becomes quite difficult to ignore the three dimensional appearance.

Scott Flinn (flinn@cs.ubc.ca)