The Offset Checkerboard (“Café Wall”) Simulation

Introduction

We’ve all experienced visual illusions, in which a figure is drawn in such a way as to give us a perception that differs from objective reality. There are many of these, ranging from the very simple to the very complex. Classic simple illusions include the vertical-horizontal illusion:

in which you’re asked to judge the relative length of the vertical and horizontal line segments, and. the Tichener Circles illusion:

in which you’re supposed to decide which central circle has the largest diameter.

Another category of visual illusions involves the effects of diagonal lines on our perception of relatively simple figures. There are many variations on this theme but one of the simplest is the Müller-Lyer illusion:

in which you’re supposed to decide which horizontal line segment is longer. A slightly more complex illusion-inducing figure (termed the context by perceptual psychologists) is the basis for the Ponzo illusion. Three versions of many that induce this illusion are:

in which you’re supposed to decide which heavy line segment in each figure is longer. You might not be surprised to learn that horses and pigeons are also susceptible to this illusion, but I suspect you’ll find it surprising that most humans are far more susceptible than chimpanzees to the version of the Ponzo illusion depicted on the right, while rhesus monkeys apparently don’t perceive the illusion at all.

The Hering illusion is another example of an illusion that demonstrates the impact of diagonal lines on our perception. You’ve no doubt seen at least one example of the Hering illusion somewhere along the line. There are a number of variants of the Hering illusion, but in each you’re asked to judge whether two lines are straight and parallel, or whether they are curved and converge or diverge toward their free ends:

Which of the above renderings of the Hering illusion is most effective for you? Do you perceive any three-dimensional effect in any of them? If so, what about the figure produces the illusion of three-dimensionality? Are there any consistencies with respect to the arrangement of the diagonal lines and the appearance of the illusion?

Another commonly encountered illusion is the Poggendorff illusion, in which one or more diagonal lines are interrupted by an intervening gap. One example of the Poggendorff illusion is:

How many diagonal line segments are drawn in the figure? Three (two on the right, one on the left)? Or, just two? If only two diagonal lines, which of the two lines – the upper or the lower – on the right side of the obscuring rectangle is the extension of the one on the left? Once you’ve decided, click here to see the same figure with the obscuring rectangle made transparent. Were you surprised at the correct answer?

Did you notice any evidence of the Poggendorff illusion in the last two Hering illusion figures? If so, does the intensity of the illusion (i.e., the amount of offset in the line segments on opposite sides of the thick horizontal lines) varies with the angle of intersection between the diagonal and horizontal lines?

Implications Of Visual Illusions

Even though – or perhaps because -- all of these illusions are based on very simple figures, they provide windows into the functioning of visual system. Indeed, a number of them are still being employed as tools in research efforts designed to give us a better understanding of how the on-off response of rods and cones to photons is converted into perception of the external environment. (there have been at least 20 research articles employing the Müller-Lyer illusion published in just the past 5 years)

As you know, the phototransducer cells – the rods and cones -- in your retina are simply on/off transducers: light strikes a particular rod/cone, or it doesn’t, and the rod/cone either absorbs a photon and respond, or it doesn’t. A single rod or cone functioning in isolation cannot possibly encode any information about the dimensions or shape of an object, whether the object is moving or stationary, or any other information that is such an integral part of our visual perception of our environment. In other words, the rods and cones, by themselves, don’t provide us with images.

The images we perceive are provided by the way the rest of the visual ‘system’ (other cell layers in the retina, the lateral geniculate body, the visual cortex, etc.) is structured and deals with the data provided by the rods and cones. This illusion, and others in this series, are provided to let you investigate some of the interesting aspects of the visual system and how it functions.

Unfortunately, the explanation for the ability of simple illusions to fool our visual perception systems is not at all clear. In fact, there is a fair degree of contentiousness in the research literature with respect to just what these illusion tell us about the visual system, and with surprising frequency, different authors report contradictory findings. Nonetheless, there is little doubt that the illusions reflect the nature of the neural network involved in the processing of information supplied by the rods and cones.

What Does The Simulation Allow You To Do?

Deceptively simple, the offset checkerboard illusion is based on a simple grid of two sets of squares of alternating color in which adjacent rows (or columns) are separated by a line of contrasting color. The illusion is created by shifting the position of squares in adjacent rows relative to each other. In order to enhance your experience of working with this illusion, controls are provided that allow you to:

1. specify the size of the grid squares;

2. specify the amount by which squares in adjacent rows are offset relative to each other;

3. switch between horizontal and vertical orientation of the rows of squares, and the direction they're offset with respect to each other;

4. specify the colors of the two sets of squares independently from each other.

What Does The Simulation's Interface Look Like?

The default grid consists of black squares alternating with white, with the squares separated by gray lines. When you first activate the simulation, you will see a display that looks similar to this:

The controls are mostly self-explanatory, allowing you to change the color of one or both sets of grid squares, change the dimension (in pixels) of the squares, and change the amount (also in pixels) by which adjacent rows are shifted with respect to each other. The “Vertical Lines” checkbox causes the orientation of the parallel lines to be switched from horizontal (the default) to vertical on the display. Selecting this option also causes the Offset control to shift the squares in the vertical plane, rather than in the horizontal plane. The “Hide Squares?” option is there mostly so you can convince yourself that the lines are straight and parallel, should the need to do that arise.