Pyramid Illusion

from “Visual Phenomena & Optical Illusions”

What to observe

In brief:
When there are many squares, an oblique light cross, like a large ‘X’, appears. This cross does not really exist.

In more detail:
In the animated image there are a number of superimposed squares, which become lighter the smaller they are. When there are only a few (below ≈7), one can clearly see that the non-occluded area of each square has constant brightness throughout. When their number increases, there is a seeming lightening at the edges, forming the ‘X’.

What to do

Press the “7 parts” button. Do you see a hint of the cross? Try the ‘+’/‘–’ buttons to find out just when the cross appears. Change between star and square by pressing the lowest button. The square shows the effect of Vasarely’s “Arcturus II”.

When you have switched to the star figure, the light X will change to a large ‘+’ symbol. But at the indented edges of the star you can now see an ‘X’ with inverted polarity.

You can play with various colours and also invert the figure: the smaller elements now become darker, and consequently the illusory ‘X’ becomes dark.

Victor Vasarely, 1966
Arcturus II

Comment

The pyramid illusion (also called the Vasarely illusion) is a striking perceptual effect related to all phenomena involving lateral inhibition, e.g., the Mach Band or the Craik–O'Brien–Cornsweet illusion. It has been incorporated into many Op Art paintings such as Arcturus II by Victor Vasarely (on the right). The effect occurs when concentric squares (or other geometrical figures like the star) of decreasing size and luminance are stacked on top of another.

[I thought I had ‘invented’ the “star effect”, however: that was first demonstrated by Martinez-Conde & Macknik at the 2001 Soc Neurosci Meeting.]

The explanation seems initially rather obvious: Consider arrangements of antagonistic centre-surround ganglion cell receptive fields convolving the image (see the figure at the bottom of the Hermann Grid page). Imagine a cell at a corner with its centre in the lighter patch, it will be inhibited by 1/4 surround from lighter patches and by 3/4 from darker patches. Voilà, the ganglion cells at the edges signal more brightness. However: for perception the ganglion cell information is integrated and the heavy luminance distortion removed – at least for all normal images, for those not called optical illusions… What needs explanation here (and I don’t know it) is why the inverse transformation applied to correct the retinal convolution breaks down in the pyramid illusion.

Sources

Hurvich LM (1981) Color Vision. Sinauer Associates, Sunderland, Massachusetts

DOG Lateral Inhibition & Pyramid, Project LITE<http://lite.bu.edu/vision/applets/Lightness/Lightness/Lightness.html>

Mach, Ernst (1913) The Principles of Physical Optics, Dover Publications, New York, 1926

Mach E (1865) Bemerkungen über intermittirende Lichtreize. Archiv für Anatomie, Physiologie, und wissenschaftliche Medicin 629–635

Ninio J (2000) Flashing Lines. Perception 30:253–257

Ratliff F, Milkman N, Bennert N (1983) Attenuation of Mach bands by adjacent stimuli. Proc Natl Acad Sci USA 80:4554–4558

Troncoso XG, Macknik SL, Martinez-Conde S (2005) Novel visual illusions related to Vasarely's ‘nested squares’ show that corner salience varies with corner angle. Perception 34:409–420

New star demo on Susana Martinez-Conde’s site

Thanks to Jan Hendrik Wold, whose photographic demonstration in Trondheim set me onto this track.