Pyramid Illusion
from Michael’s Visual Phenomena & Optical Illusions
When there are many squares, an oblique light cross, like a large ‘X’, appears. This cross does not really exist.
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’.
Press the “7 parts” button. Do you see a hint of the cross? Try the stepper buttons above 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 seeming light X will change to an eually illusuory 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 all color values: the smaller elements now become darker, and consequently the illusory ‘X’ becomes dark.
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.
Adelson EH (2000) Lightness Perception and Lightness Illusions. In The New Cognitive Neurosciences, 2nd ed., Gazzaniga M, ed. Cambridge, MA: MIT Press, 339–351, [PDF], see Fig. 24.5 2/3
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
Troncoso XG, Macknik SL, Martinez-Conde S (2009) Corner salience varies linearly with corner angle during flicker-augmented contrast: a general principle of corner perception based on Vasarely’s artworks. Spatial Vision 22:211–224
Thanks to Jan Hendrik Wold, whose photographic demonstration in Trondheim set me onto this track.