The scintillating grid (Schrauf et al., 1997) and the Hermann grid (Spillmann 1994) are two prominent examples of illusory percepts induced by vertical and horizontal grid bars, believed to result from a simultaneous lightness contrast illusion occurring in the periphery of the visual field. In the Hermann grid illusion, illusory black spots are perceived on white patches located at the intersections of the grid bars. One important difference is that the scintillating grid figure comprises physical white dots at the intersection of grey gridlines on a black ground, but they are sometimes experienced as being black when they are in fact white. With the Hermann grid, all perceived blurred dots at the intersections are actually illusory and are thought to origin from lateral inhibition within single retinal receptive fields (Baumgartner 1960).

Whether the scintillation effect and the Hermann grid illusion share the same mechanisms has been controversial. While the stimulus conditions resulting in the Hermann grid illusion are necessary, they are not not sufficient for producing the scintillation effect implying that its neurophysiological account must go beyond a simple lateral inhibition (Schrauf et al. 1997). However the lateral inhibition account for the Hermann grid illusion has been itself challenged (Schiller & Carvey 2005) as even a simple curvature distortion to the grid lines make the illusion disappear totally, while all preconditions of Baumgartner's hypothesis remain unchanged (Geier et al. 2008). Adding a stopping grid can also reduce or even totally eliminate the illusion in both types of grid, which suggests that the length of the grid bars is an important aspect to induce both illusions. The latest theories claim that a model based on cortical mechanisms is necessary, relying for example on simple-cell receptive fields found in visual area V1. It has been also suggested that the dynamics of this illusion might reflect the distribution of attention in space and time (VanRullen & Dong 2003).

Finally a very recent study (Matsuno 2020) showed that the scintillation effect can actually occur without the presence of bars, undermining the previous theories on the mechanism of the scintillating grid illusion. It instead claims that the grid bars are not actually the essential component to induce the illusion, but that the illusory spots of the scintillating grid illusion could be induced by the limited processing of the patch stimuli in the peripheral vision, and that the presence of bars may simply play a supplementary role by enhancing this effect.

With this interactive widget, you can explore the effect of several parameters on this illusion. For example, you can:

• switch between the scintillating grid and Hermann grid,
• modify the scale of the grid by changing the lines separation,
• change the polarity of the grid,
• add a stopper grid of varying thickness,
• or apply a curvature distortion of varying amplitude.

References:

  Hermann (1870) Eine Erscheinung simultanen Contrastes. Pflügers Archiv für die gesamte Physiologie 3:13–15

  Baumgartner (1960) Indirekte Größenbestimmung der rezeptiven Felder der Retina beim Menschen mittels der Hermannschen Gittertäuschung . Pflüger's Archiv für die gesamte Physiologie des Menschen und der Tiere 272:21–22

  Spillmann (1994) The Hermann Grid Illusion: a Tool for Studying Human Perceptive Field Organization. Perception 23:691–708

  Schrauf et al. (1997) The Scintillating Grid Illusion. Vision Research 37(8):1033–1038

  VanRullen & Dong (2003) Attention and scintillation. Vision Research 43(21):2191–2196

  Schiller & Carvey (2005) The Hermann Grid Illusion Revisited. Perception 34(11):1375–1397

  Geier et al. (2008) Straightness as the Main Factor of the Hermann Grid Illusion. Perception 37(5):651–665

  Qian et al. (2009) The Scintillating Grid Illusion: Influence of Size, Shape, and Orientation of the Luminance Patches. Perception 38(8):1172–1182

  Qian et al. (2012) The role of orientation processing in the scintillating grid illusion. Attention, Perception, & Psychophysics 74:1020–1032

  Bakshi & Ghosh (2020) Tiny Squares at the Hermann Grid Corners Can Completely Remove the Illusion . Perception 49(2):232–239

  Matsuno (2020) Scintillating Grid Illusion Without the Grid. i-Perception 11(4):1–11

Here is the math behind this stimulus:

  xcurve = x-sin(2*pi*y/w+pi)*(distamp*w/100)
  ycurve = y+sin(2*pi*x/w+pi)*(distamp*w/100)
  linethickness = lineth/100
  hherman = rectanglewave(xcurve,w,1-linethickness/2,linethickness)>0.5
  vherman = rectanglewave(ycurve,w,1-linethickness/2,linethickness)>0.5
  hermangrid = bool(hherman) | bool(vherman)
  vscint = pow(abs(cos(2*pi*xcurve*0.5/w)),round(1/linethickness))
  hscint = pow(abs(cos(2*pi*ycurve*0.5/w)),round(1/linethickness))
  scintgrid = (vscint+hscint)/2
  stopthickness = stopth/100
  vstop = rectanglewave(x,w,0.5-stopthickness/2,stopthickness)
  hstop = rectanglewave(y,w,0.5-stopthickness/2,stopthickness)
  stopgrid = (1-float(stopth>0)*vstop)*(1-float(stopth>0)*hstop)
  selectgrid = (1-type)*hermangrid + type*scintgrid
  polaritygrid = (1-2*inv)*(selectgrid)+inv
  z = stopgrid*polaritygrid + (1-stopgrid)*inv

Where:

  'w' is the lines separation (in deg)
  'lineth' is the lines thickness (in % of separation)
  'distamp' is the curvature distortion (in % of separation)
  'stopth' is the stopper thickness (in % of separation)
  'type' is the grid type (0: Hermann, 1: scintillating grid)
  'inv' is the polarity (0: black, 1: white background)

The whole stimulus is generated in real-time using a GLSL shader that runs right inside your WebGL-compatible browser. The plain Math behind the stimulus was converted to this optimized GLSL shader using the new Psykinematix Pro Edition. Translation to Matlab and Python code is also possible !

This whole widget was also fully generated using Psykinematix Pro Edition. The parameters that control the stimulus properties through the sliders are the same as the ones you would define as dependent or independent variables when using the stimulus in an actual psychophysical experiment run in Psykinematix. The widget creation is otherwise fully customizable with your own logo, copyright, links, etc.

To learn more about the widget creation, click on the above "Made With" button !