In this illusion named “Dialogue du vent et de la mer” by Prof. Akiyoshi Kitaoka, the image appears to wave while there is actually no moving component. The illusion is due to eye-movements and the local spatial contrast present in each element: the asymmetrical placement of the dark and bright edges around each blue element creates a local spatial luminance gradient that is replicated over space. With small eye-movements, this local spatial gradient is perceived as a local motion that spreads over space according to the distribution of the spatial gradient direction, hence the wavy nature of the perceived motion flow.

How do the properties of the local element affect the perception of this illusion? This widget allows you to play with some important parameters that directly affect the appearance of this illusion, for example:

1. Contrast: the strength of the effect is directly correlated with the contrast between the dark and bright edges around the blue element;
   
   
2. Gradient distribution: a smooth distribution enhances the illusion through spatial propagation while a local opponent distribution breaks it;
   
   
3. Color: some color combinations provide a stronger sense of motion.

Note that if you stare carefully at the image without making any eye-movement, the motion illusion may disappear ! Let your eyes wander and the illusion comes back ! Be careful, this illusion may induce nausea or some visual discomfort...

This illusion was originally created by Prof. Akiyoshi Kitaoka from Ritsumeikan University (Kyoto, Japan). Several other variations as well as some additional explanation can be found on his website:

http://www.psy.ritsumei.ac.jp/~akitaoka/wave-expe.html
Prof. Kitaoka specialized in visual perception and visual illusions of geometrical shape, brightness, color, in motion illusions and other visual phenomena like Gestalt completion and perceptual transparency, based on a modern conception of Gestalt Psychology. He became renowned through his Rotating snakes illusion. To learn more about all the illusions he created over the years, check out his website:

http://www.ritsumei.ac.jp/~akitaoka/index-e.html

Here is the math behind the basic element of the stimulus:
  
  border = r<radius & r>radius*0.8
  bordermod = cos(theta*polarbreak+angle)>0
  cntborder = 0.5+(bordermod-0.5)*cnt/100
  center = r<radius*0.8
  outside = r>radius
  zr = (1-border)*(r1*outside+r2*center)+border*cntborder
  zg = (1-border)*(g1*outside+g2*center)+border*cntborder
  zb = (1-border)*(b1*outside+b2*center)+border*cntborder
  

This element is then replicated at different positions (x_i, y_i) and modified according to:

  nbrc = 10; shift = (nbrc-1)/2; sep = radius*2.5
  for i = 0 : 99
    x_i = (floor(i/nbrc)-shift)*sep
    y_i = (mod(i,nbrc)-shift)*sep
    angle = 2*flow*atan2(y_i ,x_i )/100
    

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 !