These explorations were inspired by the paper Explaining the footsteps, belly dancer, Wenceslas, and kickback illusions by Howe et al.

They ascribe the footsteps illusion to ongoing competition between the background, leading/trailing and lateral edges of the moving rectangle. When the leading and trailing edges of the rectangle are over a low-contrast background region, the static lateral and background edges cause the entire rectangle to appear to stop moving. This is visible when the rectangle moves over the left half of the background in the demo below (fixate on the stationary target at the top).

The kickback illusion is a related phenomenon they discovered where the rectangle appears to jump backwards strongly upon encountering thin lines of opposite contrast. They believe that this is due to reverse-phi motion as the contrast polarities of the leading and trailing edges reverse twice rapidly.

The demo below can be used to explore these illusions:
Mouse Y: height of moving target for smooth pursuit fixation
Mouse X: speed of translation
UP/DOWN: height of rectangle
RIGHT/LEFT: width of rectangle (changes by one half of column widths on left half of screen each time)
ENTER: toggle yellow vs blue rectangle

Another demo was constructed to explore the reverse-phi explanation of the kickback illusion suggested by Howe et al. To test their competition-based explanation of the footsteps illusion, they showed observers a rectangle translating across a blank screen which flickered from white to black at the same frequency as its leading and trailing edges would normally pass over bars in the original illusion. This setup did not produce a footsteps illusion, since there were no static edges to ‘win out’ over the moving edges during their low-contrast periods. However, their explanation of the kickback illusion is not dependent on this kind of competition and so should be reproducible with a simple flashing screen. We have attempted to provide such a stimulus below, where the bottom half of the screen flickers at the same rate as the rectangle on the top half passes over the black lines. If the reverse-phi theory is correct, both rectangles should exhibit a kickback illusion upon central fixation. Introspectively, this seems to be the case – the rectangles can even start to appear somehow connected.

Mouse Y: height of moving target for smooth pursuit fixation