Dynamic Müller-Lyer Illusion

A straight line is the shortest path between two virtual points. Context can play a key role in interpreting a line. Müller-Lyer's illusion, due to German sociologist Franz Carl Müller-Lyer (1857-1916), proves that a segment can visually appear longer or shorter if it is framed between two angle brackets the points of which are directed either outwardly or inwardly, as illustrated in fig. 1 below.

What happens if we do add motion to the illusion? As shown on the animated gif, the central red dot is equidistant from the other two red dots, although the ends of the line visually appear to alternately stretch and shrink like a rubber band!

Using the sequence of the 26 basic frames of the animated gif, it would also be possible to create an amusing flipbook!
Below an hypnotic radial pulsating variant. Though the star seems to pulsate the blue and black segments are always the same length.

Many interesting variants

Oddly enough, the illusion seems to work even though the two segments that form the line aren’t straight, as shown in the animation below.

A lot of compelling and artistic variants can be created with my dynamic concept! The vertical color segments of the pattern below are always the same length. In these versions, comes into play the "neon color spreading" effect...

Below is a smoother version with higher frame rate, some more lines, and more acute angles;
it also involves a striking dynamic “neon color spreading” effect.

Many geometric illusions involve V-shaped lines… You can see similar effects in fabric patterns (Zöllner illusion), in the moon illusion (the moon appears larger in the horizon due to Ponzo illusion effect), in the distribution of a line in a closed space (Sander’s parallelogram), etc. A similar illusory effect applies also to time perception: time that is filled with activities (compacted line with arrow heads pointing outside) seems shorter than empty time, when we have nothing to do (unwrapped line with arrow heads pointing inside).

How did I discover this dynamic illusion?

Well, I hold many optical illusion workshops around Europe. About two years ago, I presented the Müller-Lyer illusion to children, using a hands-on exhibit of my creation. The exhibit consisted of a simple metal board onto which was painted a line with three red dots: one dot in the middle of the line, and the two other dots at its ends. A sort of clock hand could be pivoted at each dot, to empirically experiment the illusory increasing or decreasing of the segments. To my great surprise, some children played nonstop with the thin revolving hands of the exhibit, mesmerized by the illusory effect. That experience prompted me to create an animated version of the Müller-Lyer illusion.

SEE ALSO:
Autokinetic Illusions, Kinegrams, Scintillating Starburst Illusion, Master of Numbers

BLOGS:
https://www.giannisarcone.com/wp/blog/2017/10/04/dynamic-muller-lyer-illusion/
https://www.giannisarcone.com/wp/blog/2017/12/19/bidimensional-muller-lyer-illusion/

REFERENCES:
Vicario, Giovanni B. Illusioni Ottiche Geometriche, Istituto Veneto di Scienze, Lettere e Arti, p. 25, 2009.

Müller Illusion, Mathworld
http://mathworld.wolfram.com/Mueller-LyerIllusion.html

CITE THIS AS:
Sarcone, Gianni A. "Dynamic Müller-Lyer Illusion." From Sarcone’s Studio -- A Sarcone & Waeber Web Resource. http://giannisarcone.com/Muller_lyer_illusion.html