A straight line represents the shortest path between two points. However, context significantly influences our perception of a line. The Müller-Lyer illusion, discovered by German sociologist Franz Carl Müller-Lyer (1857-1916), demonstrates that a segment can appear longer or shorter depending on the direction of two end arrows—whether they point outward or inward, as illustrated in Fig. 1 below.

What happens when we add motion to the illusion? As shown in the animated GIF, the central red dot remains equidistant from the other two red dots, even though the ends of the line appear to alternately stretch and shrink like a rubber band!

You can create an entertaining flipbook by printing each of the 26 frames from the animated GIF on separate pages in the correct order. To use the flipbook, hold it in one hand and quickly flip through the pages with your thumb. This will animate the frames in sequence, bringing the illusion to life!

 

Below is a hypnotic radial pulsating variant. While the star appears to pulsate, the blue and black segments remain the same length throughout.

 

Many Interesting Variants

Oddly enough, the illusion still holds even though the two segments forming the line aren’t straight, as shown in the animation below.

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

Below is a smoother version featuring a higher frame rate, additional lines, and sharper angles. It also showcases a striking dynamic “neon color spreading” effect.

And here finally is a collection of all the possible variations that can be created with my dynamic Müller-Lyer illusion: in parallel, radial, circular arrangements, and various other structural configurations.

Many geometric illusions involve V-shaped lines. Similar effects can be seen in fabric patterns (Zöllner illusion), the moon illusion (where the moon appears larger on the horizon due to the Ponzo effect), and the distribution of a line in a closed space (Sander’s parallelogram). A similar illusory effect applies to time perception: time filled with activities (represented by a compacted line with arrowheads pointing outward) seems shorter than empty time, when we have nothing to do (illustrated by an unwrapped line with arrowheads pointing inward).

 

How did I discover this dynamic illusion?

Well, I conduct many optical illusion workshops across Europe. Years ago, I introduced the Müller-Lyer illusion illusion to children through a hands-on exhibit of my creation. The exhibit featured a simple metal board onto which was painted a line and three red dots: one in the middle and two at each end. Two pivoting hands forming arrows, like clock hands, could rotate at each dot, allowing them to empirically explore the illusion of the segments increasing or decreasing. To my great surprise, the children were mesmerized by the thin, revolving hands of the exhibit and played with them nonstop. This experience inspired me to create an animated version of the Müller-Lyer illusion.

 

My “Dynamic Müller-Lyer Illusion” won the third prize as best illusion of the year 2017. For those who may not be familiar, this annual competition—organized by the Neural Correlate Society and sponsored by Scientific American—celebrates the world’s most mind-bending visual tricks and perceptual puzzles. It's a gathering of top illusion creators worldwide, each bringing their best to make you question what you see.