Paradoxical Elastic Squares

A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?

This puzzle is available as greeting cards from my online store.

Ghost Colors

This is one of my earliest color optical illusions. There is no yellow or green in the diamond shapes, just vertical black lines! (If you don’t believe it, use a eyedropper tool to check it.) This intriguing visual effect is mainly due to “color contrast induction“.

Illusive colors
Ghost Squares / Black Diamonds (2002 – 2007)
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Scintillating Starburst: Seeing rays that aren’t there…

This is one of my oldest illusions I created in the 90s. In the picture you may see ghostlike dark radial beams. This illusion is a variant of the Herman’s scintillating grid illusion. I designed this illusion just by turning 45 degrees the Herman grid and then by applying a polar transformation.

From my book “Eye Tricks“, 2001-2007.
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Mondrian Meets… (My Tribute To Mondrian)

Here are two projects involving the geometrical-constructive art of Piet Mondrian, one of my preferred artists, the golden ratio and ϕ. For this purpose, I used the same color palette favored by Mondrian: yellow, red, blue, black and gray.

Mondrian meets Pythagoras and Fibonacci

In the first project, I used squares, that are proportional to each other by the golden ratio or ϕ, to prove the Pythagorean theorem as shown in the Zhoubi Suanjing (or Chou Pei Suan Ching – 周髀算經), one of the oldest Chinese mathematical texts (circa b.c. 200).

Zhoubi Suanking theorem Continue Reading


An op art sculpture and/or a fidget puzzle to play with over and over!

Dynacube” is a new line of 3D puzzles featuring my optical art. It isn’t just a puzzle but also a living piece of art. This 3D game is available in 4 distinct styles from Recent Toys:
Dynacube is a fun game for kids and adults alike to practice their logical thinking and motor skills.


Display with 4 distinct styles of Dynacubes

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Dynamic Müller-Lyer Illusion

Prize illusion sarcone

I am very proud that my “Dynamic Müller-Lyer Illusion” won the third prize as best illusion of the year 2017!

As you surely know, the “BEST ILLUSION OF THE YEAR CONTEST” is a yearly competition under the patronage of Scientific American, organized by the Neural Correlate Company (New York, USA).

Müller-Lyer’s illusion proves that a segment can visually appear longer or shorter depending on the sense of the arrow heads at its ends. In what consists my variant? As shown in the animation, the red dot in the middle of the line 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!

The radial version of the illusion is even more impressive:

The perceptual increasing and decreasing of the segments occurs in a very short time. Thus, I suppose it is more a physiological phenomenon, rather than a psychological bias. Our attention seems to be attracted by the receptive field WITHIN the V-shaped arrow heads, causing an illusory inward or outward shift of the ends of the line.

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Math-Magic Vanishing Space

Qaudrix puzzle 1

Inspired from the astrological tables, here is a new puzzle of my creation designed according to the ‘Golden Number Rules’, which is reflected in the proportion of each single piece of the game. Thanks to the balanced dimensions of its pieces, this puzzle acquires some intriguing magical properties!

This “math-magical” puzzle is composed of a tray in which the pieces are assembled.

Quadrix puzzle 2 Continue Reading