Optical illusions

Ananke’s Die

Gianni Sarcone

A simple study in visual perception—an exploration of how a plain hexagon can evolve into the illusion of a cube. Through precise geometry and controlled form blending, static lines awaken into rhythm and volume, giving rise to a subtle sense of depth and movement.

Constructing the Illusion

Fig. A — The Base Shape
Start with a regular hexagon. Divide it into three equal diamond shapes (rhombuses)—these represent the three visible faces of the cube. Each diamond has four equal sides: two acute angles (60°) and two obtuse angles (120°). Together, they form the geometric foundation of the cube.

Fig. B — Building Volume with Shape Blends
In Illustrator, or any other vector software, use the Blend Tool to create a shape blend inside each diamond. Start with a small central circle and blend it toward the outer edge of the diamond. Adjust the number of blend steps to control how smooth or tight the transition appears. This process builds the cube’s apparent volume and visual tension. You’ll notice that the distance from corner to corner in the nested, diamond-like shapes is slightly greater than from side to side, creating subtle gaps that lead the eye to perceive an X across the surface.

Fig. C — Perspective and Transformation
Distort slightly the hexagon to set the three diamonds in perspective. This step transforms the flat figure into a die-like cube, giving it spatial depth and presence.

ananke cube

Enhancing the Optical Effect
Next, add horizontal background lines and some color, as shown in the two examples in the image. You can also adjust the illusion by making the visible faces of the die appear slightly concave, as in the figure on the right. This effect is created by shifting the concentric, nested diamond shapes slightly off-center—the position of the central ellipse determines whether the die appears concave or convex.

two Ananke dice

Below is the finished stage of the work. Curiously, the cube appears to hover, slide, and even emit a faint blue glow—though it remains entirely black and motionless.
Ananke’s Die is a study I began in 2010, a continuing exploration of how repetitive lines and geometric precision can trick the mind into sensing motion and color where none exist.

Ananke die

You can get Ananke’s Die as a fine art print or canvas, available in different sizes and finishes.
👉 Buy it here

Why Ananke’s Die

I titled this work Ananke’s Die after Ananke, the Greek goddess of necessity and fate.
The cube, a symbol of structure, represents order and control. Yet the three visible faces that seem to define its volume are an illusion—shifting and unstable.
Under the viewer’s gaze, the shape changes, its meaning shifts, yet the form remains.
This illusory die shows the balance between order, perception, and destiny, reminding us that what we think we control often exists within the unpredictable interplay of vision and inevitability.

This image also triggers multiple associations in a loop: hexagon, cube, die, chance, illusion, order, fate, contradiction. These connections show how perception mixes stability and randomness, revealing that what we see is shaped as much by the mind as by reality.

Immergiti nel mondo dell’arte ottica!

Gianni Sarcone

Le mie opere, esposte permanentemente alla Città della Scienza e al Dipartimento di Fisica dell’UNIFI, offrono un’esperienza visiva che stimola curiosità e meraviglia. Non perdere l’occasione di vederle dal vivo!
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Dipartimento di Fisica dell’UNIFI

🇬🇧 Dive into the world of optical art!
My works, on permanent display at Città della Scienza and the Physics Department of UNIFI, offer a visual journey that sparks curiosity and wonder. Don’t miss the chance to experience them in person!

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Moona Lisa

The Responsive Eye

Gianni Sarcone

“The Responsive Eye,” held at MoMA in 1965 and organized by William C. Seitz, was a landmark exhibition in Op Art. Featuring over 100 artists—including Bridget Riley, Victor Vasarely, Richard Anuszkiewicz, and Josef Albers—it explored how geometric patterns and color could manipulate perception.

Riley stood out with her precise, rhythmic paintings that seemed to move and breathe, challenging the way we see. The show fascinated the public, drawing huge crowds, and sparked a wave of interest in optical effects across art, design, and fashion.

Critics were divided. Some celebrated its innovation and playful engagement with vision; others dismissed it as flashy spectacle, questioning the depth and seriousness of Op Art. Personally, I see it as a pivotal moment—one that reminded everyone that perception itself could be the medium, and that art could be both cerebral and exhilarating.

Bridget Riley
Victor Vasarely
Richard Anuszkiewicz
Josef Albers

Further information: https://ubu.com/film/depalma_responsive.html

Rediscovering Flutex: Simple Glass, Complex Illusions

Gianni Sarcone

I’ve been toying with the idea of revisiting an old, low-key material for my art: Flutex.

If you haven’t heard of it, Flutex is a patterned industrial glass from the 1930s and ’40s, mostly used to give a bit of privacy in bathrooms and office partitions.

In the ’70s, Op artist Sydney Cash started playing with this glass and found that its ribbed surface works like a lenticular screen—showing different images depending on how you look at it. The effect? Hypnotic, shifting artworks that change as you move around them.

It’s just simple glass, but it tricks perception in a really cool way.

I’m seriously considering giving it a try myself—there’s something about that mix of humble material and complex visual play that feels worth exploring again.

Relative Size Illusions

Gianni Sarcone

Here are two relative size illusions I described back in 1997 and 2013.

The first, called Sarcone’s Crosses, challenges classic illusions like the Ebbinghaus illusion (Titchener Circles, 1898) and the Obonai square illusion (1954). It features a cross (the test shape) surrounded by squares of different sizes.

As shown in Fig. 1.a, 1.b, and 1.c, the three blue crosses are all the same size — yet the one on the left (Fig. 1.a) appears larger. Surprisingly, the illusion still works even when smaller squares completely cover the cross (Fig. 1.c).

So, the size of surrounding shapes doesn’t always dictate how we perceive the central one.

In the second illusion (Fig. 2.a and 2.b), due to assimilation, the red diagonal inside the larger ellipse seems longer — but the blue line is actually the longest.

Perception loves to play tricks on us.

sarcone's relative sizze illusions

You can explore more of my illusions and visual inventions on my official site: giannisarcone.com

Illusive Pietà

Gianni Sarcone

Uncovering the subtle visual tricks Michelangelo wove into his masterpiece.

We’re not very good at judging the true size and positioning of objects just by looking. Take Michelangelo’s Pietà—it hides some subtle, conceptual “illusions”:

  • If they were standing, the Virgin Mary would actually be much taller than Christ, which may be surprising.
  • Her knees are slightly off-center, forming a kind of base or pedestal that supports Christ’s body.
  • And while logically the Virgin should look older, her face is almost childlike, creating a striking contrast with the mature, somber face of her son.

Michelangelo himself explained this choice:
“The mother had to be young—young enough to appear forever a virgin. Meanwhile, her son, who took on our human nature, must, in the stripping away of death, be a man like any other.”

Art is full of illusions designed to meet the visual expectations of viewers—and sometimes to correct what might seem off or unnatural to the eye. Because reality, at times, doesn’t always feel quite real or right to those who look at it.

And one last curious detail: Pietà is the only work Michelangelo ever signed. Stung by whispers that another sculptor had made it, he returned one night and boldly carved his name across Mary’s sash— “MICHAELA[N]GELVS BONAROTVS FLORENT[INVS] FACIEBAT” (Michelangelo Buonarroti, the Florentine, made this). A rare flash of pride from an artist who usually let his work speak for itself.)

Pietà by Michelangelo

Smelling the Color 9: When Numbers Take Shape and Color

Gianni Sarcone

In English, the expression to smell the color 9 describes something completely impossible…

And yet, some people have the unusual ability to mentally visualize colors or spatial patterns when thinking about units of time—or more broadly, numbers. This phenomenon, known as synesthesia (from the Greek syn, “together”, and aisthēsis, “sensation”), occurs when stimulation of one sense involuntarily triggers sensations in another. It’s not a figure of speech—these perceptions feel very real to those who experience them.

The first documented case in medical literature appeared in 1710. Dr. John Thomas Woolhouse (1650–1734), an ophthalmologist to King James II of England, reported a blind young man who claimed he could perceive colors induced by sounds.

Neuroscientist Vilayanur S. Ramachandran and his team at the University of California, San Diego, observed that the most common form of synesthesia links “graphemes“—letters or numbers—to specific colors. Since my work bridges art and mathematics, I’ll focus here on number-based synesthesia.

People who experience synesthesia in its pure form are relatively few. However, many report strikingly similar associations between numbers and colors or spatial layouts, suggesting these perceptions aren’t just products of imagination or attention-seeking. For example, number–form synesthesia may result from cross-activation between brain regions in the parietal lobe that handle numerical and spatial processing. In contrast, number–color synesthesia likely stems from an overabundance of connections between adjacent areas that interfere with each other when triggered (see fig. 1 below).

brain synesthesia

Figures 2 and 3 illustrate common synesthetic patterns—either as color associations (fig. 2) or spatial arrangements (fig. 3, based on observations by Sir Francis Galton). Statistically, people often associate the digits 0 or 1—and sometimes 8 or 9—with black or white. Yellow, red, and blue are typically linked to smaller digits like 2, 3, or 4, while brown, purple, and gray tend to be tied to larger ones like 6, 7, or 8. Curiously, it’s not the idea of the number but the visual form of the digit that seems to trigger the sensation. For instance, when the number 5 is shown as the Roman numeral V, many synesthetes report no color at all.

color number synesthesia

And you—do you see numbers in color or arranged in space? Feel free to share your synesthetic experiences with me.

Julio Le Parc – Nihil novi sub sole…

Gianni Sarcone

Although I’ve been working in the field of Op Art since the mid-1980s, it’s important to recognize that the movement itself has a deeper history. It began to take shape in the 1960s, led by pioneering figures such as Victor Vasarely and Bridget Riley.

However, the artists who truly captivate me—the ones who expanded the language of perception—are often the outsiders. One such figure is Julio Le Parc (b. September 23, 1928), an Argentine-born artist whose practice bridges Op Art and kinetic art. Le Parc studied at the School of Fine Arts in Argentina and went on to co-found the Groupe de Recherche d’Art Visuel (GRAV). His work, honored with numerous awards, holds a prominent place in Latin American modernism.

Le Parc’s recurring themes—color, light, and movement—have always resonated with me. During the ’60s and ’70s, he explored light not just as a visual element but as a living, dynamic material. Yet by the late ’70s, his presence in the art world had faded; his output became sporadic, and for decades his work slipped quietly out of the international spotlight.

 Fortunately, recent years have witnessed a renewed appreciation of his explorations in light and movement, bringing his contributions once again to the attention of a wider public.

Artist’s Website: http://www.julioleparc.org

Book: Catalog of the artist’s first solo exhibition, Paris, November–December 1966. Text in French by Frank Popper.

Misdirection → Illusion → Aha! Moment…

Gianni Sarcone

How misdirection, illusion, and wonder shape my creative process.

The path from misdirection to revelation is at the heart of how illusion and wonder spark insight. Misdirection steers our attention—often subtly—away from what truly matters. It disrupts our expectations, creating a gap between what we see and what is. Within that gap lies the illusion: a crafted discrepancy, a visual or cognitive sleight-of-hand that unsettles our perception.

But the magic doesn’t end there. When the illusion is cracked—when the mind shifts, recalibrates, and sees—the famous Aha! moment erupts. That flash of understanding isn’t just delightful; it’s deeply educational. It rewires how we interpret the world.

This sequence—misdirection, illusion, revelation—mirrors the creative process itself. It shows how confusion, when carefully designed, can be a gateway to clarity. In the right hands, illusion is not deception—it’s a tool to awaken curiosity, stretch perception, and provoke insight. Wonder, in this sense, becomes a powerful cognitive catalyst.

That’s why my art and, I believe, my writing, revolve around this sense of wonder—arguably the most direct and playful route to that pleasurable, often conflicting moment of insight: the sudden discovery of something previously unknown.

Hands-On Wonders: A Mathemagical Collection

Gianni Sarcone

Ever wondered what happens when math puts on a magician’s hat? These books are the distilled magic of my hands-on math workshops across Europe — from Paris to Palermo, Geneva to Ghent — where paper folded, minds twisted, and logic sparkled in English, French, and Italian!

Impossible Folding Puzzles

1) “Impossible Folding Puzzles and Other Mathematical Paradoxes” — a playful dive into mind-bending problems where nothing is quite what it seems. Can a puzzle have no solution… or too many? Dare to fold your brain.

Still available on Amazon.

2) “Pliages, découpages et magie : Manuel de prestidi-géométrie” — where math meets illusion to spark curiosity and creativity.
Perfect for teachers, students, and curious minds: touch, fold, cut… and let the magic unfold!
Available on Amazon.

2) “Pliages, découpages et magie : Manuel de prestidi-géométrie” — un livre où maths et illusion se rencontrent pour éveiller curiosité et créativité.
Pour enseignants, élèves et esprits joueurs : touchez, pliez, découpez… la magie opère!
Dispo sur Amazon.

Pliage decoupages

3) “MateMagica” —  They say there’s enough carbon in the human body to make 900 pencils… but just one is all you need for these clever puzzles!
Fun, surprising, and thought-provoking — because, as Martin Gardner put it, “Mathematics is just the solution of a puzzle.”
Now on Amazon.

3) “MateMagica” —  Si dice che nel corpo umano ci sia abbastanza carbonio per 900 matite… ma per questi rompicapi ne basta una!
Sorprendenti, divertenti e stimolanti — perché, come diceva Martin Gardner, “la matematica è nient’altro che la soluzione di un rompicapo.”
Disponibile su Amazon.

I write and illustrate my own books in five languages: English, French, Italian, German, and Spanish.
If you’re a publisher or literary agent seeking original, high-quality educational content that blends creativity with clarity, I’d be pleased to explore potential collaborations.