Ananke’s Die

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!

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!
Scopri di più.

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!

Learn more.

Related links:

Moona Lisa

The Cube That Lies

I’ve always been drawn to the architecture of geometry. The hexagon, with its quiet strength and symmetry, sits at the root of so many spatial illusions—it’s the seed of cubes, isometric grids, and 3D paradoxes. From this shape, I began exploring structures that bend logic and perception, eventually giving life to a trio of optical works: Enigma 1, Enigma 2, and Enigma 3.

enigma 1
Enigma 1Prints & T-shirts.
enigma 2
Enigma 2Prints & T-shirts.
enigma 2
Enigma 3Prints & T-shirts.

Each piece is built around the visual tension of the impossible cube, created by merging two tribars in perfect isometric perspective. The lines suggest solidity, yet the form escapes reality—what looks structurally sound unravels the moment the eye tries to make sense of it. That’s the game I love to play: where geometry behaves, but perception rebels.

These “Enigmas” are spatial riddles dressed in stripes and angles, each one twisting the viewer’s reading of depth, volume, and continuity in its own way.

The Story of Blue

Sonne au comble de l'or
l'azur du jeune hiv
er
– Paul Valéry

For me, blue is air, wind, melancholy. It is like a Fellini film—always haunted by the whisper of the wind, the scent of things, and the fleeting moments of time we wish we could hold in an eternal present. Blue can carry regret; it is, in a way, a conservative principle. Blue has always held a strange duality: so immediate, yet once so elusive. Looking back to antiquity, it fascinates me that Homer never described the sea as blue, but as ‘wine-dark.’ In Greek, kyaneos evoked a dark, mineral depth, while glaukos hovered between gray, green, and blue. The Romans spoke of caeruleus, tied to the sky (caelum), and of lividus, the bruised, bluish tone of flesh. They never elevated blue; it was the color of outsiders, the hue of Celts painted in woad. Only the Egyptians seemed to truly revere it. They invented Egyptian blue, the first artificial pigment, and made it the shade of eternity and the divine.

In the Middle Ages, blue nearly vanished from prominence. Christian art turned to red, white, and black, leaving blue to the margins. Yet the word itself was evolving. The Germanic blāo—and its Vulgar Latin adoption, blavus—once meant something far less precise: shimmering, lustrous, dark, gray, even pale or yellowish. That ambiguity makes me realize how fluid color once was, before language fixed its boundaries. From blāo we inherited English blue and French bleu. Meanwhile, through Arabic lazaward came the words azure, azzurro, and azul, all born from lapis lazuli.

Then, in the 12th century, blue was transformed. Artists began clothing the Virgin Mary in ultramarine, ground from lapis lazuli more costly than gold. What had been humble became heavenly. Heraldry embraced azure as one of its noble tinctures, and kings like Louis IX made blue their emblem. A forgotten hue became a sacred, regal presence.

By the Renaissance, ultramarine shone as a color of prestige, truth, and constancy. Painters reserved it for the highest subjects, poets linked it to loyalty, and explorers carried its name across the seas as azul. Blue had finally claimed its place.

The modern era democratized it. Prussian blue appeared in 1704, followed by cobalt, cerulean, and synthetic ultramarine. Blue poured into uniforms, flags, and revolutions; it became the shade of liberty, of nations, of collective identity. Goethe called it spiritual, a color that retreats yet draws the soul inward.

In the 20th century, painters gave blue an entirely new destiny. The Expressionists used blue to conjure emotion, depth, and inner turbulence—think of Kandinsky, who saw blue as moving ‘toward the infinite,’ or Franz Marc, who painted blue animals to symbolize spirituality and hope. Even Van Gogh’s Starry Night swirls with blue, capturing both wonder and melancholy. Later, Picasso entered his Blue Period, transmuting sorrow into tone. Yves Klein went further still, reducing blue to its purest intensity with his International Klein Blue, turning it into an immaterial field of experience. For Klein, blue was not simply a color but ‘the most abstract color of all,’ a space in which one could lose oneself.

Today, I see blue everywhere. In the jeans that became the fabric of daily life. In corporate logos designed to inspire trust. In flags that mark belonging. Blue is calm, yet melancholy; humble, yet exalted. Once overlooked, it is now the world’s favorite color.

Blue is more than a hue. It is an idea shaped across centuries—etymologically born of caelum, blāo, and blavus; symbolically stretched between heaven and earth; culturally tied to faith, power, and identity. Its story mirrors our own: restless, mutable, and ever searching for meaning.

I’ll end with a little story from my own family. After World War II, my paternal grandfather, a house painter, bought a massive surplus of blue paint from the military. He had so much of it that whenever a client asked how he planned to paint their home, his answer was always the same, year after year: “All in blue, yes, all in blue…” (in our dialect, tutt’azzurr, tutt’azzurr).

That simple phrase stuck. Before long, the whole village started calling our family the Tuttazzurr family, and I myself became known as Giuan Tuttazzurr. Blue marked our home, but also my identity and my story—etched in memory and in name.

Moonlight Reflections on the Waters

A memory from Japan, where I lived briefly in the 1980s. This piece recalls earthy colors, organic shapes, and fragments of that time. A circle emerges from a flowing field of triangles—like ripples of moonlight dancing on the sea near Kamakura.

Immersing yourself in my op art is an invitation into a world where opposing forces meet, attract, and interlock, creating a balance both precise and hypnotic. It is a silent yet unending dialogue between art, form, line, color, mathematical concepts, the science of perception, and, above all, symbols. The symbolic depth of my work reaches beyond surface appearance, engaging with archetypes and forgotten rites that still pulse within the collective unconscious.

This unique op art piece is available as fine art prints and canvases in my online gallery.

Rediscovering Flutex: Simple Glass, Complex Illusions

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.

The Art of Discovery Between a Question Mark and an Exclamation Point

Science — like art — doesn’t really speak in the indicative. It doesn’t say this is, it asks what if? It begins in the conditional, in the open-ended curiosity of what could be, and unfolds in the imperative, the bold call to look, try, observe.

Discovery doesn’t start with answers — it starts with a question. And when it arrives, it rarely comes wrapped in neat descriptions. It comes as a gesture, a provocation, a set of instructions that invite us to experience something for ourselves.

Think about it: no one learns to cook from a description of flavor. They follow a recipe — a list of directives. A musician doesn’t explain the music in his head; he writes a score. And when we follow it, sound becomes experience. The composer’s vision is reborn in the hands of another.

In my own work, I do much the same — though my instrument is perception, and my notes are lines, colors, forms. Each visual illusion, each image, is a kind of instructional code. Not a description of what’s there, but an opening. If you engage with it, something clicks — not because I told you what to see, but because the form guided your eyes to see it for yourself.

G. Spencer Brown wrote that the act of drawing a distinction is the first creative move — a way of bringing something into being. In that spirit, I don’t aim to define the world. I aim to make space for new ways of seeing it.

So perhaps the real language of both science and art isn’t declarative at all.

It’s performative. It doesn’t tell you what reality is — it dares you to experience it.
And in that challenge, something unexpected happens:
You discover not just what the world could be — but what you might be within it.

Title: Follow the Light
“Follow the Light” – A visual imperative that pulls the eye into the unknown. This piece doesn’t describe — it directs. It doesn’t tell you what to see — it invites you to find out. Available as a fine art print.

Relative Size Illusions

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

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

Julio Le Parc – Nihil novi sub sole…

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.