Op art

Beyond Constructible Forms: The Undecidable Bars

Gianni Sarcone

In 1934, the Swedish artist Oscar Reutersvärd sketched a peculiar triangle made of small cubes, neatly aligned on an isometric grid. Everything looked geometrically sound—until the mind tried to assemble it in real space.

Soon after, Lionel Penrose and Roger Penrose published their famous Penrose Triangle—three beams joined by apparently right-angled joints—and M. C. Escher explored similar paradoxes in works such as Waterfall and Ascending and Descending.

This triangular paradox has distant echoes in ancient Greek geometry, but Reutersvärd gave it a clear visual form: the impossible figure.

That’s the charm of impossible figures: every part looks right, yet the whole quietly breaks reality.

I began exploring these paradoxical structures in the 1980s. My interest grew naturally from the meeting point of two inclinations: a mathematical curiosity about spatial logic and a visual fascination with form. Over time I produced many variations—sometimes rediscovering ideas that others had already touched upon, occasionally arriving at configurations that felt genuinely new. In geometry, complete novelty is rare; most discoveries emerge as unexpected turns within an existing landscape.

One example from that period is the study shown here, created in the late 1990s and titled Undecidable Bars.

© Gianni A. Sarcone, 1997-2001

Parallel bars appear to run calmly side by side, yet their connections quietly sabotage the logic of space. Perspective slips from one segment to another, forcing the eye to accept incompatible viewpoints at the same time.

Each element seems perfectly normal.
Together, they form a structure that cannot exist.

Some bars appear to pass through others; some join where no joint should be possible. The geometry behaves as if the object were bending through space, while every line still respects the conventions of perspective drawing.

The result is an undecidable figure—a form the eye can follow effortlessly, but the mind cannot reconstruct.

Available as fine art print from my online gallery.

Over the years I have created hundreds of images built on similar principles, across different formats and media. If these works interest you for a book, exhibition, or monograph, feel free to contact me.

Master of Numbers

Gianni Sarcone

“The Master of Numbers” is an Op Art photomosaic portrait of the renowned physicist, created from a collection of photographs of numbers. Each detail contributes to a visual exploration of mathematics, perception, and pattern. The project took me two years to complete, photographing numbers in the most unusual places and objects, and bringing them together into a single portrait.


And a little secret: tucked inside the mosaic is a tiny portrait of me and my wife—a fun, hidden signature and a personal touch.

Limited edition posters and prints are available through my online gallery.

Creating a New Impossible Cube: From Concept to Print

Gianni Sarcone

Impossible or undecidable figures have long fascinated artists, mathematicians, and viewers alike. Their appeal lies in a delicate tension: the structure appears perfectly logical at first glance, yet closer inspection reveals spatial contradictions that cannot exist in the physical world. My latest work revisits an idea I first explored in the 1990s—an impossible Rubik’s-style cube—now developed into a new series built across several stages, from hand-drawn construction to digital refinement and photographic interpretation.

The project began with a simple geometric framework—interlocking beams arranged to suggest a stable cubic volume. The challenge was to reinterpret an apparently ordinary three-dimensional cube into an ambiguous form that still appears structurally plausible. Through careful adjustments of line weight, contrast, and directional and formal cues, the cube gradually shifts from perceived solidity to spatial uncertainty, so that as the eye moves across the image, the object quietly reorganizes itself, producing a surreal perception in place of a coherent physical structure.

impossible cube
Here is the original version of the project, refined from my initial hand-drawn construction and carefully reconstructed using FreeHand MX

Two of the final images belong to the Op Art tradition, where sharp black-and-white geometry emphasizes visual tension and rhythmic structure. These compositions highlight the cube’s architectural clarity while allowing the paradox to emerge naturally from the viewer’s perceptual processing. The remaining two images take a different path: they present the object in a photographic setting, rendered with realistic lighting and textures.

impossible cube etched
Astraea Paradox Cube: Available as fine art print.
Rubik’s Paradox Cube: Available as fine art print.

Together, the four images form a small visual narrative—construction, transformation, and illusion—showing how a purely conceptual structure can evolve into multiple aesthetic forms. The Op Art versions focus on perceptual mechanics, while the photographic interpretations suggest how an impossible form might inhabit the physical world, even if only in appearance.

Fine art prints and canvas editions from this series are available through my official gallery shop, where each piece is produced using archival materials designed for long-term display.

Collectors and galleries interested in larger formats or special editions may also contact me directly for availability and production details. This series continues my exploration of perceptual geometry, where simple shapes become instruments for questioning how we construct space, depth, and visual certainty.

Kinegram Exhibits

Gianni Sarcone

Here are two Kinegram installations I made, designed to educate, engage, and spark curiosity in visitors of all ages. These works make motion appear from static forms, offering an experience that is both playful and thought-provoking.

Kinegrams reveal movement through a sliding transparent panel printed with vertical black lines. As the panel moves over the underlying image, hidden sequences appear, animating the drawings like frames of a film. Each interaction lets the viewer explore how motion can emerge from stillness.

The concept of movement from static forms has long interested scientists and philosophers. Movement is a dimension unfolding in space and time—without time, there is no motion. Kinegrams make this idea tangible through touch and visual perception.

These exhibits are simple to set up but produce surprising results. I made the first panel for UNIFI, the University of Florence, and the second for the Mind Games Art Alive Museum in Sydney. Both projects engage and surprise visitors, combining education with visual impact.

Kinegram - UNIFI

“Twisting Cords,” Kinegram exhibit for UNIFI, Florence
As the transparent panel etched with black lines glides across the design, colorful cords seem to twist, winding and unwinding in a mesmerizing, living rhythm.

Flying Birds - Migration

“Flying Birds – Migration,” Kinegram exhibit for Mind Games, Sydney
As the transparent panel etched with black lines glides across the static design in the background, the flock of birds rises and takes wing, transforming a still pattern into living, rhythmic motion.

To see more or discuss a Kinegram installation, visit: https://www.giannisarcone.com/Kinegrams.html

Minimal Perception

Gianni Sarcone

I’ve always wondered about the limits of shape and color needed for us to represent or recognize an object. Take a stemmed glass, for example. To depict it, you might need just two circles and a straight line—and perhaps a red disc to suggest the wine inside.

But we can go further: by turning it from a flat image into a 3D form with a simple rotational movement, like in Duchamp’s rotoreliefs, the object suddenly comes alive in space.

All these graphic shortcuts rely on memory. Our brains interpret what we see based on past experience, filling in missing information and reconstructing the object from just a few essential cues. This process aligns with the principles of visual perception: the Gestalt laws of closure and continuity explain why we perceive a complete glass even when much of it is absent. Minimalist perception highlights how human cognition distills visual information, showing that a few simple shapes and colors are enough to evoke a rich, instantly recognizable image.

☞ Duchamp rotoreliefs.

Seeing Beyond Lines: The Illusion of Form

Gianni Sarcone

We usually perceive lines and shapes as forming a figure, while the paper and surrounding white space recede into the background. Yet, under certain conditions, what we assume to be background can itself acquire form and meaning. In the illustrations shown here, a clear geometric figure emerges—even though no lines actually define it. These visual phenomena are known as illusory figures.

illusory spring
What kind of 3-dimensional shape do you see?

Illusory figures depend, in part, on the presence of regular gaps within a visual arrangement. When such gaps occur, the visual system instinctively tries to resolve them into coherent forms. These gaps can be created by simple elements, such as circles. When solid black circles and partially “chipped” ones are arranged carefully, they produce striking illusory shapes.

The most familiar example is the Kanizsa triangle. Here, an illusory contour is perceived when black disks with wedge-shaped sections removed are aligned so that their edges define a triangular form in the negative space. Remarkably, this illusory region appears brighter than the surrounding page, even though its physical luminance is identical.

Kanisza triangle
Kanizsa triangle

Etherial Cross

A pattern of black dots forms a ghostly ‘X’ shape through negative space. The arrangement of dots creates a subtle sense of motion and depth. The piece combines the Ouchi effect—where contrast between figure and background generates apparent movement—with the Kanizsa illusion, where the mind completes shapes that aren’t actually drawn.

Sarcone's Illusory Cross
Fine art prints of this Op Art piece are available for purchase through my official gallery.

The effect becomes even more dramatic when the illusion is animated. Rotate the cross, for example, and the X-shaped form—with no explicit outline—appears to emerge from a rigid grid of black dots. The shape is defined solely by subtle local distortions: small asymmetric intrusions along the contours of the X disrupt the regularity of the dots, making the form pop into perception despite having no actual boundaries.

Animated Sarcone's Illusory Cross

Etherial Circle

Using the same technique, we can replace the X with a large O. Now the regular arrangement of black circles is disrupted by a ghostly central shape that seems to lift off the background, almost floating. As above, this Op Art piece combines the Ouchi effect—where the contrast between figure and background creates apparent motion—with the Kanizsa effect, where the mind completes shapes that aren’t actually drawn.

Floating O
Fine art prints of this Op Art piece are available for purchase through my official gallery.

It is also interesting to add a rotational motion to this Op Art piece. I experimented with different solutions, and this one is the simplest yet striking nonetheless.

To conclude this journey into the world of contour illusions, still using black disks as our starting point, here are a few further experiments. They explore negative superpositions, translucent effects, and the emergence of more complex forms—showing how simple elements can give rise to unexpected visual structures.

hidden beauty
Fine art prints of this Op Art piece are available for purchase through my official gallery.

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