Different but Equal

It’s not uncommon to read, on a snack package, the phrase “with chocolate taste,” often printed in bold uppercase. The wording plays a subtle trick on the mind. Most people assume the product must contain chocolate. Yet a flavor is not a substance. More often than not, what we bite into carries only the impression—an illusion—of chocolate.

The same applies to color. Our brain is just as easily misled. Colors behave like flavors: they may smell—pardon… look—like a particular hue, but they are subjective sensations rather than fixed properties of the outside world. They shift with context, changing according to their surroundings. More striking still, identical colors can appear different under certain conditions, while different colors may look the same. This phenomenon is known as color induction.

Even texture plays a role. It can alter how we perceive a color’s intensity and tone. Take beer and an egg yolk: they may share the same orange hue and gradation. Yet the brain reads them differently. The glass and the liquid are perceived as translucent, so their color seems lighter, duller, more diluted. The yolk, by contrast, appears opaque, with a richer, more glossy, more solid color.

In this picture, the beer and the egg share exactly the same orange gradation.

How a Human Bone Inspired the Eiffel Tower

Few people know that the human femur—the body’s largest and strongest bone—played an indirect role in the thinking behind the design of the Eiffel Tower.

Part of the tower’s structural logic can be traced to Swiss engineer Maurice Koechlin, chief engineer in the firm of Gustave Eiffel. While determining how forces would travel through the iron frame, Koechlin applied a principle that places material along the natural paths of tension and compression.

A comparable pattern had been described earlier by Zurich anatomist Hermann von Meyer. His research revealed that the femur’s internal structure forms a network of delicate struts known as “trabeculae.” These tiny elements follow the directions of mechanical stress inside the bone, creating a highly efficient system of support—even though the femoral head sits off-center from the shaft.

The mathematician Karl Culmann later showed that these trabecular patterns correspond closely to the principal stress lines calculated in engineering. His method, called graphic statics, provided a visual way to map how forces move through structures.

This link between anatomy and engineering influenced nineteenth-century structural thinking. The same principle—placing material only where forces demand it—guided the development of lighter, more efficient frameworks in bridges, cranes, and reinforced-concrete designs.

Beyond Constructible Forms: The Undecidable Bars

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.

Here’s a simple 18-frame animation of my Op Art piece—work in progress.

IF: The Two-State Threshold

I’ve always been drawn to impossible objects—those forms that slip between logic and illusion, never fully settling into one or the other.

This piece grew out of an old idea I felt compelled to revisit, almost as if reopening a long-forgotten door. A binary door, in fact—one that leads to two distinct worlds. Depending on how you look at it, it shifts, tilts, and reveals something else.

It starts with pencil on paper. A loose, intuitive phase where the form finds its way. From there, I move into FreeHand MS—an old tool I’ve never quite let go of. It still gives me a certain precision and feel I can’t replace. Finally, I refine the piece in Photoshop, adjusting, balancing, pushing it toward that delicate point where everything holds together.

There’s still work to be done. Something remains unresolved—but maybe that tension is part of what keeps it alive.

Creating a New Impossible Cube: From Concept to Print

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.

The Logic of Abstraction

Some say abstract art is non-representational—that it avoids visual reality and relies on color, shape, form, and gesture to trigger emotion or thought. I see it differently. Abstraction does not reject reality; it reframes it. It is a change of optics, not a disappearance of the world.

Take, for example, this video of goldfinches perched on swaying thistles. At first glance, does it not resemble an abstract painting? Rhythms, repetitions, subtle chromatic tensions, forms dissolving into movement. From there, one could push the abstraction further with the slightest shifts in shape or color—without betraying reality, only rephrasing it.

This idea is hardly new. From Cézanne’s insistence on treating nature through cylinder, sphere, and cone, to Kandinsky’s claim that abstraction reveals inner necessity rather than surface likeness, many artists and thinkers have argued that abstraction sharpens perception instead of diluting it. Even in cognitive science, perception is understood as an active construction, not a passive recording of facts.

Abstraction starts precisely there: with attention. Not with denial, not with decoration, but with the recognition that reality is already structured, already abstract, long before the artist intervenes.

Minimal Perception

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.