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.
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.
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.
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.
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.
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.
“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.
As a visual creator, over the years I have developed a broad collection of mind games and hands-on activities designed to foster visual and critical thinking while supporting the learning of mathematics. These features, created for readers of all ages, are available for licensing to newspapers, magazines, and media platforms seeking distinctive, high-quality editorial content that captures attention and sustains reader interest.
Interested in adding a fresh editorial feature that energizes your publication? Explore the available offerings at Knight Features.
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.
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.
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.
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.
“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,” 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.
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.
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.
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.
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.
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.
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 ‘glitter’ you see on this wolf spider comes from the eyes of the babies she carries on her abdomen. Like cats, owls, and other nocturnal hunters, wolf spiders possess a reflective layer behind their retinas called a “tapetum lucidum,” which amplifies even the faintest light and makes their eyes glow in the dark. This tiny adaptation turns the forest floor into a stage where predator and prey perform under the faintest moonlight.
Nature often converges on similar solutions, weaving common threads through vastly different lives. It’s fascinating to think that very different species—arachnids and mammals alike—have evolved the same “superpower”: the ability to see in near darkness.
Next time you spot a tiny flash of light on a night hike, remember: a wolf spider might be staring right back, sharing with you the magic of the nocturnal world.
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