The Geometry of Wonder

impossible objects: nested tribars

One of my finest sculptures: nested triangles, the central one in wood, the others in stainless steel…

nested tribars

Just kidding. It’s an impossible tribar composition — a sculpture that can exist only in the eye and the mind.

The Penrose triangle (or Penrose tribar) is generally credited to Roger Penrose, who, together with his father Lionel Penrose, published it in 1958 as an “impossible object.” However, the visual idea of creating paradoxical triangular forms and impossible geometries has older precedents.

Japanese visual culture is often mentioned in discussions of geometric illusion because Edo-period (1603–1868) art, decorative motifs, and craft traditions reveal a deep fascination with complex patterns, ambiguous spaces, and unconventional perspectives. Elements found in traditions such as sankaku mokkō (triangular motifs), karakusa patterns, architectural ornamentation, and woodworking designs show how Japanese artists and craftsmen explored visual structures that challenge perception. While no confirmed direct predecessor of the Penrose tribar has been identified in Japanese art, these examples belong to a broader historical tradition of creating forms that play with geometry and the limits of visual interpretation.

Japanese tribar

A glimpse below into traditional Japanese fabric patterns, where triangular designs reveal how interlaced geometry can create the sensation of impossible structures.

Kagome patterns

Your Brain vs. Geometry: Rooftop illusion

Believe it or not, the green and purple rooftops are congruent—identical in shape, size, and angles. What changes is not the geometry, but your perception of it. Perspective, orientation, and contextual cues lead your visual system to interpret the same form as two different structures.

rooftop illusion, related to shepard tables

This effect is closely related to Shepard’s tabletop illusion and earlier studies in which identical parallelograms (A and B), when rotated (and superimposed), are perceived as different shapes, as the brain prioritizes interpretation over measurement.

Since some still insist these roofs are not congruent, I’ve put together a short animation that shows otherwise.

animated rooftop illusion

Bear-ly Seal

People often ask where my ideas come from. There is no single answer. They tend to surface quietly, shaped by places I’ve seen and cultures I’ve crossed.

Seal or Bear?” grew out of that kind of moment. An animal suspended in the vastness of a frozen world—emerging from an ice hole, yet refusing to settle into a single identity. Is it a polar bear? A seal? Or something that holds both readings at once?

Bear of seal?

The idea came to me while traveling through northern Canada, surrounded by the stillness of Arctic landscapes and the deep presence of Inuit traditions. That silence has a way of sharpening perception—of making ambiguity feel natural rather than puzzling.

First created in the 1990s, the illusion went on to become a reference point in visual perception studies and later found its way into textbooks.

More recently, the “Seal or Bear?” illusion will be featured by the NHK Educational Corporation as part of a 2026–2027 educational series on psychology and visual perception.

The Borromean Tribar

This form belongs to the family of impossible figures, more specifically to the Penrose triangle, or tribar.

impossible figure

At first glance, it looks entirely manufacturable. The structure appears to be made from three identical square rings (Fig. 1), each pierced by a circular opening and arranged in three mutually perpendicular planes (Fig. 2). Together, they seem to interlock seamlessly, forming an impossible three-dimensional tribar that evokes a trefoil knot and its endless over-under weaving.

If this sculpture looks physically realizable to you, congratulations: your visual system has just accepted a geometric impossibility.

the making of the borromean tribar

Could such an object be built? Not exactly. One solution would be to twist one of the junctions slightly, but that trick would be immediately noticeable here because some of the angles would no longer appear perfectly square (90°), as shown in the picture below. Another possibility would be to leave a small gap at one junction and view the sculpture from a carefully chosen angle, allowing perspective to hide the discontinuity.

This is how a real 3D Borromean Tribar would appear

Impossible Beach Cabin

impossible house sketch

With summer just around the corner, I find myself drifting back to the shores of time, to this delightfully impossible little structure perched on the beach.

A drawing concept created for a children’s coloring book on optical illusions. Over the years, I’ve explored this theme through many curious and playful variations.

impossible house
Available as fine art print from my online gallery.

Are the kids engaging in creative activities inside the cabin or outside it?

The roof insists we’re looking at the exterior, while the floor pulls us firmly indoors. Both readings feel correct, yet they cancel each other out. So, there’s no clean resolution here—just a quiet visual paradox.

Curious to see more of my optical illusion book concepts, impossible worlds, and mind-bending creations? Take a stroll through my author page.

impossible house poster

The idea itself is far from new and has inspired countless artists, architects, and photographers. It even exists in three dimensions. A notable example is Roy Lichtenstein‘s House I (1996), an ingenious sculpture that appears to be a solid house but is actually a concave construction made of angled steel planes. As viewers move around it, the structure seems to rotate and reshape itself, turning perception into part of the artwork.

Speleology of Love – Figure–Ground Embrace

An illusion carved in emotion—can you spot the hidden lovers within?

I created this illustration for a commissioned series examining the underlying strata of interpersonal intimacy.

Gestalt vision

This black-and-white composition plays on figure–ground reversal. At first glance, it reads as a cave opening with a line of climbers moving along a rugged ridge. Look again, and the void resolves into the soft profile of two faces, suspended in the instant before a kiss.

Interested in commissioning my work to illustrate your next editorial project or conceptual series? Let’s discuss how we can bring your vision to light.

The stark contrast and clean silhouettes lend themselves naturally to large-scale applications. On a façade, the image finds a natural home as a mural in a Swiss village, where the alpine setting mirrors the climbers’ ascent.

Seeing Is Not What It Seems

Color is energy—an electromagnetic phenomenon shaped by how light is reflected from objects. What we call vision is not innate. It is largely learned, built through a slow and demanding process. We tend to take it for granted, yet someone born blind who later gains sight must spend years learning how to organize and interpret what now enters the eyes.

Seeing is neither simple nor passive. When we look at a landscape, color information reaches the visual cortex in roughly 30 milliseconds (in the occipital lobe, V1). Only a fraction later—around 70 milliseconds—shape, depth, and motion begin to emerge. In these brief intervals, the brain filters, compares, and reconstructs fragments of data, assembling them into a coherent image. What we perceive is not a direct recording of reality but a refined interpretation—an internal best guess shaped for meaning and action.

The way we see

I’ve long been intrigued by the way people with partial or total visual loss engage with the world. Any serious reflection on perception or optical illusion eventually meets its counterpoint. Understanding how they “see” without sight reveals the real weight of vision itself—and how inseparably it works with the other senses, each one calibrating the rest.

When we see, move, speak, and feel at once, what actually binds sight to touch or hearing? The truth is, we notice far less than we assume. We attend only to what matters in the moment. Without the constant support of the other senses, perception would collapse into confusion, because they operate quietly in the background, guiding everyday behavior.

A striking example comes from research on inattentional blindness. In a well-known 1999 experiment by Daniel Simons and Christopher Chabris, participants watched a video and counted basketball passes between two teams. Nearly 40 percent failed to notice a person in a gorilla suit walking through the scene, pausing, even dancing, before exiting. The demonstration is disarming in its simplicity: we do not see what we do not attend to—even when it stands directly in front of us.

Source.

Optical Waltz: Constant Motion, Perceived Oscillation

The blue and yellow arrows in this video seem to move up and down in a rhythmic dance—yet their motion is strictly horizontal and uniform. This illusion is a variation of the “Stepping Feet Motion” effect, first demonstrated by Stuart Anstis in 2003.

In the original phenomenon, two objects glide side by side at a constant speed across a striped background, but appear to alternately speed up and slow down, creating a stepping or oscillatory effect. The visual system misreads contrast differences as changes in motion, producing a false sense of vertical or staggered movement.

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.