Modern art

Exploring Tessellations & Op Art: Hidden Arrows

Gianni Sarcone

This brief tutorial explores an Op Art tessellation that plays with bistable perception, figure–ground reversal and negative space. By combining modular geometric tiles with contrasting colors, the pattern creates a visual interplay in which arrows can be perceived as either foreground shapes or background forms, depending on how the pattern is interpreted.

Experiment 1:

· Preparation — Fig. A: Start with a 3 × 3 square. Divide it along its diagonals into four triangles, then add a 1 × 1 square to the outer side of each triangle, as shown. Color the resulting cross-shaped tile with two contrasting colors, ensuring that adjacent sections are different colors. The construction produces four inward-pointing arrows.

· Preparation — Fig. B: Following the construction shown, subdivide a 2 × 2 square to create five diamonds arranged in a staggered pattern. Use the same two contrasting colors. This produces a complementary tile containing four outward-pointing arrows.

· Assembly — Fig. C: The two tiles are complementary and fit together. Interlock the cross-shaped tiles with inward-pointing arrows and the square tiles containing the diamond pattern to create a continuous tessellation.

Visual result: The alternating geometric modules form a large geometric Op Art pattern in which arrows emerge through figure–ground reversal. And hidden within it are, believe it or not, 100 arrows. Yes, one hundred arrows!

This op art work is available as fine art prints and canvases from my online official gallery.

Experiment 2:

· Preparation — Fig. D: Build a four-armed pinwheel shape from a 4 × 4 square, as shown.

· Assembly — Fig. E: Interlock the four-armed pinwheel shape with the cross-shaped motifs containing the inward-pointing arrows.

· Assembly — Fig. F: As shown, these four-armed pinwheel shapes can be assembled in four or more different ways, producing different geometric configurations.

Visual Result: As seen in the example below, the contrasting colors make the bright blue arrows radiating around the pink central hubs—the pinwheel shapes—stand out, while the yellow arrows, matching the background color, virtually disappear from view.

pattern with pinwheel shapes

Experiment 3:

· Preparation & Assembly — Fig. G: Combine square tiles containing interior diamond arrangements with tiles featuring four inward- and four outward-pointing arrows formed by negative space. Arrange them alternately to create a checkerboard pattern.

The example below shows a 3 × 3 alternating checkerboard configuration that surprisingly reveals 52 arrows in total.

Variation: Here is a striking variation of the tile with four inward- and outward-pointing arrows. The inward arrows extend into continuous paths on a white background, creating the effect of interwoven arrowed ribbons.

Extra 3D Arrow Illusion

Let’s take a different direction from the experiments above and explore a 3D isometric illusion. This construction is inspired by classic impossible figures depicting ambiguous stacks of cubes, whose apparent number can change depending on how you interpret their spatial arrangement.

Start with a hexagonal boundary (Fig. 1) and overlay a triangular isometric grid (Fig. 2). Then draw six interlocking arrow shapes around a central point, folding their tails inward (Fig. 3).

Finally, use three colors to shade the isometric planes, or apply directional line hatching, to give the flat arrows a three-dimensional, interlocking appearance.

Curious about the mathematics behind these impossible 3D arrows? Math lovers can explore the geometry and construction 👉 here.

YAACOV AGAM — YOU NEVER SEE IT ALL

Gianni Sarcone

“When I finish a work, it is just starting.” — Yaacov Agam

One of my favorite Op Art artists and a true visionary, Yaacov Agam (Hebrew: יעקב אגם) was a pioneer of kinetic and Op Art. His work explored movement, color, time, and perception, making the viewer an active part of the artwork rather than a passive observer.

Born in Rishon LeZion in 1928, Agam studied at the Bezalel Academy in Jerusalem and later with Johannes Itten in Zurich. He moved to Paris in 1951, where he became one of the leading figures of the European avant-garde. His first solo exhibition was held there in 1953.

Agam died in June 2026, at 98, after receiving the Israel Prize for Visual Arts. His work is represented in major museums around the world.

Among his most remarkable achievements is the Salon Agam, commissioned by President Georges Pompidou for the private apartments of the Élysée Palace and created between 1972 and 1974. Now in the collection of the Centre Pompidou, it is essentially a kinetic environment: walls, doors, ceiling, carpet, color and geometric forms change as the viewer moves through the space.

Agam understood something fundamental about visual art: the work is not always what you see. It is also what happens when you move, look again, and see something different.

How minimal can a drawing be?

Gianni Sarcone

How far can you strip away a design and still leave it readable? Take almost everything out, and your brain will still fight to make sense of what’s left.

Here are two experiments in pushing that boundary:

  • 24 Configuration: The curve of the 2 flows straight into the diagonal of the 4. The brain uses the Gestalt principle of closure—filling in the missing pieces so you see two distinct digits sharing a single outline.
  • 45 Configuration: Standard typography is stripped back to raw vertical and horizontal lines. The crossbar of the 4 turns directly into the top curve of the 5, relying on your memory of numbers to decode the abstract shape instantly.

When you remove the noise, viewing becomes interactive. You aren’t just looking at a drawing—your mind is actively completing it.

👉 For more patterns, and mathematical curiosities, explore these number facts.

Triple Klein Bottle

Gianni Sarcone

Τριαλάβαστρον (Trialábastron), a triple Klein bottle, is an artistic exploration of Klein bottle geometry. In topology, the Klein bottle is a non-orientable surface that cannot be embedded in three-dimensional Euclidean space without self-intersection, though it can be smoothly realized in four dimensions.

A close relative is the Möbius strip, another non-orientable surface in three-dimensional space. On such surfaces, a continuous path can return to its origin with reversed orientation, revealing how geometry can twist the notion of inside and outside.

a triple Klein bottle

Here is another representation of a triple Klein bottle—UK sculptor Alan Bennett’s striking construction of three Klein bottles nested within one another. Of course, “inside” only applies in the sense of their embedding in physical space; from a topological standpoint, they remain entirely separate, non-interacting surfaces.

recursive Klein bottle

Impossible Beach Cabin

Gianni Sarcone
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.

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.

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

The Logic of Abstraction

Gianni Sarcone

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.