Op 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.

Deconstructing impossibility

Gianni Sarcone

A quick study of impossible interlocking cubes, taking the same paradoxical geometry from line drawing to watercolor and high-contrast digital collage.

The drawings use isometric projection to represent a three-dimensional cubic structure. The geometry appears consistent at first, but the planes intersect in ways that cannot exist in physical space. What functions as a back face seamlessly projects forward to become a front face, creating a continuous spatial contradiction.

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.

Train your brain by questioning your eyes

Gianni Sarcone

For many years, I collaborated with Publications International Ltd. (PIL) on the Brain Games™ series, creating hundreds of optical illusions for three books designed to challenge visual perception, observation, spatial reasoning, attention, and visual logic.

Optical illusions are more than visual tricks: they make the brain question its first interpretation, detect discrepancies, and construct a different explanation of what it sees. In that sense, they provide a stimulating workout for perception and reasoning.

I now put my expertise in visual perception and optical illusions at the service of publishers, educational institutions, medical centers, and other organizations looking for engaging ways to challenge and stimulate the mind.

Challenge your eyes. Make your brain work.

👉 Discover the latest book on Amazon

optical illusions - Brain Games

Galloping Primes

Gianni Sarcone

Every frame in this GIF is a 3,100-digit prime number:

prime gif

Together, they recreate the world’s first motion picture: Eadweard Muybridge’s iconic 1878 “Galloping Horse.”

How it works: Each frame is converted into a grid of 1s and 8s, then slightly tweaked until the math clicks and a prime number is born. Fast primality tests spot the candidates, and rigorous checks confirm them.

The result? An animated piece of history, built entirely out of pure mathematics.

☞ Source: https://www.lbatalha.com/blog/prime-motion-picture

Minimal Cat

Gianni Sarcone

A Zen-inspired sumi-e unicursal brushstroke that gently evokes the silhouette of a sleeping cat.

sumi-e zen cat
sleeping cat
pencil studies

A single brushstroke, almost nothing… and yet the mind completes the rest.
This Zen-inspired sumi-e line suggests the presence of a sleeping cat, as the brain instinctively searches for form, balance, memory, and meaning within this minimal stroke. A curve becomes a back, a pause becomes a head, and empty space turns into stillness—peace, quietude itself. Strangely, this allegorical curve echoes the Japanese symbol ensō (円相; “circular form”), often drawn in calligraphy as a gesture that holds completeness and imperfection in the same breath.

Minimal drawing works because perception is never passive. We do not simply “see” the world; we continuously reconstruct it from fragments. A few essential marks are enough for the imagination to awaken and project life into absence. The unfinished image invites the viewer to participate in its creation.

This is one of the quiet powers of strict minimalism: removing detail does not always diminish reality — sometimes it amplifies it. In sumi-e, what is omitted matters as much as what is painted. The void is not empty; it breathes. Perhaps that is why a simple unicursal stroke can feel strangely alive.

Art begins precisely there: at the threshold where perception, imagination, and silence meet.

Speleology of Love – Figure–Ground Embrace

Gianni Sarcone

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.

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.

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.