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.

Χρόνος and Καιρός

Gianni Sarcone

“The part of life we really live is small. For all the rest of existence is not life, but merely time.” — Seneca

Chronos measures time; Kairos gives it meaning.

The ancient Greeks had more than one word for time.

There was Χρόνος (Chrónos), the time that flows relentlessly, measured by clocks, calendars, and the ageing of our bodies. It is the time that runs, pushes us forward, and often makes us feel we are always late for something.

But the Greeks also spoke of Καιρός (Kairós): the right moment, the opportune moment, the instant when circumstances come together and something becomes possible. Unlike Chronos, Kairos cannot be measured in hours or minutes. It must be recognized.

Perhaps we spend too much of our lives chasing Chronos, when we should sometimes pause and listen for Kairos.

There is a time to sow, a time to harvest, and a time to let the earth rest. There is also a time to act, and a time to wait.

Interestingly, other ancient cultures developed similar ways of thinking about time. In Sanskrit, Kāla (काल) refers to time in its chronological and universal sense, while Ritu (ऋतु) describes time as a season or a qualitative moment—a period defined by its particular nature and significance.

The curious thing is that time does not pass at the same speed for everyone. A minute of anxiety can feel like an hour, while an entire afternoon of happiness may disappear in an instant. A child experiences summer as an eternity; an adult may wonder where the years have gone.

Chronos is the time we share. Kairos is the time we experience.

The deepest mystery of time, for me, is not how quickly it passes, but why it feels so different depending on who we are, what we are doing, and what we are waiting for. Two people can share the same hour, the same year, even the same lifetime, yet experience it in profoundly different ways. The distance between them is not measured in space, but in the way they inhabit time—as if they were living in different dimensions.

Which kind of time are you living in today?

kairos, time experienced

Credit:

The image shows a relief of Kairos, the personification of the opportune moment. Why the long hair at the front and the bald back of his head?

The symbolism is brutally simple: when Kairos approaches, seize him by the hair. Once he has passed, there is nothing to hold on to. No amount of regret can bring the opportunity back.

The original reliefs associated with Kairos are preserved today at the Archaeological Museum of Trogir, Croatia, and the Kunsthistorisches Museum in Vienna.

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.

In Between the Strokes

Gianni Sarcone

These two minimalist Zen compositions exploit our brain’s tendency toward pareidolia and the Gestalt principle of closure: we instinctively connect isolated strokes, filling in what is missing until a familiar presence begins to emerge.

A few seemingly unrelated brushstrokes can be enough to suggest something—or someone—we recognize.

Can you see the hidden figures?

☞ For further exploration, visit my Subliminal Faces gallery.

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.

Is Nature Already a Work of Art?

Gianni Sarcone

Art may not be exclusively a human affair. Nature has its own creative force and aesthetic power. Crystals, shells, clouds, and landscapes produce forms and patterns that we often find as fascinating as works made by artists.

Without disturbing Kant too much—and his somewhat dated distinction between natural and artistic beauty—where does art actually begin?

Nature: the original artist?

Nature creates without any apparent intention. It does not try to please us or express an idea, yet it can produce forms of extraordinary complexity and beauty.

  • Spontaneous beauty: Crystals, landscapes, spirals, symmetries, and biological patterns can display structures we perceive as beautiful.
  • Creation without a plan: Nature produces forms without an artist, a blueprint, or even an audience.
  • Our first inspiration: From the beginning, humans have observed, imitated, and transformed natural forms into their own creations.

For Kant, this is precisely where the difference lies: a work of art involves intention and a concept of what it is supposed to be, whereas natural beauty can be appreciated without knowing any purpose behind what we see.

But is intention really necessary?

Does art require intention?

The idea that we must know what an artist intended in order to understand or judge a work has been questioned for a long time. In 1946, William Wimsatt and Monroe Beardsley famously called the attempt to use an author’s intention as the basis for interpretation the “intentional fallacy.”

And art can go even further.

It can be improvised, accidental, discovered rather than made. It can emerge from a chance encounter between an object and a particular way of looking at it.

Leonardo da Vinci already understood this. He suggested looking at stains and irregular patterns on old walls because they could trigger visions of landscapes, battles, figures, and strange compositions. Chance could become a generator of images.

In other words, the work is not always entirely in the object.

Sometimes, it appears in the eye of the beholder.

Take a stone polished by the sea. It might suddenly remind you of a sculpture by Henry Moore. Nobody sculpted it. Nobody intended it to represent anything. Yet your brain detects a form, gives it meaning, and perhaps even sees a sculpture.

So—is it art?

From found object to readymade

With Marcel Duchamp, things get even more complicated.

The readymade takes an existing object, removes it from its ordinary context, and presents it as art. Duchamp began exploring this idea as early as 1913 with Bicycle Wheel.

The object itself may have little or nothing to do with traditional ideas of beauty. What changes is the context, the choice, and the way we look at it.

Art therefore moves, at least in part, from something made by the artist to something that can be selected, discovered, and reframed by the artist.

And this makes the boundary between creating and discovering surprisingly thin.

A natural form can resemble a sculpture. A stain can become a landscape. An ordinary object can become a work of art. And sometimes a work becomes art only because someone recognizes it as such.

Perhaps the artist does not always create something from nothing.

Sometimes, the artist does something more subtle:

he reveals what everyone else was looking at but never saw.

So where, exactly, do we draw the line between art and non-art?

And ultimately, what makes something art: the object, the artist’s intention, or the eye of the beholder?

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.

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

The Deceptive Oriental Fan

Gianni Sarcone

One of my earliest color illusions, created back in the 1990s, when I was immersed in exploring the physiology of color perception.

Do the pleated sections of the fan really have two different shades of brown?

They don’t. Every pleated “accordion” section is exactly the same brown. Only the thin light and dark bands bordering each fold differ. Those subtle edge contrasts trick your visual system into seeing alternating tones where none exist.

The color is perfectly uniform, but your brain interprets it differently depending on the surrounding contrast—a classic example of simultaneous brightness contrast.

Art as an Open Circuit

Gianni Sarcone

Art is sharing—an offering from the artist to the audience. Every audience calls for its own officiant.

In technological terms, a work of art is an output searching for an input. Without that exchange, it remains only a possibility. It comes into existence through its encounter with another mind, where it can generate emotion, doubt, rejection, or wonder. A work is born once in the artist’s mind, and then again in the mind of the person who experiences it.

The artist is a translator between an inner vision and the outside world. They offer a fragment of themselves, without ever being able to control how that offering will be interpreted. Every audience recognizes the artists who resonate with its own sensibility, its questions, and its time. Every audience calls for its own officiant.

But does an art exist that cannot be shared?

If we define art not as the final object—the painting, the book, the symphony—but as the state of consciousness and the act of creation itself, then that art is fundamentally impossible to communicate. The finished work is only a trace, the imprint of an inner experience that no one else can truly access. What the audience receives is never the act of creation itself, but its remainder: its echo, its shadow, and sometimes even its misunderstanding.

share your art
(To illustrate this point, I’ve added an ironic image circulating on the net. I hope you appreciate the irony—and my sense of humor.)