Embarking on a journey in a Klein bottle? Absolutely. A Klein bottle is a mind-bending non-orientable surface, defying the usual inside-outside norms. Technically, the ship’s navigating the interior…
Snag prints and cool merch from my online gallery.
Even bounded, my dynamic Müller-Lyer illusion works perfectly; the static segments of the star appear to alternately contract and expand.
With this work, I aim to push geometry to its limits, transcending the confines of color. My goal is to showcase the creative potential of simple concentric squares as a medium for experimentation and the discovery of new op art patterns. By delving into this exploration, I strive to unveil captivating illusions of color and mesmerizing motion.
Draw a large and a small square with thick lines and center them (Fig. A). Next, blend the inner and outer squares in six steps to create a set of concentric squares. Reproduce the set to form a larger square pattern, as shown in Fig. B.
In these minimalist op art pieces, I delve into the metaphoric realm of geometric shapes, with a particular focus on the hexagon as the foundational element for creating cubes and other simple three-dimensional regular shapes.
The artworks I present depict solid or three-dimensional structures that appear plausible and real, yet are in fact illusions known as ‘impossible figures.’ However, discerning these impossible figures isn’t immediately evident; one must concentrate on specific areas of the representation to grasp that they could never exist in reality! Drawing an impossible stereographic structure becomes achievable by merging two or more contrasting viewpoints or perspectives of the same object, or even by blurring the boundaries between the exterior and interior of an object…
The more ‘normal’ and ‘simple’ an impossible figure appears, the more captivating it becomes! Indeed, impossible objects aren’t created solely to bewilder the eyes; their purpose lies in confounding the mind and challenging one’s acquired visuo-spatial skills and stereographic knowledge.
The two intricate drawings displayed above and below combine two tribars to form an impossible isometric cube, showcasing a mesmerizing interplay between form and illusion.
Although NOTHING moves on the gif below – only the colors change! – it’s easy to spot which direction the wheel is “rotating”… But which side is in front? Which side the back?
Another hypnotic version in which still squares and diamonds seem to move, but only colors change slightly!
Inspired from the astrological tables, here is a new puzzle of my creation designed according to the ‘Golden Number Rules’, which is reflected in the proportion of each single piece of the game. Thanks to the balanced dimensions of its pieces, this puzzle acquires some intriguing magical properties!
This “math-magical” puzzle is composed of a tray in which the pieces are assembled.
Puzzle Quadrix (aka Quirinus), © 1992, G. Sarcone.
Some simple geometric patterns and designs, when repeated, can induce strong illusory shape distortions. Thus, visual misperceptions are very common in the op art world.
If dark and clear rectangular tiles are arranged in a checkered fashion, as shown below, there is obviously no illusion, but wait, just add at the intersection of these tiles some transparent dark and clear square patches, et voilà, magic appears!
So, transparencies can produce apparent linear distortions. The parallel red lines in this example look like being convergent / divergent.
Below are two neat optical illusion projects for which I was commissioned by “Art of Play”. From one perspective, the grooves in the metal die-cut bookmarks seem to be an abstract design but place the pattern against a solid clear or dark background and a familiar figure pops into view! These bookmarks are a sliver of wonder that hides between the pages to guard your place in any story.
Everything is relative with this magical bookmark of my creation depicting the famous theoretical physicist. Engraved with one of Einstein’s most famous quotations: “The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom the emotion is a stranger, who can no longer pause to wonder and stand wrapped in awe, is as good as dead; his eyes are closed.”
Geometric shapes are not limited only to the figurative aspect, they can also play active roles, for instance, serving in microelectronics to build operational printed circuits such as: small inductors (magnified, fig. a below), resistors (fig. b) and capacitors (fig. c). (image taken from my book “Almanach du Mathématicien en Herbe“)
I really love puzzle with less pieces as possible and with a contemporary design… This neat three-piece puzzle has been invented by Robert Reid and designed by puzzle-master Oskar van Deventer. The fit of the puzzle is perfect, though assembly can be really challenging.
