I am working on a new two-dimensional variant of the Müller-Lyer illusion… You may be surprised to know that the Müller-Lyer illusion isn’t only linear: it involves plane geometry too! In fig. A shown below, the ends of the blue and red collinear segments, arranged in a radial fashion around a central point, delimit two perfectly concentric circles. However, for most observers, they seem instead to define a large ovoid that circumscribes another one, slightly eccentric (Fig. B). This comes from the fact that the red segments seem to stretch towards the lower part of the figure, while the blue segments seem to stretch towards the upper part of the same. As you can see, in this variant comes also into play the “neon color spreading” effect. In fact, a bluish inner oval-like shape appears within the black arrow heads (Fig. A), though the background is uniformly white.
Geometry
The Astounding Art of Arrangements
Sometimes, man lets himself go to this abstracted ‘diversion’, which involves assembling or arranging pieces, counters or any small familiar object. This compulsive behavior is evidence of a geometrical sense, which is natural and irrepressible. This is the same behavior, which drives some birds instinctively when they collect and group shells, glittering or colored objects to lavishly decorate their bowers. So, assembling and arranging objects is not only a cerebral activity but, indeed, a primitive geometric urge.
Continue Reading
Optical Illusions Using Typography & Shadowcasting
With help of typography and light you can make a lot of amazing visual effects! The game is all a question of symmetry…
A l’aide de la typographie et de la lumière, on peut créer beaucoup d’effets visuels intéressants! Le tout tourne autour de la symétrie…
Snowmen Are Boring
Winter is approaching. Here is a geometric construction you can build with your children in your backyard: a perfect pentagonal snowdodecahedron…
Fibonacci’s dog
Did you know that Fibonacci had a golden retriever who inspired his spiral aptly called “Golden Spiral”? (Hey, I am joking!)
The Fibonacci spiral is frequently regarded as an approximation to the “golden spiral”, which is a logarithmic spiral whose growth factor is ø, the golden ratio.
You Can’t Possibly Color This!
An Impossible Optical Illusion Activity Book
No mere coloring book, You Can’t Possibly Color This! is an eye-spinning experience that will inspire and astound. That’s because you’ll be coloring in optical illusions — things that can only exist on the page. With a just a few tips, you’ll be coloring in things that will bulge, expand, and even rotate. Other objects will leave you confused as you try to figure out the “trick,” while mandalas, complex patterns, and labyrinths will mesmerize you. Also included are fun activities for drawing and creating your own optical illusions.
Typographical Curiosity About Numbers
“Why do the digits look like they do?” to answer this recurrent question one may find on the web many strange and diverse theories on the origin of the shapes of our modern, Hindu-Arabic numerals. Unfortunately, most if not all of those theories are patently false! One that went viral claims: “Our present method of writing figures is based on an early Arabic geometric design (see below) where each digit contains its own number of corners or angles, for instance the digit 1 contains one angle, the digit 3 has three angles, the digit 7 has seven angles and so on.” It’s not an exaggeration to say that it’s just plain nonsense!
Let us leave aside these abstruse theories, as there are a whole range of serious and documented books on the origin of numbers, including Georges Ifrah’s excellent book “Universal History of Numbers“.
However, there is nothing preventing us from finding or inventing original and / or fun typographic methods to create numbers, like the one illustrated below, which requires only two stylized numerals: a 4 and a 8.
Would you dare run on it?
This wavy floor is actually a mind-boggling optical illusion that discourages people from running down the hallway (in fact, the floor is a completely flat surface!).
Manchester firm Casa Ceramica used a neat combination of black and white tiles to make the floor along the hallway look as though it is uneven making the tiles appear to slope away into a dip.
The illusion only works in one direction, so you will be perfectly safe on the way out.
The making of the floor.
Many visual illusions have already been used to try and slow down traffic like this 3D-painted zebra crossing trialed in Iceland that provides an illusory effect of white blocks floating over the road.
Turning Klein’s quartic curve inside out
Klein quartic has 24 symmetries forming a group isomorphic to the rotation/reflection symmetry group of a tetrahedron. Algebraically speaking, this group is S4: the permutations of 4 things.
Art & Math
Pattern with Arabesque paths moving in a linear fashion induces rotational motion to a hexagonal device.
