XIV:Magical Geometrical-Optical Illusions

XIV : Magical Geometrical – Optical Illusions 
         [Contd.A Journey to the Wonderland of Math.by Ajay Kumar Chaudhuri]

Our eyes cannot always be believed absolutely. As mirages in deserts appear real to us, so also many other things those perceived by our vision. Do your eyes ever play tricks on you? May be you have seen something that puzzled you so much that you had to rub your eyes and look again? Chances are you may have been tricked by an optical illusion. Literally, optical means relating to light or optics and illusion means an erroneous mental representation or a false idea. So, optical illusion is actually an experience of seeming to see something that does not exist, or in other words, optical illusions are images or pictures that we perceive differently than they really are. In fact, optical illusions occur when our eyes send information to our brains that tricks us into perceiving something that does not match with reality.

But we are interested particularly in geometrical optical illusions. What are those illusions? Geometrical optical illusions are visual illusions, also optical illusions in which the geometrical properties or what is seen differ from those of the corresponding objects in the visual field. So, geometrical optical illusions are closely related to optical illusions and hence let us explore the charms of optical illusions first.

Basically they are of two types : physiological and cognitive. The physiological illusions are caused by some sort of physical means in the eyes or brain. In general, optical illusions are the use of shapes, colours, and line distortions to trick eye and brain. When viewing confusing images, our brain can sometimes interpret visual information incorrectly, or sometimes our brain simply does the job of filling in the missing pieces. So we end up getting deceptive or misleading images to our brain. As a result, there is a good chance that our universe is interpreted by our brain differently than what it really is, as well as many things that we encounter in our daily life. Then could we simply be getting distorted images about our whole life? Or, are optical illusions limited phenomenon to only certain cases that are explained scientifically? Briefest reply it may be suggested that don’t believe your eyes always for granted, as they may sometimes mislead you. Let us first look at some interesting images as in Pic. No. 23(a) and 23(b).

In Pic. No. 23a the horizontal lines (black & white) look tilted a little bit upwards or down wards, but in reality they’re straight. In Pic. No. 23b, stare at the centre of the circle, and move your head back and forth towards picture and away from it. The circles appear to slide back and forth.

                 Pic. No.23a.

                                                Optical illusion--horizon lines look tilted

                                                      (Popularly known as Cafe Wall illusion)    

       Pic. No.23b

                                                                A sliding circle.           

The other type of illusion is cognitive illusion, as has already been mentioned. These types of
 illusions are assumed to arise from misinterpretations of the visual world by our mind in the process of acquiring knowledge and processing thoughts leading to “unconscious inferences”. This very idea of the cognitive illusions was first suggested by German physicist and physician Hermann Helmholtz.

So, physiological illusions are the effects on the eyes or brain of prolonged stimulation of a specific type: brightness, tilt, colour, movement. While the cognitive illusions interact with different levels of perceptual processing and inbuilt assumptions or “knowledge” become misdirected.

Perhaps the greatest of the mysteries known to us is the highly complex human mind and its strange behaviours. As cognitive illusion is a child of our mind, so let us first look into our mind, at least in a nut shell.

The most perplexing questions are: What is happening when we think? Is our mind just the result of electrochemical activity? Or is there something more to our consciousness – something beyond physical measurement? Is the human mind the ultimate unexplored frontier?

The human race has explored mysteries in seemingly every corner of creation. To satisfy our boundless curiosity we have ventured into the highest mountains, death-trapping deserts, expedition to the perilous South Pole of the Earth, the hazardous journey to space including to the moon. Even where we cannot go ourselves we are sending machines to explore for us, hurtling complex probes to the very edges of our solar system and beyond.

Yet even as human beings apply their marvelous minds to the understanding of the unknowns before us, one area remains, perhaps, the greatest mystery of all: the human mind itself!

In many ways Science in recent years has come to understand more about our brain than ever before. Our brain has different parts and each part has an important role to play, such as related to reason, thought and emotion – even to moral judgement – are beginning to yield some of their secrets.

But as more is learned about the human brain, the human mind seems ever more mysterious! Some of the scientific findings concerning the brain and mind seem contradictory, pointing to a marvelously complex physical structure, but also to something that extends beyond not only the physical but also beyond our ability to measure or count.

So, what is it about the human mind that makes us so remarkably different than the animals around us – capable of so much more? What is the answer to the mystery of our mind?

Modern researches on human mind and brain have findings seem to show clearly that much of – who we are, our personality, our ability to make moral choices and judgements are profoundly dependent on our physical brain. So, the pertinent question is: is the human brain all is to human mind?

Many scientists answer, “Yes”. Most researches in the field of neuroscience conclude that our entire individual identify – our likes and dislikes, our values, our personality – is completely dependent on physical combinations of molecules and electrical impulses in our brain. For them, there is no mystery of the mind, because they have concluded: there is no mind!! In their view, human thought, consciousness, moral judgment, free will – everything we call the “mind” – is an illusion, perpetuated by physical brain acting mindlessly according to the laws of chemistry and physics, and the chance of combinations of chemicals in our brain matter.

But this view, however, is increasingly being challenged by further findings that seem to demonstrate that human mind is very real, and is somehow much more that cannot be explained by a physical brain alone.

In fact, up till now scientists have not been able to disprove undoubtedly the existence of mind. On the contrary, there are evidences that despite a human having virtually no brain may be otherwise normal. The interesting and much debated research of the British neurologist John Lorber, (a Hungarian) of Sheffield university published in 1982 has taken many by surprise, as he has studied startling cases of people who have led otherwise normal lives despite having almost no brain at all. One of the most illustrious cases involved a “Socially completely normal” college student with an IQ of 126. (We may recall here that the famous Scientist Stephen Hawking and Albert Einstein each has an I.Q of 160) who had earned a first class honours  degree in mathematics. Yet scan of this amazing young man’s skull indicated that he had virtually no brain.

If human mind is nothing more than human brain, how are such cases explained? Moreover, scientific research is beginning to demonstrate more clearly than ever that the human mind and free will are not mere illusions generated by the physical brain.

Some scientists opine that mind is supposed to be merely the effect and physical brain the cause. But studies are demonstrating that the reverse can also be the case. Far from the brain creating mind, Scientists are discovering that mind can change brain – it is a “two way street.”

Hence in fine, we may conclude that a human being may be “brainless” but not “mindless”. So, if someone asks you, “is your brain really necessary?” The answer will be a big “No”.

Now let us see how often we are misled or befooled by cognitive optical illusions – the handiwork of our mind. They may appear before us broadly in three ways as – ambiguous, distorting and paradox illusion. These illusions occur when our brain automatically make assumptions based on the information sent from the eyes. They are sometimes called “mind game”.

Have you ever seen a picture that may be both a duck and rabbit at a time or a young lady and an old lady simultaneously or any such pictures? These are a few examples of ambiguous optical illusions.

So, ambiguous illusions are pictures or objects that generally present the viewer with a mental choice of two interpretations, each of which is valid. Often the viewer sees only one of them, and only realizes the second, valid, interpretations after some time or prompting, when they attempt to simultaneously see the second and first interpretations, they suddenly cannot see the first interpretation any more, and no matter how they try, they simply cannot grasp both interpretations simultaneously – one occludes the other.

Here are three very interesting and famous ambiguous optical illusions as we see in Pic. No.23(c), (d) and (e).

            Pic. No.23c.

                                                                        Rabbit or Duck?

             Pic. No.23d.

                                                                 

                                                                 The Rubin Vase.

                           

                     Pic. No.23e.

                                                                  Young or Old lady?

What do you see in the Pic. No. 23c, rabbit or duck , duck or rabbit – or neither of the two? That’s the question taking social media by storm and debate rages about what the image really is, despite being drawn more than 100 years ago, the image is an illusion which can tell a lot about how a person’s brain works.

Although it appeared in German magazine about in 1892, it was later made famous by U.S. psychologist Joseph Jastrow in 1899.  Jastrow used the illusion to make the point that we ‘see’ with our brains as well as our eyes. The research suggested that more creative people were able to switch between images of the two animals more quickly than other people.

When testing children at different times of the year, the results change. During Easter, they are more likely to see a rabbit first. In October, seeing a duck first is more ‘common’.

But for social media users, reactions range from surprise, amazement and frustration, to ridicule of the image.

Another very interesting and famous optical illusion is “The Rubin Vase” illusion as shown in Pic. No.23d. It was first developed by a Danish psychologist Edger Rubin, although similar images can be found in the eighteenth century French prints. This was first introduced in 1915.

This illusion generally presents the viewer with a mutual choice of two interpretations, each of which is valid. One interpretation is of two black faces in the fore ground with a white back ground. The other is a white vase in the foreground with a black back ground.

The Rubin vase illusion is considered to be one of the best of an optical illusion.

World’s most famous, mindboggling and brain – teasing another example of ambiguous optical illusion is the portrait of a young lady and an old woman as shown in Pic. No.23e, named fondly “wife and mother-in-law” by its creator Edwin Boring (1886 – 1968), an American experimental psychologist, a professor of psychology who wrote a paper about it in 1930 and was interested in illusion and perception.

This illusion has a venerable history. The first documented instance of it is in a German postcard from 1888. This is the most detailed version there is, with a lot of shading in the hair and eye- ear. This shading and detail work may be why the old women seem to be most prominent in the picture.

Ambiguous illusions are so powerful because even after we know that both images are on the page, we can only see one of them at a time. When we see the young girl, we can’t simultaneously see the lines in context of the mother-in-law. When we switch our perception, the young girl disappears and we only see the old woman. Generally, we switch from one to the other by focusing on one part of the image. Looking at the cheek and nose in profile make the young girl spring forward Looking at the “eye” will let us see the old woman. Essentially, when we focus in on certain details, our brain makes sense of the rest of the image around these contours. Ambiguous illusions show the way that vision is a work of both the eye and the mind. The eyes take in a set of lines, and depending on what they see, the brain organizes then into a recognizable pattern which we then ‘see’. We can’t see both images at once because, at least at first it isn’t possible for the brain to construct both the images and over lay one on the other, while it is possible to train the mind into recognizing two sets of pattern at once, that fact that it is a process shows that “Seeing” is still a matter of mental practice, not simply taking in an image passively with one’s eyes.

Another cognitive optical illusion we come across sometimes in our everyday lives are the distorted or deformed appearance of objects in our perceptions which is called “distorting optical illusions.”

Distorting illusions are characterized by distortions in length, size, or curvature (the degree to which something curved). A striking example of this type of optical illusion is the “café wall” illusion (which we have seen in Pic. No.23a as a physiological illusion). It was first described by Dr. Richard Gregory observing the curious effect in the tiles of the wall of a café at the bottom of St. Michael Hill, Bristol. This optical illusion makes the parallel straight horizontal lines appear to be bent.

There are some classic examples of distorting optical illusions such as Mueller – Lyer illusion, Ponzo illusion, Hering illusion and many others.

The Mueller – Lyer illusion [Pic. No. 24a] is an optical illusion consisting of nothing more than an arrow. When viewers are asked to place a mark on the figure at the mid-point, they invariably place it more towards the tail end. Another variation consists of two arrow-like figures, one with both ends pointing in, and the other with both ends pointing out. When asked to judge the length of the two lines, which are equal, viewers will typically claim that the inward pointing pair is longer. A possible explanation is that the line with arrows pointing inwards may simply appear longer because the arrows themselves extend past the line. In Ponzo illusion [Pic. No.-24b] a pair of converging lines distort the perception of two identically sized lines.

          Pic.No.24a.

                                                                Mueller-Lyer illusion.

             Pic. No.24b.    

                                               

                                                                     Ponzo illusion.

                                                                                    

The Hering illusion is, one of the geometrical - optical illusion and was discovered by the German physiologist Ewald Hering in 1861. The theme of the picture is: When two straight and parallel lines are presented in front of radial back-ground (like the spokes of a bicycle), the lines appear as it they were bowed outwards. [Pic. No. 24c]

           Pic.No.24c.

                                                                      .

                                                                  Hering illusion.

There is another type of optical illusion, called “paradox illusion.” When our eyes see an object of the visual world, send an image to our brain then responds at once to make sense of it. But sometimes our brains get it wrong, leading to conclusions appear to be fine to our eyes, but in fact are self-contradictory, even absurd though may be true. These situations are referred to as “paradoxes”.

We have already seen some examples of paradox illusions, such as Penrose impossible triangle, Penrose stairs and M.C. Escher’s paradoxical waterfall in pictures No. 22 (c), (d) and (e), relating to tessellations. These are a good many examples of unbelievable and amusing optical paradox illusions in the visual world around us.

Why is the nature so beautiful? Why does the sight of flowers, butterflies, rainbows fill our hearts with joy unspeakable?  The world is dotted with spectacular natural oddities that may seem too strange to be real. But they are indeed, real – why? The answer to this profound puzzle lies a little beyond the reaches of present day science, but in the realms of the super-consciousness.

Mother Nature is a perennial source of beauties and aesthetic ideas to us. She never ceases to amuse us. You find so many surprising things in nature around you that will make you astounding how great an artist is she! Let us discover some illusions of her artistic creations.

Illusions in nature offer you some unique fantasy that appears in nature at some places and have been captured by people who were amazed at them. Let us see some of those masterpieces with our own eyes.

In Pic. No. 25a, you can clearly see the shape of lips in this flower which is really ante and looks absolutely magnificent. You must have seen a lot of different kinds of flowers. Some of them definitely amazes with their colours and fascinating shapes. This flower is not an exception. But the photograph taken from a unique angle makes it special. How it will look, if taken from any other angle is of course, definitely not known. It is really amusing how nature has crafted this world with her intrinsic art.

               Pic. No. 25a

                                                         Illusion of lip in a flower.

Are we seeing the image of Eve, the progenitor of human race or the figure of Mother Nature herself in this tree trunk in Pic. No. 25b? After all it is her work and she had crafted the tree with her artistic approach. The artist who captured this impactful illusion through his lens so perfectly the appropriate angle deserves heartful praise.

Another wonderful paradox illusion in nature is this tree in a dancing posture of a young girl. We can clearly perceive the figure of a girl who is supposedly performing a dance move, lifting one of her leg in the air. The two branches those are projecting upwards fill in for her hands. Surprisingly enough, we can even make out the chest line in the Picture No. 25c.

                   Pic.No25b.

                                                          Illusion of a female figure in a tree.

                                                                              
             Pic. No25c

                                                         Illusion of a dancing girl in a tree.                

Thanks to the photographer for choosing an excellent camera angle making the photograph so vivid that it does not need much to explain the context. A work of nature is indeed glorified by him.

The picture in 25d is self-explanatory. We are viewing a beautiful seascape from a part of an island. But what is surprising, a thirsty horse apparently drinking water touching the water surface. So, undoubtedly it is also an excellent image of illusion in nature.

            Pic. No. 25d

                                                       Illusion of a thirsty horse in a rock.

So, we have a glimpse of different types of optical illusions, their causes, some of their characteristics and types with some wonderful and amazing images. These illusions are actually the handiwork of either our two human organs – eyes and brain or of our unfathomed mysterious mind. As we are exploring the intrinsic role of mathematics around us, so the pertinent question arises: Has mathematics any direct or indirect role to play in these illusions? Let us try to find an answer, whatsoever.

Visual illusions with different effects can be found in numerous places, challenging the interests of scientists, artists and artisans. Artist M.C. Escher utilized several optical illusions in his works, which we have already seen, baffling the minds of mathematicians, scientists and all other viewers. Optical illusions play an important role in both for our appreciation and perception of the physical world. Many optical illusions are very mathematical and geometrical in nature.

Though it cannot be said definitely about the mathematical significance of illusions, yet we can show some ways that mathematical concepts can help explain optical illusions.

As we live in a three dimensional world (objects having length, breadth and height are of three dimensions) so the important question is: how does our visual system recover three dimensional information? The answer is: our retinal images, whether from a two dimensional image or from the three dimensional world, are flat representations on our curved retinal surface. Yet, for the most part, we perceive an accurate world of depth, surfaces and objects.

Among many kinds of optical illusions, some have elements of geometry in their construction or in the way scientists analyse them. The main point of optical illusions, however has nothing to do with geometry, unless it is a negative connection: our eyes and parts of our brain that process vision, were not designed with the need of geometers in mind.

Yet it may be said that most optical illusions involve math, because they are tricks based on human perception of space. However, the trick to most optical illusions is not the math, but the way the human mind perceives or misperceives colour, shape and/or spatial relationship.

But there are some optical illusions and other similar works that involve more math than others, specifically things like, Penrose triangle [Pic. No. 22(c)], café wall illusion [Pic. No. 23(a)], Muller Lyer illusion [Pic. No. 24(a)], Ponzo illusion [Pic. No. 24(b)], Hering illusion [Pic. No. 24(c)] etc. which we have already come across.

These are basically the examples of geometrical optical illusions. But before going to study the interesting geometrical optical illusion and some more examples of it, let us see how do we “see”, along with what are two dimensional (2D) and three dimensional (3D) images we see every now and then anywhere and everywhere.

We know light is a form of energy and gives us perception of vision of this beautiful world. Scientists have brought to light many mysteries of light. One of them is that, it propagates through electromagnetic waves and another is: White light is composed of lights of seven colours --- violet, indigo, blue, green, yellow, orange and red, abbreviated as VIBGYOR, which was conclusively proved by the famous scientist of all ages, Isaac Newton.

We see the world in colours of red, green, and blue, but most other animals only see in yellow and blue. Some species - fish, reptiles and birds have four colour visions and are able to see ultraviolet or infrared light too.

The structure of human eye is so complex that it is hard to believe that it is not the product of intelligent design, but by looking at the eyes of other animals, scientists have shown that it evolved very gradually from a simple light-dark sensor over the course of around 100 million years. It functions in a very similar way to a camera, with an opening through which the light enters a lens for focusing and a light-sensitive membrane at the back.

The amount of light that enters the eye is controlled by the circular and radial muscles in the iris, which contracts and expands to alter the size of the pupil. The light first passes through a tough protective sheet called cornea, and then moves in to the lens. This adjustable structure bends the light, focusing it down to a point on the retina, at the back of the eye.

The retina is covered in millions of light sensitive receptors known as rods and cones. Each receptor contains pigment molecules which change shape when are hit by light triggering an electrical message that travels to the brain via the optic nerve and gives us perception of vision. From Pic. No. 26, we may get some idea about different delicate parts of other most important and precious organ, eye.

Pic. No. 26

                                       

                                                             Science of our vision.

Our eyes are only able to produce two- dimensional images, but with some clever processing, the brain is able to build these flat pictures into a three dimensional view.

We have met earlier several times this terminology of “dimension”. A material body whatsoever, a solid or a fluid (in a container) invariably has length, breadth and height, each of these quantities is termed a “dimension”.

The image of such a body of three dimensions (3D) on a flat surface, as on a sheet of paper, is of two dimensions, having length and breadth. So the image of a real flower is not the flower itself. Painting photographs and computer images are in 2D regardless of what they depict. Sculptures on the other hand, are in 3D.

All illusions, including illusions with geometrical figures, are visual and optical in nature. The main feature of geometrical optical illusions is that the geometrical properties of what is seen differ from those of the corresponding objects in the visual filed. It may be playful not only for kinds but also for the elders.

Geometrical optical illusions are examples of how our mind attempts to find orderly representations out of sometimes ambiguous and disorderly two–dimensional images transmitted from our retina to our brain are imperfect representation of reality as our eyes are capable of producing two dimensional images but not the three dimensional objects accurately.

Geometry is a branch of mathematics that is concerned with the properties of configurations of geometric objects like points and circles being the most basic of these Although the word “geometry” derives from the Greek geo, means earth and metron means measure which points to the practical roots. So, in studying geometry, one concentrates on the position of points, on the length, orientation and curvature (the degree to which something is curved) of lines. So, geometrical optical illusions then relate in the first instance to object characteristics as defined by geometry. Though our vision is three  dimensional, in many situations depth can be factored out and alteration concentrated in a simple view of two-dimensional tablet.

Optical illusions have been a part of our day-to-day experiences from times immemorial. Once people understood the science behind illusions, a lot of experimentation was done in the form of painting and other visual arts.

. Many artists, scientist, psychiatrist and persons of other walks of life also created and designed many optical illusions including geometrical illusions. Each of such illusions is named after its creators. You may also try to create one or more such hoodwinking and mind duping tricky illusions.

Galileo Galilei perceived this universe as written in the language of math and letters are triangles, circles and other geometrical figures. There is math, so to say, geometry strewn around us in nature. We have already seen many amusing optical illusions among which some are geometrical in characteristics.

Many things cause geometrical optical illusions among them are location of an object in the visual field, whether the extent of an area is filled or empty, contour, contrast and perspective.

Have you ever noticed that an empty room looks smaller than when it is furnished? Or walls covered with a paper pattern look larger than painted in a uniform colour? Or (most probably and controversially) women wear horizontal stripes in order to look taller?

These things occur for optical illusions to our eyes. Let us see some interesting geometrical optical illusions and enjoy their fantasies.

It will be interesting to note that when a stick say, one metre of length, looks longer when it is held upright or vertical than when it lies on the horizontal ground. This is a simple case of illusion , the vertical – horizontal illusion. This illusion is more prominent in case of a position like inverted T (丄). Here involves a bisecting component that causes the bisecting line to appear longer than the line that is bisected. We often overestimate or underestimate the length of the bisecting line relative to the bisected line of the same length. This may even happen if we are aware that the lines are of the same length. [Pic. No. 27a]
           
             Pic.No.27a.

                                                               Vertical- Horizontal illusion.

                      

There are mainly three configuration of the vertical- horizontal illusions, such as the L configuration, plus (+) configuration and inverted – T ( 丄) configuration. Of these three the inverted configuration produces the highest but when the bisecting line of T illusion is configured horizontally, the illusion magnitude is lowered.

Sometimes angles cause optical illusions. For example, in the vertical-horizontal illusions, the right angle (90 degree) plays the leading role. Similarly acute angles (less than 90 degree) may also create optical illusions. Such an illusion is the Zollner illusion. It is a classic optical illusion named after its discoverer, a German astrophysicist Johann Karl Friedrich Zollner. In the Pic. No. 27b, the black lines seem to be unparallel, though parallel in reality. The shorter lines are at an angle to the longer lines. This angle helps to create the impression that one end of the longer lines is nearer to the viewer than the other end. Probably, the Zollner illusion is caused by the impression of depth.

               Pic. No. 27b.

                                                                Zolner illusion.

If this illusion is printed in green on a red background and the red and green are equally bright, the
  illusion disappears

In 1860, Zollner sent this discovery in a letter to the physicist and scholar Johan Christian
Poggendorff, editor of a scientific journal of physics, who subsequently discovered a similar type of illusion, Poggendorff illusion, named after its discoverer.

The Poggendorff illusion [Pic. No. 27c] is a geometric optical illusion which involves the misperception of the position of one segment of a transverse line (slanting line) that has been intercepted by the outline of an intervening structure, here a shaded rectangle in the adjoining picture. The illusion is a straight black and red line is obscured by a grey rectangle. The blue line, rather than the red line, appears to be a continuation of the black one, which is clearly shown not to be the case on the second picture. Instead there is an apparent position shift of the lower portion of the line. The magnitude of the illusion depends on the properties of the obscuring pattern and the nature of its borders.

              Pic. No.27c.

                                                                    Poggendroff illusion.

                    

The amusing fact is that there is similarity among zollner illusion, Proggendorff illusion, Muller-Lyer illusion and Hering illusion. Al these illusions demonstrate how lines can seem to be distorted by their background.

There is another type of geometrical optical illusions, which evoke perception of an edge without a luminance or colour change across the edge, called illusory contour. The name of the German Psycologist Walter Ehrenstein (1899 – 1961) is closely associated with such illusions – the Ehrenstein Illusion.

In fig. 27d, the sides a square placed inside the pattern of concentric circles take an apparent curved shape.

            Pic.No.27d.

                                                                    Ehrenstein illusion.

                                                          

In fig. 27e, we can readily perceive the illusion of a circle, an example of illusory contour sometimes dubbed as “Ehrenstein” in honour of its designer.

          

                       Pic. No. 27e.                                    

                                                                     Illusion of a circle.

Adding a circle destroys the illusion. Have you realized that the apparent figs have the same colour as the background, but appear brighter.

A similar famous illusory contour we perceive in the fig 27f. We can see clearly a white triangle and a white square on the background defined by a sharp illusory contour occluding three or four black circles and a black-outlined triangle, a square whose sides consist of spatially separated fragments.

           Pic. No. 27f

 

                                                         Kaniza illusion in a triangle.

                                  

Gaetano Kanizsa’s 1976 American paper makes the resurgence of interest in illusory contours for vision scientists. This illusion is named Kaniza’s Triangle as a mark of respect of its designer. However, illusion contours were present in art dating back to the middle ages.

The list of geometrical optical illusions in particular and optical illusions in general is dynamic and hence may never be able to satisfy particular standard for completeness. More and more are expected to be included in this list in coming days. Any person interested in this field, including yourself, may enrich it by discovering or designing an amazing illusion which may be dubbed by your name.

Now, before leaving the labyrinth of the world of illusions, let us have a glimpse of three more optical illusions relating to geometrical figures.

In fig. 27g, we see an optical illusion at relative size perception. The two black circles are exactly of the same size, have been placed near to each other and one is surrounded by annulus. The interesting fact is that the surrounded circle appears larger than the unsurrounded circle if the annulus is close, while appearing smaller than the non-surrounded circle, if the annulus is distant.

Pic. No. 27g

                                                      Delboeuf illusion of two black circles

This is known as “Delboeuf illusion” after the name of its discoverer a Belgian philosopher, mathematician, experimental psychologist, hypnotist and psychologist Joseph Remi Leopold Delboeuf (1831 – 1896).

All of us are familiar with grills, fitted in our houses. Many of them are crisscross frame work of spaced bars that are parallel to or cross each other, called a grating or a grid.

The two most common types of grid illusions are Hermann grid illusion and Scintillating grid illusion. [Pic. No. 27h]

         Pic. No. 27h

                                                               Hermann grid illusion.

                                                               Scintillating grid illusion.

The Hermann grid illusion was first introduced by Ludimar Hermann, a German physiologist and speech scientist in 1870. The illusion is characterized by “ghostlike” grey blobs or beads perceived at the intersections of a white or light-coloured grid on a black background. The grey blobs disappear when looking directly at an intersection.

Another grid illusion, similar to that of Hermann grid illusion, is the Scintillating grid illusion discovered by E. Lingelbach in 1994. It is constructed by superimposing white discs on the intersections of orthogonal (means perpendicularly) grey bars on a black background. Dark dots seem to appear and disappear rapidly at random intersections, hence the name Scintillating” meaning thereby sparkling or shining brightly. When a person keeps his or her eyes directly on a single intersection, the dark dot does not appear. The dark dot disappears if one is too close to or too far from the image.

The difference between the Hermann grid illusion and the Scintillating illusion is that the Scintillating illusions have dots already in place at the intersection, whereas there are no dots already in place at the intersections of the Hermann grid illusions. The other difference is that the Scintillating illusion does not occur with an isolated intersection, as in the case of the Hermann grid. It is found from observations that a minimum of 3x3 evenly spaced intersections with superimposed discs are required to produce the effect.

The last example with which we shall depart from this funny world of illusion is “White’s illusion”. It is essentially a brightness illusion.

White’s illusion is made up of a series of black and white horizontal bars, forming a grating along with two grey rectangles, one of which covered by the black horizontal stripes (rect. A), while the other covers those black bars (rectangle B). Observing the   Pic. No. 27i, it appears that the grey bars surrounded by the white stripes are definitely lighter or of higher luminance than the grey bar surrounded by black stripes.

Pic. No. 27i

                                                                 Whites illusion.

                                                             

If the on other hand, the grating consists of coloured stripes instead of black and white, a similar illusion occurs but bears a name – Munker-White illusion.

White’s illusion, as well as other numerous visual and perceptual illusions are not only a stock for fun but also provide valuable way to investigate how the eye and brain process visual information. Equally they are used by artists for visual effect, entertaining and satisfying the endless fascination human beings have with novelty and creativity.

                                                                                                                          [To continue]

Reference Internet.[All the images of this article( except otherwise stated ) are downloaded from Public Domain under Creative Cosmos CCO.]
Attribution: Pic No.23a--Cafe wall illusion (https://commons.wikimedia.org/wiki/File:Caf%C3%A9_wall.svg )
                   Pic.No24a--Mueller-Lyer illusion (https://en.wikipedia.org/wiki/M%C3%BCller-Lyer_illusion#/media/File:M%C3%BCller-Lyer_illusion.svg )
                   Pic. No24c--Hering illusion

 (https://commons.wikimedia.org/wiki/File:Hering_illusion.svg )

                  Image credit:Pic No25a--Illusion in a flower ,25b--Illusion of a female figure in a tree,25c--Illusion of a dancing girl in a tree,25d--Illusion of a thirsty horse in a rock.
Genius Puzzles:
(https://gpuzzles.com/optical-illusions/nature/)

                Pic.No26--Science of our vision:Attribution--Creative Cosmos
 (   https://commons.wikimedia.org/wiki/File:Schematic_diagram_of_the_human_eye_en.svg )

                  Pic. No27b--Zolner illusion:Attribution--Creative Cosmos((https://commons.wikimedia.org/wiki/File:Zollner_illusion.svg )
                 Pic. No27c--Poggendroff illusion:Attribution--Creative Cosmos (https://commons.wikimedia.org /wiki/File:Poggendorff_illusion.svg )
                  Pic.No27e--Illusion of a circle--Wikipedia ( https://en.wikipedia.org/wiki/Ehrenstein_illusion#/media/File:Ehrenstein_figure.svg )
                 Pic.No27f--Kaniza illusion of a triangle Attribution:Wikimedia Cosmos
   (  https://en.wikipedia.org/wiki/File:Kanizsa_triangle )
                 Pic. No27g--Delboeuf illusion of two black circles:Attribution
(https://commons.wikimedia.org/wiki/File:Delboeuf.jpg)
                 Pic.No27i---Whites illusion:Attribution
(https://commons.wikimedia.org/wiki/Fil)
Pic,No27f:Kaniza illusion--sent mail:https://www.illusionsindex.org/i/kanizsa-tri
                 Kaniza illusion of a square :https://www.researchgate.net/figure/Brighter-Kanizsa-sq