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“Here’s a special offer fail for you caused by mixing a pre-christmas special offer with a post-christmas sale.”

Thanks Stephen!

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Tau is introduced in The Tau Manifesto (by Michael Hartl and motivated by Palais, Robert [“Pi Is Wrong!“, The Mathematical Intelligencer, Volume 23, Number 3, 2001, pp. 7-8.]). It suggests that it is more natural to use the constant =2, rather than , for the circle constant.

Also, check out Vi Hart’s video about .

If you’re a -hater then just think, double the pie mmm…

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Source

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Introduction

The Sierpinski triangle is a fractal, attracting fixed points, that overall is the shape of an equilateral triangle. The triangle, with each iteration, subdivides itself into smaller equilateral triangles. The Sierpinski triangle is amongst patterns that are mathematically generated and can be reproduced, regardless of the reduction or magnification. 

Waclaw Sierpinski, a Polish Mathematician, was the first to study the fractal, examining in depth its mathematical properties. However, centuries before the works of the Polish Mathematician, artists and sculptors had made the pattern part of mosaics and artworks gracing the walls of cathedrals, churches, and basilicas. Perhaps, it is the elegance of the Sierpinski triangle that had made it such a celebrated decorative pattern even hundreds of years before the acclaimed mathematical publications of Sierpinski, after whom the gasket is infamously named. 

Amongst the oldest records of the fractal, the cathedral of Anagni, Italy, stood tall, adorning Cosmati mosaics, which were created using self-similar structures. A few other historical records of the fractal before Sierpinski’s works were found wreathing the carpets of the Roman Basilica of Santa Maria in Cosmedin. 

Like all knowledge, the Sierpinski triangle doesn’t originate at a single point in time but has had predecessors sharing some of its fundamental properties, such as the Apollonian gasket. It was first described in the 3rd century BC by Apollonius of Perga and further studied extensively in the 17th century by Gottfried Leibniz. 

How to make Sierpinski Triangle

The construction of the fractal is possible through various methods, ranging in complexity and application but rest assured, the end result is always a symmetric masterpiece.

The Trema Removal —

The process starts with a single equilateral triangle.

For the first iteration, the shape is subdivided into four congruent, equilateral triangles where the center-most triangle is removed.

Once the first iteration has taken place, the same step can be repeated on each of the remaining three triangles, as was performed on the original shape, for the second iteration.

The principal step can be repeated an infinite number of times, with the remaining triangles.  The removal method is based on the finite subdivision rule and conceptually is the easiest to understand and reproduce.

Shrink & duplicate —

Surprisingly this method doesn’t need to start with an equilateral triangle; in fact, it doesn’t even require a triangle at all for a Sierpinski triangle construction. 

So to begin, select any geometrical object. 

Once the decision regarding the shape has been made, the first iteration can be introduced by shrinking the shape two times and making three copies. Two of the three copies should form the base, whereas the third copy should be on top. 

Similar to the previous method, the principal step of shrinking and duplicating is to be repeated at each iteration for each of the copies made

Chaos game —

Even amidst chaos, the construction of a Sierpinski triangle is made possible. This method, by far, is the most creative and elaborate way to produce this fractal. Chaos game goes one step further than the selection and duplication method by not requiring a geometrical shape to begin at all.

To begin, select three points that can be connected to create a triangle. However, there’s no requirement to actually form the triangle, just that these initial points shall be referred to as the main points.

After the main points have carefully been marked, select another point within the triangle formed by the main points, this will be referred to as the current position.

Further, randomly select any one of the main points and by stretching an imaginary line between the current position and the selected main point, select the midpoint of the imaginary line. The midpoint is the new current position.

The previous step can be repeated an infinite amount of times, each time with the new current position.

The selected points naturally accumulate in the pattern of the Sierpinski triangle.

The Arrowhead construction —

The process comprises repeated tempering of simpler curves until a Sierpinski triangle is formed.

The process begins with an individual line segment in the plane.

Each of the line segments of the curve is repeatedly replaced with three shorter segments that form 120° angles between two consecutive segments between each junction.

The first and last segments of the curve must either be parallel to the original line segment or form a 60° angle with it.

With each repetition, the curve becomes continuous. It approaches the shape that could trace out to form the Sierpinski triangle by a single continuous directed path, also known as the Sierpinski arrowhead.

A binary description of the Sierpinski triangle

A 17th-century French mathematician named Blaise Pascal studied a triangular array, which can be constructed by adding adjacent elements in preceding rows. The triangular array of the binomial coefficients is named after the French mathematician and is referred to as Pascal’s triangle.

The pascal triangle, at first sight, might only seem to share the triangular exterior with the Sierpinski triangle. However, upon further examination, it concludes that all in all, both of them are discussing the same geometrical pattern.  

Here’s how to identify Pascal’s triangle as a Sierpinski triangle:

Construct Pascal’s triangle with 2n rows, where the even numbers can be colored white and the odd numbers red.

By simply assigning different colors, the Sierpinski triangle becomes evident.

Interestingly enough, as the limit of the 2n row Pascal’s triangle approaches infinity, it becomes the Sierpinski triangle in all aspects.

Towers of Hanoi

The ages-old puzzle, known as Towers of Hanoi, where disks of different sizes are to be moved between three pegs, starting from an initial peg and finally reaching the last three pegs. However, the rule that strictly must be followed is that no disk can be placed atop a smaller disk.

When the disks are moved from one state to another, the sequence can be translated to a Hanoi graph, a graphical representation of the remaining triangle after the nth step. In the limit, as n approaches infinity, the sequence of the Hanoi graph becomes more visible as an analog of the Sierpinski triangle. 

The Sierpinski Triangle Formula

Perimeter of the Sierpinski Triangle:

With each iteration, the perimeter of the triangle increases by a factor of 3/2.

For example, at n=0, the perimeter of the triangle is unit 3, assuming length of each side is unit 1. Further at n=1, the perimeter of the triangle equals 9/2. And so on, with each recursion, the factor of 3/2 gets added to the previous perimeter.

Using this understanding of the perimeter, a general function of the number of iteration is arrived at to find the perimeter of the specific iteration:

         P_n= P₀ x (3/2)ⁿ

Taking the limit of the perimeter function above, it’s proved that the perimeter of the Sierpinski triangle:

Area of the Sierpinski Triangle:

With each iteration, the area of the Sierpinski triangle reduces by a factor of 3/4.

For example, at n=0, the area of the triangle is unit 1/2, assuming the length of each side to be unit 1. Further at n=1, the area of the triangle equals 3/8. And so on, with each recursion, the factor of 3/4 is deducted from the previous area.

Using the understanding given above, we conclude the general function of the number of iteration, to find the area at the specific iteration:

      A_n= A₀ x (3/4)ⁿ

Taking the limit of the area function above, it’s proved that the area of the Sierpinski triangle is zero:

Dimension of the Sierpinski triangle:

Depending on the dimensions of an object, when a side of the object is doubled, it tends to make particular set of copies. For instance, a 1 dimensional object, when doubled makes 2 copies, whereas, a 2 dimensional object when copied makes 4 copies and lastly, a 3 dimensional object makes 8 copies. This measure is important in determining the degree of roughness for a fractal.

A Sierpinski triangle tends to make 3 copies of itself when a side is doubled, therefore, it has a Hausdorff dimension of 1.585.

The Sierpinski Triangle Algorithm

The construction of a Sierpinski triangle might seem like an intricate job for any coder, regardless of the language. However, understanding the key elements of the geographical pattern makes it far easier to make the fractal. 

The algorithm of the triangle is based on an infinite recursion, and the computation of one Sierpinski triangle comprises the construction of another. Thus, the algorithm must take into consideration its undying nature. The algorithm must be recursively infinite, for there isn’t any final form of the figure itself. 

The algorithm on how to make a Sierpinski triangle can be defined as such:

Step 1: Draw an equilateral triangle, using points x, y, z

Step 2: Create three more Sierpinski fractals, each having the following vertices:

x, midpoint (x, y), midpoint (x, z)

y, midpoint (y, x), midpoint (y, z)

z, midpoint (z, x), midpoint (z, y)

How to make a Sierpinski triangle using Python

Due to the infinite nature of the Sierpinski gasket, it can be reproduced using the recursive function and turtle module of python.

Before delving in to the details of the code, it is imperative to understand what the recursive function exactly is. Recursion is a function in programming that calls upon itself. The basics behind a recursive problem solving is that the problem is divided into smaller, more easily manageable problems. Programmers generally define a base case to the recursion, allowing it to eventually stop the recursive function. In the absence of such a case, the recursion goes on infinitely. 

The code for drawing a Sierpinski triangle using the turtle module of Python:

# Program to print Sierpinski Triangle
import turtle
def drawTriangle (points,color,myTurtle) :
	myTurtle.fillcolor(color)
	myTurtle.up()
	myTurtle.goto(points[0][0] ,points[0][1])
	myTurtle.down()
	myTurtle.begin_fill()
	myTurtle.goto(points[1][0],points[1][1])
	myTurtle.goto(points[2][0],points[2][1])
	myTurtle.goto(points[0][0],points[0][1])
	myTurtle.end_fill()
def mid(p1,p2):
	return ( (p1[0]+p2[0]) / 2, (p1[1] + p2[1]) / 2)
def drawsierpinski(points,degree,myTurtle):
	colormap = [‘blue’,’red’,’green’,’white’,’yellow’,violet’,’orange’]
	drawTriangle(points,colormap[degree],myTurtle)
	if degree > 0:
    	drawsierpinski([points[0],
                    	mid(points[0], points[1]),
                    	mid(points[0], points[2])],
         	      degree-1, myTurtle)
    	drawsierpinski([points[1],
                    	mid(points[0], points[1]),
                    	mid(points[1], points[2])],
               	degree-1, myTurtle)
    	drawsierpinski([points[2],
              	      mid(points[2], points[1]),
                    	mid(points[0], points[2])],
               	degree-1, myTurtle)
def main():
   myTurtle = turtle.Turtle()
   myscreen = turtle.Screen()
   myPoints = [[-100,-50],[0,100],[100,-50]]
   drawsierpinski(myPoints,3,myTurtle)
    myscreen.exitonclick()
main()

Sierpinski triangle applications

The idea of fractals has existed for as long as human intellect began exploring different art forms and decorating cathedrals and churches with intricate geometrical patterns. Still, the term fractal was coined much later in 1975.

The Sierpinski triangle holds a long history of being carved into the walls of cathedrals and woven into carpets for royalty. Even today, the intricacy and elegance of the pattern leave much to desire and much to wonder. Artists have described the incorporation of fractals in their art pieces as chaotic yet something having a definite form.

However, the use of the Sierpinski triangle has not been limited to Catholic art, as it has revolutionized multiband communication, enabling, through its intricate pattern, to build and study antennas that can be used in any communication system with the requirement of high bandwidth, different frequency bands and through all operating frequencies, a constant radiation pattern.

The Sierpinski triangle also plays a vital role as a defining property of Rule 90. To elaborate on the concept of Rule 90, it is a one-dimensional cellular automaton with a binary state of existence, based on the exclusive conjunction function, where the state of any given cell can only be determined on the current state of the cell and its two nearest neighbors. In the time-space diagram of Rule 90, when the beginning stage has a single, non-zero cell, the diagram takes on the appearance of the Sierpinski gasket. And due to the strong tie between the Sierpinski triangle and Pascal’s triangle, the rule 90 time-space diagram represents a modulo-2 Pascal’s triangle.   

The study of fractals has also greatly enabled scientists and astronomers to better understanding the peculiarities of the world around them. From the cones of the mountains, ridged surfaces, and snowflakes to the uniformness of space, fractals have hugely impacted the way we perceive our universe.

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Answer fail

I don’t understand basic math…

The “six” of diamonds

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Bonus points for this guy!

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Research Cam:

Big bang theory:

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Math and Star Wars…

Thanks to LanceAF for this submission!

Source: http://www.mathplane.com/gate_dwebcomics/math_comics_archive_winter_2013

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Very nice motivation.

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The illusion was created by web designer Nobuyuki Kayahara and the question is “Which direction is the dancer spinning?” That is, is the dancer is spinning clockwise or counter-clockwise?

Introduction

Every person has their own way of perceiving how things happen. In this case, the spinning dancer illusion is a shadow of a female spinning dancer. Thus, if the viewer perceives that the foot on the ground is the left one, then it will appear that the dancer is turning clockwise, and vice-versa. Yet, it is likely that the same viewer will visualize the dancer whirling in both directions. The variation in direction is sometimes influenced by blinking or focusing on an object for a lengthy amount of time.

Spinning Dancer – What Is It?

You may have come across the term ‘ambiguous illusion.” Well, this offers the best example of what the spinning dancer actually is. Initially, the spinning dancer can be seen as an ordinary shadow of a woman performing pirouette. Yet, to most people, the image will suddenly change her dancing direction after some time. This illusion has eluded the viewers’ sanity for many decades. Although the dancer depicts a person’s brain ability to decipher things, Nobuyuki Kayahara, warns that the illusion is not a brain test. Thus, it is just an optical fantasy. https://en.wikipedia.org/wiki/Spinning_dancer

Scientists have extensively analysed various types of illusion images including this one. This will enable them to understand more about the behaviour of the human optical system. The spinning dancer silhouette does not have depth signs. As such, your eyes may at times visualize the dancer standing on the left leg, while rotating to the right. In some cases, you will see the dancer standing on the right leg, while rotating to the left. 

In most cases, if you look intently at the image, you are likely to see the dancer turning in both directions. Necker cube (a cubic wire-frame), is perhaps the most analyzed reversible image. The image lacks depth signs, as well. Hence, the front part of the cube may, at times, appear to be on the left. In other circumstances, it moves to the back; hence, shifting of its front part.

At times, one may intently look at an image without noticing any reversal. Dr. Thomas C. Toppino at the Villanova University psychology, says that the spin is something that occurs within our visual systems. If only we could understand why and how the reversal of the dancing direction occurs, then it would be better for us. This could make us learn more with regard to how our visual systems contribute to our cognizant experience. You may gaze at the picture, and you don’t see it turn around. http://www.whatispsychology.biz/spinning-dancer-silhouette-illusion#:~:text=This%20popular%20illusion%20created%20by,spinning%20in%20a%20clockwise%20direction.

Dr. Toppino recommends looking at one part of the picture, like the foot, and most often, it will finally spin. For those who don’t see the turnaround, it could mean that there is one dominant underlying neutral composition. However, the moment you are able to visualize the spin, you will find it happening more frequently.

The Analytical Survey of the Spinning Dancer

In a bid to unveil the spinning dancer perception mystery, there is a need for an in-depth survey. According to the 2008 reports by Munger, it is unlikely for the illusion to determine whether one is left-brained or right-brained. So, what is it that affects our acuity observation? 

Most of the 1,600 online survey participants agreed that “ambiguity” is the most exciting part of the spinning dancer illusion. Thus, it may seem to be revolving both anti-clockwise and clockwise. At first, about 2/3 of participants were able to record clockwise results. The rest saw things otherwise. In another observation, most of the participants altered their initial observation. 

 Amusingly, this aptitude was influenced by the initial motion direction. If your initial answer was that the dancer was spinning anticlockwise, then you are most likely to change it. There could be some sense here, considering that most of the participants advocated for the clockwise rotation. It can be assumed that most people see things moving clockwise naturally. For this reason, it is extremely hard for the observation to change from clockwise to anti-clockwise compared to otherwise. 

How then is it possible for a person to visualize a single object moving in both directions? Since the image does not have depth signs for profundity, you can choose to view the image from two distinct viewpoints. The vacillation that occurs between two perceptual situations is now the bistable perception. 

The inherent image ambiguity portrays our visual organs with distinct versions of a similar effect. This is contrary to the single unique version we are used to in life. By making use of simple techniques like rapid blinking, head tilting or visual focus narrowing, we are able to move from one viewing angle to the next.

Different Types of Perceptual Illusions

The mind can sometimes decide to make fun of you, particularly in optical illusions. The best example of this is the popular hag and young lady illusion. Here, the young lady changes into an old woman based on your visual focus. However, perceptual illusions, work in various ways to mystify your true perception. Perceptual illusions vary significantly from optical illusions.

They are typically images with contradictory data that makes one to view them in their own way rather than their true pictures. Generally, optical illusions can work with specific visual antics. The tricks help to trigger certain beliefs in the human perception. In reality, the illusion we are referring to here is the image itself. While a perceptual illusion isn’t an optical occurrence, it is actually a cognitive experience. The fantasy happens the same way your brain treats the visual details transmitted to it.

A nice graphic that illustrates how the dancer can be observed as spinning in either direction is below. By simplying adding some lines to the original image you you can give direction to the dancer. The left image shows the dancer spinning clockwise, while the right image shows the dancer spinning counter-clockwise. https://www.bustle.com/p/how-does-the-spinning-dancer-optical-illusion-work-this-brain-trick-will-make-you-dizzy-25697

The Silhouette Illusion

The way we observe the spinning dancer has no connection with our personalities. Whether we are right or left-brained, that is upon our creator. However, the illusion is commonly used to measure these attributes in most e-quizzes. To determine whether the dancer is spinning clockwise or anticlockwise depends on the position of the viewer. This is according to (Nikolaus F Troje, PhD.) “Our optical system, in case it can choose, tends to advocate for viewing from the top”, Dr. Troje adds. “It is a perceptual preconception. It is logical to believe that we are more focused on objects on the ground than those above us,” he asserts. 

Concerning the silhouette illusion, a shadow of a woman is visualized flipping on one foot while extending her leg. The most interesting thing about this illusion is the manner in which the woman is spinning. She can be seen spinning in both directions, which raises a lot of doubts.

Bistable Perception

While the spinning dancer may seem to have occupied our minds, there are also other illusions revolving around the same ambiguity. For instance, there is this one category known as multistable (bistable) perception, and the Necker Cube is the best example. Based on the viewer’s perception, the obvious spinning direction can change in many ways. This is typical with bistable percepts including the Necker cube. This type of illusion can be perceived at any time when observed both from below and above. The changes are impulsive and can occur randomly without any alteration within the intention or viewer stimulus. 

Yet, some viewers may find it hard using averted vision. Some people may be able to perceive a shift in direction easily by simply narrowing their visual focus to a specific area of the image. These may include the spinning shadow or foot beneath the dancer and gradually staring upwards. 

More so, you can achieve this by tilting your head to observe change in the direction. Alternatively, you can observe the shadow foot base, and make up your toes facing away from you, and be able to change the original direction. You may also try to close your eyes and imagine that the spinning dancer is moving in a certain direction. And by the time you reopen your eyes, you should be able to perceive change in direction. 

Again, you can still make up direction changes by waiting for legs of the dancer to cross the projection. You can still use your peripheral vision to block your brain’s most dominant part. By doing this, you should be able to visualize the spinning dancer moving in the opposite direction. Perhaps, the simplest technique is trying to blink faster. You should repeat this several times until you start seeing the image moving in the opposite direction. By the time you open your eyes, the new spinning direction should be normalized. It is possible to observe the fantasy in a manner that the spinning dancer has stopped flipping, but she is only turning back and forth at an angle of 180⁰. The adjusted versions of animation have been generated with an extra optical cue to allow viewers who cannot tell the direction of the spin. As a result white edges and labels have been included in the legs to enable viewers to see the foot moving in front and vice-versa. By staring at either of these, you are likely to see the original picture dancer image flipping in the same direction.

Auditory Illusions

Perceptual illusion may also be regarded as auditory. Diana Deutsch (Psychologist) unveiled various musical auditory illusions. The most popular of these illusions is the “phantom words”. You can perceive these through a sound recording featuring repeated phrases and words. 

As you pay close attention to the sound, you are likely to pick phrases that aren’t actually included. Perhaps, your mind will be trying to create some sense from the pointless sound, and filling in what is essentially meaningful of the noise.

Sensory Illusions

Sensory illusions can also be considered as perceptual. R.L Gregory, observes that perceptual illusions happen the moment our sensory organs submit a deceptive message to the brain. The phantom limbs phenomenon is a good example of this. This is where a person with an amputated limb claims to be feeling it even thought it no longer exists. There are actually many types of perceptual illusions including. They include Troxler fading, Tactile, etc. and by closely looking at them, you will find that they are far from the truth.

Facts About The Right Vs Left Brain

Can the spinning dancer illusion diagnose our inner brain functioning? Is our right or left brain dominant? In this case, if you look at the dancer and think that she is rotating clockwise, then it means that you are applying your right-brain most, and vice-versa. According to findings by Dr. Troje and his group, a VFA (view-from-above) bias is actually what makes us perceive the silhouette in a particular way. It is not through our personality or whether we are right or left-brained. 

In one study, participants were told to stare at the spinning dancer and report on what they are able to see. 24 of them said the woman was spinning anticlockwise when observed aerially, and clockwise if observed from below. Hence, the angle at which the viewer is standing is actually what brings about the perceptual variation. This hypothesis can be practical to other common illusions, as well. These include a Necker Cube, which is mostly applied in personality online interviews. The spinning dancer is neither a test for personality nor the determining factor of which part of the viewer’s brain is more dominant. https://www.medicaldaily.com/right-your-eyes-science-behind-famous-spinning-dancer-optical-illusion-336122

In a paper published in 2014, the brain activation is described as shifting of perception. The switching can be attributed to a section of the right side parietal. This is when MRI is used in people who can change their spinning direction at will. Research has unanimously linked this form of brain activation to the spontaneous brain changes.

What Do We Learn From the Spinning Dancer?

It can be somewhat confusing staring at the spinning dancer. While some of us may see the woman spinning in the clockwise direction, others will see her whirling in the opposite direction. Moreover, other people have the ability to determine the woman’s actual spin switch direction. 

Many study reports have confirmed that the dancer’s spinning direction is not a sign of whether one’s thinking is inclined clockwise, or anticlockwise. 

People who are considered left-brained are believed to be rational, logical, objective, sequential, and analytical and focus on sections. This group of people should be able to see the dancer spinning anticlockwise. On the other hand, right-brained people are considered intuitive, random, synthesizing, subjective, holistic, and focus on wholes. They should therefore see the dancer spinning clockwise. https://psych2go.net/optical-illusion-explained-way-dancer-spinning/

In this case, if you see things in either of the two perspectives – clockwise and anticlockwise, should be able to know what kind of person you are then. Take for instance; your perception is that the dancer is flipping clockwise; thus, a Mr. Rational. On the other hand, your wife looking at the same image reports the opposite. Thus, she sees the same dancers moving counter-clockwise; hence, making her a “Mrs. Rational”. 

Going by the example above, the predictions are unlikely to be correct. For instance, you may categorize students according to their majors in university; thus: Hard sciences, economics, math/engineering/computer science, humanities, and the like. In this case, the scientists, engineers, and economists are likely to be dominantly left-brained. They should therefore look at the woman and report that she is rotating counter-clockwise. 

Those studying humanities and other non-economics sciences should see things differently as they are presumed right-brained. Below is how these numbers are likely to indicate who, in the first place, perceives the dancer spinning anti-clockwise. Thus, the higher the number of reporters, the higher the chances of them being rational:

Economists – 26.7 percent (N=60) Scientists – 31.0 percent (N=29) Mathematicians/Engineers/Computer programmers – 21.8 percent (N=55) Humanities – 42.9 percent (N=28) Social Scientists – 36.2 percent (N=47) 

Agreeably, these aren’t the huge example sizes; yet, the findings may hardly be far away from the apparent predictions of the theory. Ironically, this theory seems to have the ability to determine how logical an individual can be. You only need to alter your perception about which direction of the dancer matches the right or left-brain thinking. Or could it be a misconceived prediction by the researchers? – Thus, most people will tend to see the dancer as rotating counter-clockwise. 

Taking the above data into account, you will realize that only 30% of the participants reported a counter-clockwise spin in their initial viewpoint. Often, we might be able to come up with an accurate guess of gender by looking at the names. In this case, 36% who saw the woman spinning counter-clockwise were women, while 30% were men. In short, the confusion keeps on widening making it hard for one to decipher any meaningful conclusion in the spinning dancer prediction.

Debunking the Spinning Dancer Illusion Myth

The optical illusion of the spinning dancer has been trending on the internet for quite long. Some text articulates that if you see the female figure flipping to the right (clockwise), then you are more creative (right-brained). However, in case you see her flipping to the left (anti-clockwise), then you are more logical (left-brained). The left/right-brained belief is hooey; hence, not actually what the fantasy is meant for. The end results can only be deduced following a psychological analysis.

The demo should therefore provide evidence through the above bias viewpoint, which affects the viewers’ perception. While maintaining an anticlockwise percept the viewer assumes a viewing angle below the spinning dancer. If viewers perceive the original dancing silhouette as flipping clockwise more frequently, then there are two key likely possibilities. They could bear a bias to perceive it rotating clockwise, or also have a bias for an above viewpoint. 

To make out the difference between the two observations, it is important for scientific research to devise their own way of seeing things. This is especially when it comes to the original dancing silhouette illusion. They achieved this by recreating the spinning dancer and altering their camera elevations. This allowed for the clockwise-from-above, as well as clockwise-from-below pairings. The findings here indicate that there existed nothing like clockwise bias, but only a viewing-from-above bias. More so, the bias depended entirely on the elevation of the camera. Thus, the greater the elevation of the camera, the more frequent a viewer perceived the spinning dance from above.

The Final Thought

In real sense, the spinning dancer doesn’t offer any precise measure of a person’s brain-part dominance. It is only a visual preference sign of the viewer. According to scientific studies, our vision bears numerous preferences. For instance, we are meant to believe that lightning comes from above and all smaller objects are a distance away from us. 

Our decision to look at the dancer as whirling clockwise is influenced by our preference to observe things from above and not below. The researchers argue that a viewer’s perception is bound to shift when the GIF is observed from different angles of the camera. For instance, at 10⁰ above the horizontal, you should be able to visualize the image flipping anti-clockwise 60% of the overall time. If the demo is repeated with 10⁰ beneath the horizontal, you should be able to see the object rotating clockwise for the time’s 60%. 

To wrap it up, our brain has a tendency of staring at the ground to see if there is anything dangerous there. And that is why we see the GIF as flipping clockwise. However, the image does not relate, in any way, to the brain hemisphere and innovation. It is only a myth that should not be taken seriously.

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