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Chapter 3 • Patterning


Creative practitioners are always involved in recognizing and creating patterns. Recognizing patterns involves identifying a repeating form or a plan in a seemingly arbitrary arrangement of things or processes. Recognizing is the analytical part of patterning, while forming is basically a creative act of constructing new patterns. For example, when architects study a landscape and then utilize the patterns they see to design a building they are both recognizing and creating patterns. Because there is a finite number of basic structures they can work with, architects must rely on both their understanding of existing patterns, along with their own creativity, to produce something new. Innovative writers and poets also do this, relying on their knowledge of linguistic patterns and structures, with their own innovations, in order to dream up a new story, poem, or other form of writing (Root-Bernstein, 2003; Gardner, 1983)

There would be no such things as jokes if human beings weren’t inclined to recognize patterns in the first place. As the psychologist P. C. Dodwell put it, “The ability to synthesize proteins, respond reflexively to a stimulus, get across the road, choose a mate, or decide among complex problem-solving strategies all depend on this skill.” Every moment of every day we organize the random events we see, hear, or feel by grouping them…. [92 ]

Our chapter of patterning begins with the discussion of riddles. It is said that the difference between a good riddle and a bad riddle is the comedian’s ability to create the necessary expectation in the audience (pattern number one), or if the audience fails to perceive the apt nature of the joke’s resolution (pattern number two), the joke falls flat. No expectancy, no surprise; no surprise, no fun. This link is to a book of vintage riddles that definitely achieve the two-part pattern of successful riddles.

This additional YouTube clip featuring Batman and Robin solving some of the Riddler’s classic riddles can be used as an example of The Search for Solutions quote, “’To perceive a pattern means that we have already formed an idea what’s next’. Our ability to recognize patterns is the basis for our ability to make predictions and form expectations” (page 92-3). This quote in the Bernstein-Root text is an excellent explanation as to how, over time, Batman and Robin were able to not only anticipate the riddles that the Riddler created, but to also became quite apt at discovering their punch line quickly in order to defeat him and save Gotham City. Please, click the following link or the image below to view this YouTube Clip.



Patterns, however, can help us do more than anticipate what’s next in life. Artist like Guiseppe Arcimboldo uses his artwork as a visual equivalent of a joke because when we, “then try to fit new observations and experiences into these expectations. Discovery occurs when, willy-nilly, something about our observations and experiences forces us to make another pattern” (page 94). This is in essence what occurs when at first you experience a pattern of a standard artwork of fruit in Guiseppe’s painting, but it’s only when you turn the painting upside down that you experience and altogether new and unexpected pattern of a face in the fruit. In the images that follow, look closely at each of Guiseppe’s art works and discover all of their hidden patterns created with the arrangement of their individual elements. With many Guiseppe’s "The Gardener" painting, it said that the viewer undergoes a “gestalt shift”. A “gestalt shift” is what psychologist call it when the same sensory information can take on two or more noncommensurate meanings. To better understand this idea, view the followingslideshowlink of some of Guiseppe's work (including "The Gardener"). Some are quite comical while others are actual replicas of Gestalt’s artwork. Each individual observer makes the image he or she recognizes, as well as its meaning. [96]

ab.EscherImages.JPG
Escher Images...


Some additional artists that were stated to be masters of pattern recognition were M.C. Escher and Max Ernst. “Escher’s genius was to see in a regular, repeating polygon the possibility of fish, birds, lizards, angels, devils, and other unexpected surprises –and to teach us how to see these things, too” (page 95). To another extreme, the surrealist painter Ernst, “stuck indoors at a seaside inn because of heavy rain, found inspiration in the patterns of a wood floor…within a short time, Ernst parlayed his fascination with pattern recognition into several new techniques that revolutionized modern art” (page 95-6)


Rhythm is a skill that is best learned through the ears and legs, not through the brain. [99] Most professional dancers can perform without music as they can feel the rhythm in every part of their body. They move to the rhythm within their legs and arms to form choreographic figures. Ashley Sattler, co-director and choreographer at Technique Studio of Dance in South Hadley, Massachusetts, says, "... [Jazz dance] utilizes your legs, your core, your arms, your upper body, everything. You really want to get into it and think about going into the ground... There's no right way to do it. You just have to get into it and feel the music." In her free tutorial on Advanced Jazz Dance Moves, she explains how you can start forming choreographic figures with basic steps.



As in any form of pattern recognition, one must know what to expect and how to compare things before the patterns become evident. [101]
It seems quite comical when someone points out to you a pattern that you see everyday and never recognized. For instance, most people know the nursery rhyme "Twinkle, Twinkle, Little Star" but don't recognize it is the same tune as "Baa, Baa, Black Sheep, Have you any Wool?". But has anyone ever pointed out to you that the alphabet song also goes to the tune of twinkle twinkle little star. Think about it, or listen to the video below. Just imagine how many patterns you don't recognize in your day to day life.



Mysteries also motivate scientists to look for patterns in the apparent chaos of nature. Most scientists believe that no matter how complex nature appears to be, the basic principles and laws are cogent and comprehensible. Sometimes all it takes to make a discovery is to recognize the patterns in front of our eyes. [103-104]

One could reasonably characterize medical diagnosis as pattern recognition, in which visual, tactile, auditory, olfactory, and technical information is combined and compared with existing descriptions of disease. Discoveries in medicine therefore often involve paying attention to new kinds of information or finding new ways to use existing information. [104]
Scientific puzzle solving is like jigsaw-puzzle solving in another way as well. When enough pieces have been fitted together, they may define either a whole or a hole. Both are valuable. The whole is a new structure that makes sense of the available data. But the hole—what is not there—is also useful because it is a valuable clue to the shape of our ignorance. [105-106]
… the jigsaw puzzle, a broken pattern if ever there was one, is a powerful metaphor for scientists even when they apply it to theoretical or conceptual issues rather than to purely observational ones like a map. [104] The geologist Alfred Wegener was the first serious scientist to piece the continents together with substantial evidence forming Pangaea. His contributions led to many more scientists adding to his theory. The clip below is from National Geographics and shows Wegner's drawing of Pangaea as well as other theorist's designs.



Scientific puzzle solving is like jigsaw-puzzle solving in another way as well. When enough pieces have been fitted together, they may define either a whole or a hole. Both are valuable. The whole is a new structure that makes sense of the available data. Btu the hole—what is not there—is also useful because it is a valuable clue to the shape of our ignorance. [105-106] In the Waterfall puzzle below, the big picture or final product is shown as a guide to the puzzle solver. Without this image, the puzzle takes on a different level of complexity. Even more so, if the pieces to multiple puzzles were all mixed together and the size of the pieces fluctuated the difficulty would increase. Unfortunately, scientific problem solving is more like the later. The puzzle solver has to define the outline and then find those key pieces to help fill in the holes.

jigsaw-puzzle-waterfall.jpg
Waterfall Puzzle- found at brainsbreaker.com

Patterns exist as tokens of our culture. A lot can be said about a people's culture simply by looking at the patterns they create. In the 1950s, when the American space program began to take shape, local architects were influenced by the "space-age" theme of the period. This cultural dynamic was eventually termed the "Googie" style. It can still be found in buildings all across the country, although it remains most prevalent in the Western half of the United States. The Googie style is unique in that simple shapes are used in a variety of formats to make it easily identifiable. Here are a few examples of the Googie architectural style in signs:

bicycleshopgoogie.jpg
bicycleshopgoogie.jpg
driveingoogie.jpg
driveingoogie.jpg


pridecleanersgoogie.jpg
pridecleanersgoogie.jpg
lasvegassign.jpg
lasvegassign.jpg

  • these images are the property of Flickr.com


It's very common in Islamic architecture to shape mosques according to specific patterns. Although the shape of mosques depends upon the cultural heritage of Muslims, they all share a set of features. For example, minarets are tall and slim, and can be round, square or octagonal. This is a key feature of the male dominance in Islam.

Egyptian mosque
Egyptian mosque
Turkish mosque
Turkish mosque
Pakistani mosque
Pakistani mosque


So how special are patterns? People are naturally attracted to patterns. For one thing, they're easy to remember and have personal associations. Twenty years ago, Swiss graphic designer Jean Robert discovered a face in a padlock. Since then, he and his brother Francois have been photographing the smirks, smiles, and pouts in everyday objects, finding uncanny resemblances to human and animal faces in everything from buildings to mops to shoes. In the lively spirit of Play with Your Food comes Faces, their collection of over 150 whimsical photographs that communicate a world of expression—all in one satisfyingly chunky book. Each beautifully designed page features a different object with its own quirky personality—and a hidden face guaranteed to make anyone smile. People have the tendency to 'look for familiar patterns in unfamiliar places.' [112]

facesbookcover.jpg
facesbookcover.jpg


Pattern recognition and formation is cross-cultural and interdisciplinary. Artists, musicians, dancers, physicists, mathematicians, and inventors imagine and make new patterns all the time and with almost any type of starting materials, physical or mental. And as they ivent new patterns, they often find that those patterns already exist but have previously been overlooked. To understand order it is often necessary to learn to create it. [116-117]

Citadel 1962 by Gene Davis
Citadel 1962 by Gene Davis


The entire painting actually revolves around the three colors that appear only once each: red, yellow, and grass green. Rather than stand out from the other panels, they focus the pattern because mixing red, yellow, and green paint creates the color olive. [117]

Pattern recognition is also common in science. A Moire pattern can be regarded as a mathematical solution to the interference of two pereiodic fuctions. [124]

Moving parallel lines
Moving parallel lines
Moire_angular_gap.png
Two similar patterns rotated by an angle alpha.


The patterns are superimposed in the mid-width of the figure. Let us consider two patterns made of parallel and equidistant lines, e.g. vertical lines. The step of the first pattern is p, the step of the second is p+δp, with 0<δ<1.

If the lines of the patterns are superimposed at the left of the figure, the shift between the lines increases when we go to the right. After a given number of lines, the patterns are opposed: the lines of the second pattern are between the lines of the first pattern. If we look from a far distance, we have the feeling of pale zones when the lines are superimposed (there is white between the lines), and of dark zones when the lines are "opposed".

The middle of the first dark zone is when the shift is equal to p/2. The nth line of the second pattern is shifted by n·δp compared to the nth line of the first network. The middle of the first dark zone thus corresponds to n·δp = p/2 that is. The distance d between the middle of a pale zone and a dark zone is the distance between the middle of two dark zones, which is also the distance between two pale zones. From this formula, we can see that :
  • the bigger the step, the bigger the distance between the pale and dark zones;
  • the bigger the discrepancy δp, the closer the dark and pale zones; a great spacing between dark and pale zones means that the patterns have very close steps.

Of course, when δp = p/2, we have a uniformly grey figure, with no contrast. [Wiki Pages on Moire Pattern]

Moire patterns have also yielded great discoveries in semiconductors. When overlaid, graphene sheets can help understand the conductibility of electrons.

Moire_periodic_grids.jpg
Moire periodic grids superimposed to study sheets of graphene.


Working in the early 1820s, well before synthesizers or electronic equipment were available, Joseph Fourier wanted to describe such complex waves, whether they represented sound, electricity, heat, or any other physical agent or process. [125] But just as Simha Arom discovered that tribal music is based on the juxtaposition of simple repeating elements, so Fourier discovered ...[125] Simha Arom specialized in African music. He analyzed several hundreds of their polyrhythmic music to help understand how informally trained amateurs could produce such complex rhythmic patterns. The answer was the patterns these indigenous were using. He discovered that each group played a very simple beat, and when all these beats were superimposed, the resulting music was by far too overwhelming for anyone to comprehend as is. The video below provides an example of the Aka Pygmy music. Notice how complex the rhythm is, yet it is performed by a combination of rudimentary music. This brings us back to the proof that 'rhythm is a skill that is best learned through the ears and legs, not through the brain.' [99]



Patterns have made their way through the microcosm of electronics. Synthesizers are able to reproduce music because they are able to recognize the musical patterns. The same synthesizer can reproduce a Bach cantata, sitar or sarangi music from India, shamisen or koto music from Japan, or the heaviest of heavy metal bands. And it does so by adding trigonometric functions. Now that’s universality. [126] The video below shows a synthesizer reproducing the Sinfonia from Bach's Cantata "Wir danken dir, Gott, wir danken dir" - BWV 29-GPO4. Notice how the synthesizer juxtaposes the waves produced by the notes.



Modern mathematicians have discovered that other simple operations can generate complex patterns with surprising properties. [127] There's sometimes no need to carry out a multiplication, especially if the numbers are high. For example, 11 x 11 = 121, 111 x 111 = 12321, 1111 x 1111 = 1234321, and so on. Keep doing that until you get to 111,111,111 x 111,111,111 and see if you've applied the pattern correctly. Check your answers here. And find more examples here.

You'll find a whole lot of patterns pertaining to numbers, but not all are practical. For example, you may notice that the square of a number is the sum of as many odd numbers as the number itself. For example, the square of 2 is 4=1+3, of 3 is 9=1+3+5, of 4 is 16=1+3+5+7, and the square of 12 is the sum of the first 12 odd numbers (144=1+3+5+7+9+11+13+15+17+19+21+23). Can you find the square of 26 in this same way? Would it be practical to use this method to find the square of big numbers like 87? In this case, performing the multiplication would be easier. The point here is that not all identified patterns are useful or practical.

Simple geometric shapes can yield interesting figures. For example, circles can be combined to form shapes other than circular ones. They can form tear-like shapes, propellers, and many other unusual shapes. An index of circle patterns provides plenty of such examples.

Patterns exist everywhere, but we hardly notice their importance. Food experts have discovered that giving particular shapes to foods can be appealing to kids.

Pac-Man, Camambert style.
Pac-Man, Camambert style.
Native carrots.
Native carrots.


Some food patterns go all the way as to explain some lifelike situations, like how birds feed their offspring.

Bird feeding offspring in food shape.
Bird feeding offspring in food shape.


Writers obviously work their magic by combining a relatively small number of words into sentences, paragraphs, poems, stories, and books. Less obviously, they structure their words by forming patterns out of diverse experiences. [128]

Speakers also rely on experiences that can range from very common daily encounters such as greeting people to more complex ones such as paying tributes or making speeches. These experiences probably brought semanticpatterns into existence. Consider how you would greet a close friend and a stranger. A simple 'Hi' would suffice to a friend but would be completely preposterous to a stranger, in whose case a whole set of adequately chosen words would be more appropriate. This is also the case when translating from one language to another, where culture epitomizes language patterns. For example, it's very common among Arabs to grace people after a shower or a haircut with the word NA-EE-MEN, meaning that their sins have hopefully been washed or cut away. However, such a linguistic pattern doesn't exist in any other language (from experience and not research), and would offend non-Arabs, who would consider it an insult. "Do you actually mean I was dirty before I had a shower?" is a common reply. The point here is that speakers form linguistic patterns (in this case grace pattern) to construct sentences that convey a meaning specific to a particular experience, which may differ from one language to another.

As helpful as identifying shapes might be, one has to be very careful about how to interpret them. As Dr. Michael Shermer. points out in his article titled Patternicity, people's brain tends to form patterns that may be real or not. People tend to see patterns based on their culture and background. Dr. Michael contends that people see what they choose to believe. He calls these pattern recognitions patternicity and apatternicity. Dr. Michael goes even further in one of his talks on TED on Strange Beliefs to explain how " UFOlogists see a face on Mars, Religionists see the Virgin Mary on the side of a building, [and how] paranormalists hear dead people speaking to them through a radio receiver." The pictures below represent examples of Dr. Michael's talk on TED.

These identifications would probably be made by astronomers.

Face on Mars
Face on Mars
Happy face on Mars
Happy face on Mars


Dr. Michael believes people identify faces because faces are very important to us. See a whole range of pictures of faces on Mars here.

And these ones would be made by religionists.

The nun bun
The nun bun
The Virgin Mary's apparition
The Virgin Mary's apparition
external image grilled_cheese_virgin.gif

People recognize patterns in sounds, like the ones who believe that the dead talk to us. Dr. Michael explains how reverse speech can cause this phenomenon towards the end of his talk. When the lyrics are played backward, one can hear a sequence of words completely different from the ones in forward mode, thus hearing a 'hidden' message.

Conclusion
Although recognizing and identifying patterns can be performed by almost anyone, these two processes require an experienced eye. One has to know what to look for in order to make sense of the patterns observed. Otherwise, these patterns may pass unnoticed or may not be utilized to a good end. When scientists carry out a series of experiments, they observe subtle changes, identify repeated results, and are watchful of unusual outcomes. When the German scientist Roentgen discovered X-rays, he had no intention of doing so. He was just fiddling with his instruments as part of his experiment. He evacuated his tube of air, filled it with a special gas and passed a high voltage through it. The result he saw, which was a green light appearing on a screen after he had covered his instrument with heavy black paper, made him wonder what it could be. Had he not noticed the unusual pattern of the green light appearing although it should have been blocked by the heavy black paper, he wouldn't have actually discovered X-rays. It's true that Roentgen was not expecting light to appear from underneath the black paper, but he definitely needed to have a keen eye to realize that such light was different from the kind of light we're all familiar with.

Just like scientists, teachers need to be aware that patterning plays a crucial role in education. For one thing, patterns are appealing and easy to remember. In maths, identifying patterns in geometrical forms or numbers can be fun and beneficial for solving problems. Students play around to figure out how different shapes can form various figures. In science, students can sharpen their understanding of how chemical substances react together. In literature, students explore the variety of rhythmic patterns and their musical associations, eventually creating their own poems. After all, patterning does not work in isolation. It's just one link in a long chain of thinking tools.



Activities
pattern_mosaic.jpg
pattern_mosaic.jpg

This section of the chapter offers examples and exercises to further your understanding of patterning.


 Riddles
Lest you think this is all nonsense, be assured it is not. The subject of this chapter is recognizing patterns, and there is a pattern, a repetitive form or plan, to these crossing riddles. [92]

1. What do you get when you cross a snowman with a vampire?
Answer: frostbite

2. What do you get if you cross Santa with a detective?
Answer: Santa clues


Games
“Both young and old can look for patterns in words. [113]
One of the most famous word games is Scrabble. The following video shows the game in a very interesting light.




Art
Add Leonardo Da Vinci to the list of artists that used pattern recognition to come up with new ideas. [96]
Leonardo Da Vinci
Leonardo Da Vinci


Based on the following examples, you can see how Da Vinci inspired other artists to apply new patterns to one of his most famous pieces of art – the Mona Lisa:

mona-lisa-painting.jpgmona-lisa6.jpgmona_ad.jpgmegamonalisa_punk-mona-lisa.jpg

Skill building exercises
Now that you have some additional ideas about patterns, try your hand at creating a crossing riddle, play an online Scrabble game, or create your own work of art using one of your favorite artists' work as an inspiration.


Activities on Moire patterns
Here's another way to help students understand what the Moiré Pattern Effect is. Check out the following weblink to view Moiré patterns interactively. The user can learn how to build patterns out of Moiré interference layers. This software was written with OpenGL, providing hardware accelerated Moiré interference patterns. The user can provide their own interference patterns, or use a combination of the 21 patterns provided.