Gestalt Principles and Dynamic Symmetry
Nature's Design Connections to Our Built World

| Thomas Detrie | Professor Emeritus | Arizona State University |
© 2002. all rights reserved.
|

Mt.St.Joseph logo UC DAAP
20 Nov 2002
Art Department
College of Mount Saint Joseph
Cincinnati OH 		22 Nov 2002
Junior Seminar (G.Salchow)
University of Cincinnati DAAP
Cincinnati OH

| Contents | Summary | Glossary | Bibliography | Profile |

Abstract

'Graphic designers give visual form to ideas through formmaking. Formmaking calls for proficient machine and manual skills, and engages critical thinking and decision making. Results grow to maturity with guidance from experience, intuition, and visual principles. It is highly useful to build these personal traits into components of a work process. Further, a documented work process is useful to communicate your problem-solving approach, and support individual decisions in a team-based workplace.'
Prof Detrie follows precepts that stress the use of personal knowledge resources, cross-cultural and cross-disciplinary awareness, and attention to human perception and mentation to solve human problems more effectively. 'We are born with innate design potential through our connection to natural order and our figure-based perceptual system. We do not add design topics into our world. Instead, we grow design potential from our internal nucleus. Viewer connection is an event. The viewer connects with the visual form when we prepare the form and context to engage the viewer's perceptual response. While the message may be external, communication results when the meaning forms internally in the viewer's mind.'
The presentation content forms three parts. Part 1 is about our connection to the natural world through perception. Prof Detrie discusses visual perception in the context of the Gestalt principles of visual organization. Part 2 discusses the visual connection of Botany's growth spiral (phyllotaxis) to mathematics' equiangular spiral. The visual link of the phyllotaxis to the Golden Section made it useful to solve visual composition problems through Dynamic Symmetry. Part 3 presents the work of Bradbury Thompson to show visual principles applied in a professional context.
| Michael Kroeger | College of Mount Saint Joseph | http://www.msj.edu/kroeger/ |

Contents


Introduction

My presentation discusses some natural principles important to visual design. These are detailed topics. However, this discussion limits its scope to an introductory awareness. It is well worth your time to look further into these topics for application to your design work. Later, we shall see some of these principles applied. Finally, we will see some advanced applications in the work of the twentieth-century designer, Bradbury Thompson.
I begin with the term formmaking and four suggestions that I think we all could find helpful in our design studies.
Graphic designers give the visual form to ideas through formmaking. The visual principles we discuss today, particularly dynamic symmetry, are tools to increase our formmaking productivity and effectiveness. Formmaking calls for proficient machine and manual skills, and engages critical thinking and decision making. Formmaking is complex, and seldom resolves in a single event. Results grow to maturity with guidance from experience, intuition, and visual principles.

My four suggestions are that:
(1) It is highly useful to build our own attributes and experiences into components in a personal work process. A process methodology increases productivity and heightens creativity. Further, a documented work process is useful to support individual decisions in a team-based workplace.
(2) We often overlook our own broad personal knowledge as a resource to apply to design learning and practice. We should use what we know to learn what we do not yet know.1
(3) Knowledge about human-based disciplines such as the arts, literature, and the social sciences, is highly useful to us in our work. We can transpose to our work the countless good ideas, techniques, and processes from other disciplines and cultures.
(4) It is important for designers to understand how humans process information because we solve human problems. Learning about perception and mentation, especially through cognitive psychology and human-computer interaction (HCI), will help us improve our work process, and help us work better with colleagues and clients.


1.0 Our Connection to Nature's Order


1.1 Perception

We know Nature is a highly complex and highly ordered system of systems (a meta-system). We understand this ordered complex through scientific analysis expressed in scientific language, and through philosophical thought and literature's poetic language. However, we connect to this ordered complex through the involuntary and subconscious workings of our perceptual system. We are constituent to nature's configuration, and so also comprise Nature's ordered complex.
We make sense of the world by processing sensory data into meaning. The biological process is continuous and automatic.
Biological components aside, personal experience, and cultural worldviews most greatly regulate perception. Differences in personal experience and culture are under considered. We graphic designers should understand the varying cultural components of perception, and follow a broader, more informed approach concerning the variety of perceptual worlds through better cross-cultural awareness.2
Many factors influence how we find meaning in things and events in our environment. Although, time constraints prevent us from discussing in detail these factors here, I will list them for your further study.
Factors affecting perception are: Projection, Expectation, Memory, Selectivity, Habituation. Salience, Normalizing, Dissonance, Word influence, Human influence, Culture, Deviation, Intuition, and Creativity.
Our search for meaning in the physical world is automatic and continual. Closure is the attainment of this meaning we instinctively seek. Factors like habituation, salience, normalizing, and word influence simplify closure. Dissonance however makes closure more difficult. Closure can be so difficult to gain, that we may try to reject the stimulus. When closure is easy, the stimulus attracts but does not hold our attention. Certain stimuli continue to hold our interest even after repeated exposure. We usually associate this quality with great works (figure 1 and figure 2).

A.Hofmann Butterfly poster butterfly
Figure 1 and figure 2. Poster by A.Hofmann. Image by John Gerbach.

Promised closure holds an audience's attention. As much as we seek it, we have a recurrent willingness to delay closure, such as in literature, film, and theatre. In these situations, we feel secure in expecting that we will eventually get to closure. That is, the writer or filmmaker will eventually resolve the story line. We can connect this idea to web-page design where the user stays with the interaction only as long as the closure expectation remains active.
We use the term perception in multiple ways. It can regard responses of the nervous system to external stimulation (sensation), or to primitive awareness (survival instinct). Perception can also regard more complex and higher-level thought processes (cognition). Psychologists today believe that sensory stimulation determines perception less, and that cognitive factors such as expectancy, normalizing, and verbal coherence control perception far more than once thought.
We are not consciously aware of our receptor's sensations. For example, when we hear a sound we do not feel our eardrums vibrate. We are unaware of sensations themselves, and respond to the meaning that these sensations form in our consciousness. Although sensations are physiologically predictable, perceptual differences can make the same sensations have different importance or meaning.
Factors independent of the stimulus itself that affect perception are: cultural conventions such as learning, experience, expectancies, beliefs, and values: physiological factors such as mood, temperament, age, and health: and environmental conditions (ecological habitat). Therefore, human perceptions can vary and are unpredictable.

1.1.1 Gestalt Principles of Perceptual Organization
While perception involves all the senses, Gestalt psychology, the early twentieth-century German school of psychology derives mainly from visual perception. Today, cognitive psychology and human-computer interaction (HCI) are also important to our understanding of perception and mentation.
Gestalt theorist intended their ideas to have general applicability. However, they induced the main tenets almost exclusively from observations on visual perception. This approach limited its efficacy. However, we now accept these observations as general principles and know them as Gestalt principles of perceptual organization. Although Gestalt principles have limited value in psychology, they are highly useful to visually based disciplines. Graphic designers regularly use these principles even if only subconsciously. There are many gestalt principles, each worth study and today I will mention several. You have experienced all of them and some you may already know.
The main idea in Gestalt psychology is that we perceive visual data in organized or configurational terms. The German word Gestalt means 'configuration.' Patterns take precedence over elements and have properties that are not inherent in the elements themselves. The often-used phrase that characterizes Gestalt theory is: 'The whole is more than the sum of its parts.' Figure 3 and figure 4 are examples.

gestalt example
Figure 3. We perceive images as a configuration instead of only a sum of distinct component parts. The whole takes precedence over the parts, and has properties that are not inherent in the elements themselves. Image by M.Kroeger after G.Kanizsa.

H.Lupin poster
Figure 4. Another example that shows we perceive images as a pattern or whole instead of only a sum of distinct component parts. Here, we do not merely perceive elemental dots aligned on a page, we perceive a dotted line pattern. Poster by Herbert Lupin.

Gestalt's most general organizational principle is that the particular perceptual configuration achieved will be as good as the context permits (Prägnanz principle). We can connect this principle to the communication theory about how noise affects a signal and message (m=s/n).3   Several properties comprise good configurations, such as continuity, regularity, simplicity, stability, and unity.

Other Gestalt principles are the:
Closure principle that denotes the fact that we make whole images from partial visual data. For example, we see a circular figure with small gaps in it as a full or closed circle. Similarly, we perceive a whole figure even if a part of the image of the figure falls on the blind spot of the retina;
Continuity principle that describes our tendency for smooth contours to dominate irregular, abruptly changing contours. This is strong support to include form studies (curve and shape) as fundamental to visual education;
Proximity principle (grouping) that activates when the vertical distance between elements is less than the horizontal distance, and the elements organize perceptually into columns;
Similarity principle (grouping) that determines like elements connect or group. Similarity covers visual characteristics, including size, shape, color, texture, material, surface.

The last two factors I will mention concern movement.
The Common fate principle (movement) that determines that we perceive stimulus elements as a unit if they move together. For example, imagine a camouflaged military vehicle in the field. When stationary, the elements of the vehicle visually organize into the background patterns, and the vehicle is difficult to detect. However, the vehicle is easily visible when it moves. We perceive the vehicle, with all its elements moving in unison, as a unitary figure, distinct from its background (figure 5).

animation
Figure 5. Animation.

The Phi phenomenon (movement) that denotes that we can perceive movement without actual physical motion of the stimulus. The phi phenomenon is common to theatre marquees and basic to motion picture and television production. The film or video screen, for example, presents a series of briefly visible, still images that concatenate into motion. However, the movement we see is a creation of our own perceptual system. We work with this phenomenon when we build animations on the computer.

animation
Figure 6. Animation.

1.2 Nature's Growth Spiral

Now that we have touched on our innate order and organization in perception, we can discuss briefly Nature's unity, order, and organization.
Research on natural form denotes Nature's unity in the remarkable irrational number, 1.618. That there is a basic unity among Nature's diversity is a centuries old observation. Mathematicians, philosophers, and scientist have long considered the principle 'unity in diversity.'
Snow crystals are a good example of this principle. Their hexagonal configuration unites all snow crystals, yet each is unique. Inorganic patterns are more consistently ordered than inorganic patterns. Further, hexagonal patterns, like the snow crystals, are more common in inorganic than in organic nature, which favors pentagonal patterns (figure 7).

snow crystal: inorganic: hexagon-based and starfish: organic: pentagon-based
Figure 7. Snow crystal: inorganic: hexagon-based and starfish: organic: pentagon-based.
Images by Eric Gravel and Scott Johnson.

The icosahedron, one of the Platonic solids (polyhedrons), shows an interesting connection between the hexagon and pentagon. The icosahedron has twenty triangular faces, and shows a pentagonal outline in a point view and a hexagonal outline in a face view (figure 8). In addition, the icosahedron has diagonal planes of 1.618 proportions. This helps us consider connections between inorganic and organic configurations.

icosohedron
Figure 8. The icosahedron shows a pentagonal outline in a point view and a hexagonal outline in a face view. Model and image by M.Kroeger.

The spiral is another recurring configuration throughout organic nature. Botanists call the spiral growth configuration in plants phyllotaxis, and it has the 1.618 proportion. The 1.618 proportion appears in the curve-cross configuration of the pineapple, pine cone, and sunflower, and in the animal world for example, in the spiral of snails and the chambered nautilus (figure 9), and in the proportions of the human body. Later, we shall see why the phyllotaxis is the essential point to our discussion.

chamered natilus
Figure 9. The chambered nautilus is an example of the spiral configuration recurring throughout organic nature. Image by Dorling Kindersley.


2.0 Nature's Connection to Our Built World

Now that we have discussed our connection to the natural world, let us discuss Nature's connection to our built world.

2.1 Historic Precedent

Nature has long guided architects, artisans, artists, scribes, and typographers in the shaping of our built world. Certain proportions recur in their work, and comprise simple geometric figures: equilateral triangle, square, regular pentagon, hexagon, octagon, and others. Often, builders based measurements and proportions on the human body (anthropomorphism). These proportions have endured a critical examination over time and formed the built habitat in many different ages and cultures. They recur widely in human-made works from Renaissance Europe, Tang dynasty and Song dynasty China, early Egypt, pre-Columbian Latin America, and ancient Greece and Rome (figure 10).

Trajan Column, Caravaggio/Seurat painting, Incunabula page
Figure 10. Trajan Column, Caravaggio/Seurat painting, Incunabula page.

2.2 Golden Section

We learned that the irrational number 1.618 describes Nature's growth spiral. We know 1.618 as the Golden Section, and Phi, the twenty-first letter of the Greek alphabet is its symbol. The Golden Section was shown first by Pythagoras (580-500 BC) through his study of musical scales.

pythagoras
Figure 11. Pythagoras. Image by Culver Pictures.

The Golden Section derives from many mathematic and geometric methods.

Here are three:
(1) Two elements embody the Golden Section when the smaller is to the larger as the larger is to the sum or a:b = b:(a+b);
(2) If we convert the 1.618 proportion to percentages, the smaller part is about 38% (38.2%) and the larger 62% (61.8%) of the whole;
(3) The equation (1 + √5) ÷ 2 = 1.618.
??? Early Greek geometers and architects much admired the Golden Section. Phidias, the master planner of the Acropolis, and Ictinus, the architect of the Parthenon, proved the design potential of the Golden Section. The Greeks were the first to show that the human figure comprises the Golden Section proportion(figure 12).

Greek vase
Figure 12. ???

2.3 Summation/Fibonacci series

A unique number series also comprises the Golden Section. The series is: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. We know number pattern as the summation series because each term sums the two preceding terms. We also it as the Fibonacci series, named for the thirteenth-century mathematician from Pisa, Leonardo Fibonacci (figure 13).

Pisa tower
Figure 13. Pisa tower (poster). [Galileo]

Each adjacent term of this series divided into the other equals 1.618, and so 1.618 is commensurable (coherent) with the series. The lower numbers are only whole number approximations of the Golden Section. However, accuracy increases with the higher numbers in the series such as 118, 191, 309, 500, 809, 1309, 2118, 3427, and so on.
An example of how to use the summation series in graphic design is type size choice. We can choose type sizes for a composition according to the summation series: (a) 5, 8, 13, 21, 34, 55, 89, .... These sizes alone satisfy many typographic tasks. Other possibilities include (b) 6, 10, 16, 26, 42, 68, ... or (c) 4, 7, 11, 18, 29, 47.... The combination of a and b is a two-string series that forms a versatile scale of type sizes: (d) 6, 8, 10, 13, 16, 21, 26, ....

2.4 Hambidge's Dynamic Symmetry

Architects, artists, philosophers, from Plato, Polycletes, Pythagoras, Vitruvius, in classic Greece, and Dürer, Leonardo, Michelangelo, and others in the Renaissance4 all produced their own canons that described their aesthetic ideas.
After the Renaissance, through the Ages of Enlightenment and Rationalism (1700s) the validity and application of the Golden Section faded. In the early twentieth century, Jay Hambidge (1867-1924) was central in the Golden Section's revival as a design methodology. Hambidge, was an author and teacher, whose book The Elements of Dynamic Symmetry first appeared in 1920.
Dynamic Symmetry is the natural design methodology based on Nature's growth spiral. Hambidge took the expression 'dynamic symmetry' from the Plato's writings, and one of his information sources on classical proportion was the first-century BC architect and scholar, Vitruvius. The term 'dynamic' regards growth energy, and the term 'symmetry' regards its older definition of commensurability.5
The pine cone and sunflower are ideal natural models to study the basis of dynamic symmetry. The pine cone shows the cross-curve phyllotaxis in three dimensions, and the sunflower shows the cross-curve phyllotaxis in two dimensions (planar) (figure 14).

pine cone and sunflower
Figure 14. The pine cone is a three-dimensional cross-curve phyllotaxis and the sunflower is a planar cross-curve phyllotaxis. Image by John McCoffamn.

Hambidge found that Nature's phyllotaxis was the same as mathematics' equiangular spiral (logarithmic spiral). He visually linked the Golden Section to this spiral, and reduced the equiangular spiral from a curve figure to a straight-line figure. This made it useful to solve composition problems and connects design closely to natural order (figure 15).

equiangular spiral
Figure 15. equiangluar spiral.
 
Hambidge tells us that the importance to design of the curve-cross phyllotaxis is that it is commensurable, and that it is commensurability that gives dynamic symmetry its greatest design value. The persistence of the 1.618 proportion brings the conclusion that commensurability reflects Nature's growth energy, while figures lacking commensurability are static. This is the essential point of our discussion.
Hambidge put strong emphasis on the diagonal and he formed a series of dynamic rectangles based on a projection of the square's diagonal. Dynamic symmetry derived rectangles are also commensurable. That is, although the size may change, the shape remains constant. The first rectangle, the root-2, forms from the arc of the square's major diagonal (corner to corner). The resulting rectangle has a 1.4142 proportion. We sometimes confuse it with the Golden Rectangle that forms from the arc of the square's minor diagonal (mid-point to corner) (figure 16). The remaining dynamic rectangles are the root-3, the root-4, and the root-5 rectangles (figure 17). The root-5 rectangle comprises the Golden Rectangle extended in opposite directions (figure 18).
The Golden Rectangle, the Dynamic Rectangles, and knowledge about how to use them are highly useful tools to guide our design decisions for size, placement, and many other factors. [connect GS - GR - GT ]

root-2 and GS rectangles compared
Figure 16. The root-2 Rectangle and Golden Rectangle compared.

the dynamic rectangles
Figure 17. The dynamic rectangles are the root-2, the root-3, the root-4, and the root-5.

root-5 and GS rectangles compared
Figure 18. The root-5 rectangle comprises the Golden Rectangle extended in opposite directions.

I will close this section on nature's connection to our built world with what Jay Hambidge tells us in the Preface to Elements of Dynamic Symmetry. He says that dynamic symmetry is not a 'short cut' to creativity and that mere mechanics are no substitute for thinking. Studying and understanding the working of this natural design methodology opens the mind for creation, and enables us to actualize ideas that otherwise dissipate in indecision.


3.0 Bradbury Thompson

Part three of this presentation is from a personal project called 'Learning from Mentors I Never Met.' Its purpose is to acknowledge what I learned about design by studying the work of designers I never met. Bradbury Thompson is the mentor here. After a brief biography, I will call your attention to some of Thompson's work.
Bradbury Thompson (1911-1995) was born in Topeka, Kansas. He grew up there and graduated from Washburn College. In 1938, he moved to New York City and began a distinguished career as a graphic designer that spanned more than fifty years. He also taught for many years at Yale University.
Thompson's graphic design production is extensive, and of outstanding innovation and quality. I will mention a few major works before we see several examples.
Thompson's first commission in New York was the design of Westvaco Inspirations. Inspirations was a periodical published by the Westvaco Corporation between 1925 and 1962 as a showcase for its printing papers. Under Thompson's direction, it became one of the leading avant-garde publications in the field. Most of today's examples come from Inspirations.
Thompson's next important work was Art News. He served as its design director between 1945 and 1972. For Thompson, Art News was an extraordinary opportunity because it brought him into association with American and European modernist artists (Miró, Matisse, and others) who greatly influence his work.
The principles Thompson formed in his work for Inspirations and Art News he later refined and restated in the books he designed in the 1960s and 1970s, particularly the celebrated Washburn College Bible of 1979. While, the design of the Bible was his own in every detail. It was also a collaboration with his friend and longtime Yale University associate, Josef Albers, who contributed three frontispieces. In addition, it was a collaboration with Jan Tschichold, who made the new typeface Sabon available for the Bible before general release. The effect of the Bible's typography on the graphic design community was immediate.
It was Thompson's search for visual principles and his generosity in sharing his discoveries that made both his teaching and his work as a designer so remarkable.
Thompson's influence on American and international graphic design is pervasive. Although his profession honored him highly, he remained a quiet, humble person.
Alvin Eisenman says in his Foreword to The Art of Graphic Design that Bradbury Thompson had a strong intuitive design sense. He also had a deep interest in design principles, precepts to guide his own work and by example to guide the work of future designers.

Note: see the Bibliography for resources about Thompson and his work.


Acknowledgements

I thank you (the audience) for the opportunity to meet you, and to discuss some of these design ideas. I also thank Professors J.Bellas, B.Belknap Brann, M.Kroeger, and K.Salchow for making this presentation possible.

Closing Remarks

Finally, please take these two ideas with you.
(1) We are born with innate design potential because of our connection to natural order and our figure-based perceptual system. We do not add design topics into our world as we mature, instead wegrow design potential from our internal nucleus.
(2) Viewer connection is an event. The viewer connects with the visual form when the visual form allows the event to happen. This results when we prepare the formal visual context to engage the viewer's perceptual response. While the message may be external, communication results when the meaning forms internally in the viewer.

Appendix


Part 1.0 Summary

To review this section on our connection to Nature's order, what we have discussed is that:
1.0 We are part of Nature's ordered complex, and so have an innately ordered sensibility.
1.1 Perception is how we make sense of the world through processing sensory data into meaning. This process involves primarily biology. However, personal experience and cultural background highly affect perception.
Four factors that shape perception are:
(1) mental operations that affect how we attribute meaning to stimuli (for example, habituation, salience, normalizing, dissonance, and closure);
(2) the effects of words on perceived meaning;
(3) the interplay between perception and behavior (for example, the presence or absence of other people); and
(4) the framing of both perception and behavior by social or cultural context (for example, learning, socialization, deviance, creativity).
1.1.1 Gestalt principles of perceptual organization are factors that determine what percepts will emerge from a complex visual stimulus. These principles state that whenever possible we will perceive some figure and, that we will articulate the visual field into figures and patterns of figures. We understand that such emerging patterns are not in the stimulus, and although the stimulus allows them, the perceptual system alone creates them. Things look to us as they do because of the organization imposed by our perceptual system.
1.2 The irrational number, 1.618 comprises Nature's unity.
'Unity in diversity' is a centuries old observation.
Phyllotaxis is the spiral growth pattern in plants. The phyllotaxis has the proportion 1.618. The 1.618 proportion also appears in the curve-cross configuration of the pineapple, pine cone, and sunflower, and in the animal world in the spiral of snails and chambered nautilus, and in the proportions of the human body.

Part 2.0 Summary

To review this section on nature's connection to the built world, what we have discussed is that:
2.0 Human kinship with nature guided the shaping of the early built world. Early cultures linked mathematical systems with design, and science and art often found commonality in the search for their ideal aesthetic form.
2.1 Human-made works across the ages and cultures show certain recurring proportions. Many of these proportions are inherent in simple geometric figures: equilateral triangle, square, regular pentagon, hexagon, and octagon. Often, builders based measurements and proportions on the human body (anthropomorphism). These proportions have endured a critical examination over time and formed the built habitat in many different ages and cultures.
2.2 We know the irrational number 1.618 that describes Nature's growth spiral as the 'Golden Section.' The Golden Section was first shown by Pythagoras through his study of musical scales.
Two elements embody the Golden Section when the smaller is to the larger as the larger is to the sum, or a:b = b:(a+b).
The 1.618 proportion comprises the pentagon, a regular five-sided polygon and the pentagram, a five-pointed star.
The Acropolis, and the Parthenon, exemplify the design potential of the Golden Section. The Greeks first showed the Golden Section proportions in the human figure.
2.3 The Fibonacci series describes plant phyllotaxis and the Golden Section. The series is: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. We also know it as the summation series because each term sums the two preceding terms.
Each adjacent term of this series divided into the other equals 1.618, and so 1.618 is commensurable with the series.
2.4 Dynamic Symmetry is the natural design methodology based on Nature's growth spiral. Dynamic regards growth energy, and symmetry regards its older definition of commensurability (coherence).
Jay Hambidge found that the phyllotaxis was the same as the mathematics' equiangular spiral curve (logarithmic spiral). He visually linked the Golden Section to this spiral, and reduced it to a straight-line figure that made it useful to solve composition problems.
It is the persistence of the phyllotaxis proportion, and characteristic of commensurability that gives a design scheme its dynamic value.
Hambidge formed a series of dynamic rectangles based on a projection of the square's diagonal. The first rectangle, the root-2, forms from the arc of the square's major diagonal (corner to corner). We sometimes confuse it with the Golden Rectangle that forms from the arc of the square's minor diagonal (mid-point to corner). The remaining dynamic rectangles are the root-3, the root-4, and the root-5 rectangles. The root-5 rectangle comprises the Golden Rectangle extended in opposite directions.


Notes

1. S.Kroeger refers us to Lev Vygotski (1896-1934) and his Constructivism.
2. Natural world (physical), Built world (physical), Human worlds (perceptual and multiple). See also Nelson Goodman. Ways of Worldmaking. Hackett. Indianapolis IN. BH301.S8 G6x 1978.
3. See Jeremy Campbell. Grammatical Man: Information, Entropy Language, and Life. Simon and Schuster Touchstone Books. New York City NY. Q360 .C33 1982.
4. The Divine Proportion (De Devina Proportione) written by Fra Luca Pacioli in 1509 contains one of the earliest definitive statements about the formal order of aesthetic form and proportion.
5. 'Dynamis, the Greek word for dynamic, means power. Symmetria, symmetry in the Greek sense, means the due proportion of the several parts of a body to each other [coherence, commensurability]. In design, it is symmetry in this sense that governs the "just balance of variety in unity." Together, then, these two words express the basic function of the proportion-principle they name. Thus the series of spaces, the rectangle of dynamic symmetry, direct a way of thought and so become an instrument of design.' -from Christine Herter. Dynamic Symmetry: A Primer W.W.Norton. New York City NY. NC660.H4 1966. xi.

Miscellaneous
- Golden Section derivation
http: //www.public.asu.edu/%7Edetrie/pages/design_fundamentals/pages/ex_3.1_6.1.1_121.html
- Golden Section composition
http: //www.public.asu.edu/%7Edetrie/pages/design_fundamentals/pages/ex_3.1_6.1.2_121.html
- glossary
http://www.public.asu.edu/%7Edetrie/pages/design_fundamentals/pages/glossary.html
- bibliography
http://www.public.asu.edu/%7Edetrie/pages/reading/index.html
- 'Rhythm is in time what symmetry is in space.'
- Type, image, space, and their controls
- Dynamic Symmetry as a formmaking methodology.
- 'If it sounds good, it is good.' -Duke Ellington
- 'hide' example for camouflage point
- Socrates taught Plato, Plato taught Aristotle, Aristotle taught Alexander the Great (BC 356-323).
- Plato transposed the idea of correlated proportions from Pythagoras and his conception of musical harmony.
- Symmetry means consonance (unity) between the whole and its parts..
- Work backward to the square: square -> GS -> √5 -> √4 -> √2 -> square
- organic - inorganic | internal - external | macro - micro
- see Ghyka, 173 - Aristotle metaphor quote.
- The 1.618 proportion makes a rectangle that Hambidge named the 'rectangle of the whirling squares.'
- Hambidge pointed out that the diagonal of a rectangle, when joined with a perpendicular leading to one of the corners created a 'harmonic subdivision.'
- 'suspension of disbelief' -Coleridge - Unity in diversity -> the slides are diverse yet unified by like visual principles.
- The pentagon, a regular five-sided polygon, and the pentagram, a five-pointed star also comprise the 1.618 proportion.
- Here are four suggestions that I think we all could find helpful in our design studies.
(1) First, adopt a documented formmaking process.
(2) Second, use what you already know to learn what you do not yet know.
(3) Third, learn and transpose across disciplines and cultures.
(4) Fourth, study perception and mentation, especially through cognitive psychology and human-computer interaction (HCI).


Glossary

anthropomorphism
n. 1. Attribution of human motivation, characteristics, or behavior to inanimate objects, animals, or natural phenomena.
configuration
n. 1. a. Arrangement of parts or elements. b. The form, as of a figure, determined by the arrangement of its parts or elements. 2. Psychology Gestalt.
cognition
n. 1. The mental process or faculty of knowing, including aspects such as awareness, perception, reasoning, and judgment. 2. That which becomes known, as through perception, reasoning, or intuition; knowledge.
coherence
n. 1. The quality or state of cohering, especially a logical, orderly, and aesthetically consistent relationship of parts.
commensurable
adj. 1. Measurable by a common standard. 2. Commensurate; proportionate. 3. Mathematics Exactly divisible by the same unit an integral number of times. Used of two quantities.
configuration
n. 1. a. Arrangement of parts or elements. b. The form, as of a figure, determined by the arrangement of its parts or elements. 2. Psychology Gestalt.
dynamic
adj. 1. a. Of or about energy or to objects in motion. b. Of or about the study of dynamics. 2. Characterized by continuous change, activity, or progress. 3. Marked by intensity and vigor; forceful. 4. Of or about variation of intensity, as in musical sound. n. 1. An interactive system or process, especially one involving competing or conflicting forces. 2. A force, especially political, social, or psychological.
irrational number
n. Mathematics 1. Any real number inexpressable as an integer or as a ratio between two integers.
mentation
n. 1. Mental activity; thinking.
perception
n. 1. The process, act, or faculty of perceiving. 2. The effect or product of perceiving. 3. Psychology a. Recognition and interpretation of sensory stimuli based chiefly on memory. b. The neurological processes by which such recognition and interpretation are effected. 4. a. Insight, intuition, or knowledge gained by perceiving. b. The capacity for such insight.
polyhedron
n. 1. A solid bounded by polygons.
proportion
n. 1. A part considered in relation to the whole. 2. A relationship between things or parts of things with respect to comparative magnitude, quantity, or degree. 3. A relationship between quantities such that if one varies then another varies in a manner dependent on the first. 4. Agreeable or harmonious relation of parts within a whole.
ratio
n. 1. Relation in degree or number between two similar things. 2. The relative value of silver and gold in a currency system that is bimetallic. 3. Mathematics The relation between two quantities expressed as the quotient of one divided by the other: The ratio of 7 to 4 is written 7:4 or 7/4.
symmetry
n. 1. Exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis. See note at proportion. 2. A relationship of characteristic correspondence, equivalence, or identity among constituents of an entity or between different entities. 3. Beauty as a result of balance or harmonious arrangement.  

Selected Bibliography


1.0 Perception and Gestalt


Peter Baumgartner and Sabine Payr, editors. Speaking Minds: Interviews with Twenty Eminent Cognitive Scientists. Princeton University Press. Princeton NJ. BF311.S657 1995.

Carolyn M. Bloomer. Principles of Visual Perception. Second Edition. Design Press. New York City NY. N7430.5.B57 1990.

Richard L. Gregory, editor with the assistance of O.L. Zangwill. The Oxford Companion to the Mind. Oxford University Press. Oxford GB. BF31.O94x 1987.

Gaetano Kanizsa. Organization in Vision: Essays on Gestalt Perception. Praeger. New York City NY. BF203.K29 1979.

Kurt Koffka. Principles of Gestalt Psychology. Harcourt Brace. New York City NY. BF203.K64 1963.

Wolfgang Köhler. Gestalt Psychology. Liveright. New York City NY. BF203.K6 1947.

Michael Leyton. Symmetry, Causality, Mind. MIT Press. Cambridge MA. 1999.

Colin Ware. Information Visualization: Perception for Design.

Max Wertheimer. Productive Thinking. University of Chicago Press. Chicago IL. BF455.W46 1982.

Robert A. Wilson and Frank Keil. The MIT Encyclopedia of the Cognitive Sciences. MIT Press. Cambridge MA. 1999.


2.0 Dynamic Symmetry and Nature's Growth Spiral


R. Tucker Abbott and S. Peter Dance. Compendium of Seashells. American Malacologists. QL404.A18 1986.

R. McNeill Alexander. Bones: The Unity of Form and Function. Weidenfeld and Nicolson. London GB. QM101.A38 1994.

Adrian D. Bell. Plant Form: An Illustrated Guide to Flowering Plant Morphology. Oxford University Press. QK641.B45 1991.

Charles Bouleau. The Painter's Secret Geometry: A Study of Composition in Art. Thames and Hudson. London GB. ND1263.B613 1963.

Samuel Colman and C. Arthur Coan. Nature's Harmonic Unity. Putnam. New York City NY. 1912.

Samuel Colman and C. Arthur Coan. Proportional Form. Putnam. New York City NY. 1920.

Theodore Cook. The Curves of Life. Dover. New York City NY. 1979.

György Doczi. The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture. Shambhala. Boston MA. BH 301.C84 D62 1985.

Matila C. Ghyka. The Geometry of Art and Life. Sheed and Ward. New York City NY. N76.G52 1946.

Le Corbusier. Towards a New Architecture. Architectural Press. London GB. NA2520.J412x 1982.

Jay Hambidge. Dynamic Symmetry: The Greek Vase. Yale University Press. New Haven CT. NK4645.H25 1920.

Jay Hambidge. The Elements of Dynamic Symmetry. Dover Publications. New York City NY. NC703.H25 1967.

Jay Hambidge. The Parthenon and Other Greek Temples: Their Dynamic Symmetry. Yale University Press. New Haven CT. NA275.H3 1924.

Jay Hambidge. Practical Applications of Dynamic Symmetry. Yale University Press. New Haven CT. NK1505.H33 1932.

Christine Herter. Dynamic Symmetry: A Primer. W. W. Norton. New York City NY. NC660.H4 1966.

D'Arcy Wentworth Thompson. On Growth and Form. Abridged edition edited by John Tyler Bonner. Cambridge Univ. Press. Cambridge GB. QP84.T4 1966.

Rudolf Wittkower. Architectural Principles in the Age of Humanism. Imprint: Academy Editions. London GB. 1998. ISBN/ISSN 0471977632.


3.0 Bradbury Thompson

Allan Hurlburt. Bradbury Thompson. Communication Arts. Jan/Feb 1980. 88-104.

Philip B. Meggs. A History of Graphic Design. Second Edition. Van Nostrand Reinhold. New York City NY. ISBN 0-442-31895-2.

Bradbury Thompson. Bradbury Thompson: The Art of Graphic Design. Yale University Press. New Haven CT. Z116.A3T45 1988.

R.Roger Remington and Barbara J. Hodik. Nine Pioneers in American Graphic Design. MIT Press. Cambridge MA. NC998.4.R4 1989.

Profile

Thomas Detrie is a designer and Professor Emeritus in the ASU College of Architecture and Environmental Design. He began his career in 1970, and since 1984 has been at Arizona State University where he has been the Graphic Design Program Coordinator and the School of Design Foundation Program Coordinator. He has also taught at Louisiana State University and Ohio University, and has been a guest lecturer at Rhode Island School of Design. He has made presentations at Boston University, College of Mount St Joseph (Cincinnati), Facultad del Habitat, Universidad Autonoma de San Luis Potosi, Mexico, Microsoft Corporation, and University of Cincinnati DAAP. Prof Detrie will again co-facilitate a typography workshop for the California State University Summer Arts Program 2003 in Fresno.
Prof Detrie earned BFA and MFA degrees from Louisiana Tech University, and an MFA (foreign equivalent) from the Basel School of Design in Switzerland where he studied for three years, 1980 through 1983.
Design Quarterly, Typography: Form and Communication by Carter, Day, and Meggs, publications by Armin Hofmann, and the Swiss Journal of Typography (TM) include his work in letterform, typography, and visual communication. Prof Detrie has done font design work for the American Mathematical Society, The Font Company, IBM, and the Rocky Mountain Mathematical Consortium. He is also a contributor to Graphic Communications: The Printed Image by Z.A.Prust (Z244.P958 1998).
Prof Detrie's interests include: Aesthetics and Visual Principles; Cognitive Psychology and Modular Intelligence; Design as Education; Design Fundamentals Education; Design's Cultural and Historical Context; Digital Color and Digital Printing; Font Design; Semiotics; and Human-computer Interaction.
| Thomas Detrie | detrie@asu.edu | http://www.public.asu.edu/~detrie/ |