Essays

UNDER CONSTRUCTION

As such, there is very little discussion as to the nuances and intricacies of parquet deformation design, even from William Huff himself. Recently (2021), I have been invited to contribute an 8–10 page article, of a tutorial premise, for a forthcoming book on the subject, by Werner Van Hoeydonck. In the course of this, I compiled a draft containing some aspects of relevance, such as defining a parquet deformation (which is more difficult than may otherwise be thought), the advantages of the computer (as against hand drawn instances), and more. However, not all of this material will be retained in the article. Be that as it may, the text still serves as an excellent guide as to the many nuances and intricacies, and so I have decided to place here under the generic title of ‘Essays’, pending a more expansive, dedicated piece of writing for each topic. Each essay is of a self contained nature, independent of others. To this end, each this has its own set of references.

Contents

1. Defining a Parquet Deformation

2. The Advantages of the Computer

3. Experimentation

4. The Two Types of Huff-Inspired Parquet Deformations

5. The Strip Width

6. Colouration

7. Viewing

8. Aesthetics

9. Transition Zones

10. Music Analogies

11. Further Possibilities (Subdivision, Mirror, Rotations, Translation)

1. Defining a Parquet Deformation

I begin by first repeating Huff’s definition in Hofstadter [*], which differs a little from my own, but not in fundamentals, and contrasts our definitions.

Huff:

The deformations are not arbitrary but must satisfy two basic requirements: (1) there must be change only in one dimension, so that it is possible to see a temporal progression in which one tessellation gradually becomes another, and (2) at each stage the pattern must constitute a regular tessellation of the plane, that is, there must be a unit cell that could combine with itself so that it could cover an infinite plane exactly. 

Bailey:

A parquet deformation is one in which a regular tiling of the plane (or more rarely a non-periodic tiling) gets deformed progressively, typically in one dimension as a strip, although two dimensions are permissible. The general process is a tiling as a column, followed by a column as a transition region, of which the process then repeats until the deformation has run its course. The transition column, which contains tiles that possess elements of the preceding and following columns, will thus not tile by itself. 

I have quibbles with the two points given by Huff. In (1), the main difference is that he rules out two dimensions. Curiously, though, in practice he breaks these rules; there are many two-dimensional instances from his students. In (2), I find this imprecise. As change is involved, there must inevitably be a loosening of the tiling condition. Huff also adds another condition, of ‘allowed parquets’. Upon correspondence, he informed me that some of mine broke his rules [*], [*].


2. The Advantages of the Computer

The computer has many different advantages, depending on mathematical ability, but at its basic is accessible to all. There are * main reasons for this:

(1) At its most basic, speed. With copy/paste, much more can be achieved than otherwise, for example, of my favoured 4-unit strip, detailed below, simply drawing a single row, and then repeating three times, obviously only requires a quarter of the time by hand. By hand, the process is most laborious.

(2) Productivity. The time saved as above can be used to draw more works, using the example above, four times as much.

(3) Error-free work. With undo/redo mistakes can easily be removed that a work with a pen is otherwise impossible, of which with many lines can so easily occur, not to mention the additional fatigue factor. 

(4) It encourages experimentation that would otherwise be impractical by hand. An instance as such is an assembly into ‘super deformations’ as discussed below. And further, other configurations.

Even so, when learning, pen and paper has an immediacy that the computer lacks. Be that as it may, once the basic principles have been grasped, it is relatively easy to transpose those onto the computer. A lot depends on one’s experience. Certainly, CAD programs seem better suited than illustration (e.g. Adobe Illustrator) and geometry programs (e.g. GeoGebra). And further, in the right hands, the computer can be used to expand on the ‘simple premise’ Huff instances. The work of Kaplan [*]  exemplifies this, and, to a lesser degree at least in terms of the extent, Edmund Harriss [*]. However, Kaplan’s work, involving advanced algorithms, is somewhat of an outlier. Harriss’s work is on aperiodic tiling. Furthermore, there is the Parakeet plug-in as shown by Esmael Mottaghi and Arman Khalli Beigi [*]. A major advantage here is in the swiftness of execution; a completed, intricate deformation once set up can be composed instantly that otherwise undertaken in Huff’s day would require many hours, if not days! Another computer approach is with a specific goal in mind e.g. deform a given Laves tiling to another. Kaplan [*] shows ten of the eleven possible instances (the eleventh was in ?). However, this typically involves more advanced knowledge required, way beyond most design-focused people. Typically, the first approach will be invariably adopted by the typical design student in the field.


3. Experimentation

A feature of the Huff process is that the deformations arose as a result of experimentation i.e. without a goal polygon/s in mind (as against, say, beginning with a square to a rectangle). By this, I mean that once the deform is started, with any of the standard devices, the outcome is not predetermined in a visual sense; only upon completion does it become obvious. Hofstadter himself alludes to this [*]. As a result, not all deformations are as picturesque as another. Some flow smoothly, with elegance, whilst others simply jar.



4. The Two Types of Huff-Inspired Parquet Deformations

The Huff-inspired studies can be described broadly as of two types, of ‘simple’ or ‘intricate’. Both types can be seen in Hofstadter's article (some are of a dual placing, as blurring occurs): e.g. Fred Watts’ Fylfot Flipflop and Noel Japach’s Arabesque, respectively. As a rule, I favour drawing the simpler type, in both aesthetics and practical terms. To me, the complicated instances appear to be an exercise in intricacy just for the sake of it. The time taken, for what must have been countless hours, is out of all proportional as to inherent worth. I could easily imagine that this would require the same time as say of ten or more simple deformations. I can certainly admire and appreciate it, but can the time expanded be justified? For me, no. Further, such instances by hand can now be considered as outdated. Esmael Mottaghi and Arman Khalli Beigi show in their Parakeet plug-in (for Rhino) that such types can now be composed, once set, instantaneously. On the grounds of near impracticality by hand and the speed and efficiency of Parakeet, I summarily dismiss such types in the following tutorial.


5. The Strip Width 

An open question is to the ideal thickness, in terms of units, of the strip. Again, as with tempo matters, this is subjective; there is no one single best. A minimum strip, of 2 units, is judged too brief. Although this is sufficient to show the tiling premise, this is only barely so and can be considered as parsimonious in the extreme.

On the other hand, a strip of say 10 units (or more) is judged more so than is necessary to show the tiling premise.

In practice, it will be found that 4 units (Fig. *), commensurate with a square here, are judged ideal. However, 6 units are still an eminently viable proposition, and perhaps even 8 units. A tiling rule that I follow, of my own devising, transposed to parquet deformations, is that when one can see that the repeat nature is obvious then there is no need to show more, and so 4 units are judged as ideal.


6. Colouration

Invariably, the Huff student-inspired deformations are shown without colour, but this is not discussed in the literature. However, there is a reason for the omission. In private correspondence [*] he told me:

Incidentally, while we were studying "pure" parquets---no deformations, we did color many of them black and white, etc. But when we concentrated on the parquet deformation, we did not "color" them, because we saw the beauty in the line.....the shapes of the tiles were secondary...not unimportant, but secondary.

One can surmise here that colour would be a distraction from the core premise. Be that as it may, colouration remains a possibility, essentially as an addition, or an option, to the core-value line deformation, but it is not an important matter in itself. Indeed, although the possibility seems obvious, this is generally neglected by the designer. One notable exception is that of Kaplan [*]. Here he shows computer colouration instances, of map colouring contrasting colours, as well as gradients. 

Another possibility is that of using different coloured lines, where the deformation is in effect an overlay, for example, Fig. * [*]. However, such instances are rare. Again, it should be considered as an addition or option.

Add Klee’s quote to this passage somewhere?

This reminds me of Paul Klee's famous quote ‘A drawing is simply a line going for a walk’.



7. Viewing

Interestingly, Huff wrote on this, linking it with the viewing of Sino-Japanese landscape handscrolls [*]. Typically, with the premise of linear viewing, I favour beginning with the deformation reading from left to right, typically with a square with increasing angularity of lines. Viewing this way, is, to me, more natural, given the western practice of reading left to right. Other cultures read from right to left, and so the deformation should begin at the right. Further, other cultures read vertically, top to bottom, and so in such cases are better presented as accordingly to custom. However, I do not consider the issue a major concern.


8. Aesthetics

Of fundamental importance is what I term as the aesthetics of a parquet deformation. In short, whether this has artistic integrity, or, even blunter, is good or bad. It is a relatively easy task (especially with computer assistance) to compose numerous parquet deformations, essentially to the point of triviality. However, not all can be described as aesthetic, which of course should be the standard to aim for. So, what is it that makes for an aesthetic parquet deformation? As such, this is perhaps somewhat subjective; a strict set of rules is difficult to define. Symmetry is a rough guideline but is not infallible. Instances that are symmetrical can be described as aesthetic and non-aesthetic, whilst instances that are non-symmetrical can also be described as aesthetic and non-aesthetic. 

To aid the discussion, I show instances of the four types, Figs. 1-4. Without too in-depth an analysis, the aesthetic instances, Fig. 1 and Fig. 2, transition from basic, core value tiling polygons of a square to rectangle and two right-angled triangles (set within a square) to rectangles respectively, in a ‘natural’, flowing manner. In contrast, the non-aesthetic instances, Fig. 3 and Fig. 4, although beginning also with core value tiling polygons, two right-angled triangles (set within a square) and a parallelogram, simply do not flow, and can be described as jarring and ‘unnatural’, elongated tiles respectively, and furthermore, transition to essentially nondescript tiling polygons within a square. Detailing exactly the differences is not straightforward, but the most obvious test is a simple, visual one, of which at-a-glance matters of aesthetics are, or should be, self-evident.

Fig. 1. Aesthetic, Symmetrical

Fig. 2. Aesthetic, Non-Symmetrical
Fig. 3. Non-Aesthetic, Symmetrical


Fig. 4. Non-Aesthetic, Non-Symmetrical

9. Transition Zones

A basic premise of a parquet deformation is that of tiling, and of which Huff specially refers to, in Hofstadter [*]: 

The deformations are not arbitrary but must satisfy two basic requirements: (1) there must·be change only in one dimension, so that it is possible to see a temporal progression in which one tessellation gradually becomes another, and (2) at each stage the pattern must constitute a regular tessellation of the plane, that is, there must be a unit cell that could combine with itself so that it could cover an infinite plane exactly. 

However, this is not made clear in visual form. Although Huff’s comments are indeed of the guiding premise, I find his comments and intentions are a little imprecise, and open to interpretation. One interpretation is that all the tiles in the deformation will tile. However, this is not so. By its very nature, with changing tiles, it is simply impossible to compose a parquet deformation in which all tiles will tile. Rather, his explanation would have been served with the use of the words transition zone (or transition stage). This serves as the intermediary stage of the deformation in which the tiles do not tile, whereas on either side, they do. (They are close to tiling, but do not.) I would prefer the following, of which I insert ‘transition zone’ to Huff’s text:

The deformations are not arbitrary but must satisfy two basic requirements: (1) there must·be change only in one dimension, so that it is possible to see a temporal progression in which one tessellation gradually becomes another, separated by a transition zone, and (2) at each stage the pattern must constitute a regular tessellation of the plane either side of the transition zone, that is, there must be a unit cell that could combine with itself so that it could cover an infinite plane exactly.

A diagram below makes this clearer than any amount of words will do. The red colouring shows the transition zone, in a series of columns.

Fig. *. Parquet Deformation showing the transition zone (in red)

10. William Huff and Parquet Deformation Music Analogies

Of note (ahem!) is the frequent use of parquet deformation musical analogies used by William Huff (and Douglas Hofstadter) in their various writings. However, as the material is scattered among other non-musical analogy discussions, finding (by remembering) such references is not easy. To this end, I have thus compiled the listing below, with all the references to hand. Possibly, there may be more. 

For ease of findings, I have highlighted the word music (and derivatives) in red. Also, where there is an implied music discussion, I have highlighted this in blue. Eight distinct appearances are found, of varying depth and length. Of most note is the Hofstadter reference, of a substantial discussion. The text length shown generally varies according to ease of accessibility; sometimes it was possible to copy from a PDF, and others not. To type out in full where otherwise is judged not a productive use of time. Instead, I show excerpts in such cases.


1979. William S. Huff. The Parquet Deformation The Mirror-Rotation, 1979

1983. Douglas R. Hofstadter. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American, 1983, pp. 14–20

1984. Anon. Science Digest, Vol. 98, 1984 Page 19, 25? Issues 7-9

1990. William S. Huff, ‘Students' work from the Basic Design Studios of William S. Huff’. In Intersight One. State University of New York at Buffalo, 1990. 10, pp. 8085.

1991. Charles Talley (Editor). Surface Design Journal - Volumes 16-17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.

1996. William S. Huff ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag, 1996, pp. 307–314.

2010. William S. Huff. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010, 128 pp.

2012. Stavros Laparidis. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012,  P. 22. 

1. William S. Huff.The Parquet Deformation The Mirror-Rotation Symmetry’, 1979

As such, it is unclear as to quite what this single page document is. From its style and appearance, it appears to be a class guideline.

Two mentions of music analogies.

...These continuous deformations are most often developed along syngenometric lines. The total compositions are not intended to be viewed spatially, but temporally, as a sort of visual music. The Oriental scroll paintings are one of the great few temporal, visual compositions. Viewing them, then, is akin to the manner in which film is seen, poetry read, and music heard.

Also see entry 4: ‘Students' work from the Basic Design Studios of William S. Huff’ , where the same broad text is recycled.

2. Douglas R. Hofstadter. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20

Twenty-five mentions of music analogies! Of note (ahem!) here is the sheer extent and depth of the music references. To better understand the context, I have largely included the surrounding text, despite this thus resulting in a somewhat lengthy document. However, without it, the story would only have been partial, and so I have judged a more thorough treatment is in order. 

P. 14

What is the difference between music and visual art? If someone asked me this question; I would have no hesitation ill responding. To me the major difference is temporality. Works of music intrinsically involve time; works of visual art do not. More precisely, pieces of music consist of sounds' intended to be played and heard in a specific order and at a specific speed. Music is therefore fundamentally one dimensional; it is tied to the rhythms of our existence. Works of visual art, in contrast, are generally two- or three-dimensional. Paintings and sculpture seldom have any intrinsic "scanning order" built into them that the eye must follow. Mobiles and other pieces of kinetic art may change over time, but often without any specific initial state or final state or intermediate states. You are free to come and go as you please. There are, of course, exceptions to this generalization. European art has grand friezes and historic cycloramas, and Oriental art has intricate pastoral scrolls up to hundreds of feet long. These types of visual art impose·a temporal order and speed on the scanning eye. There is a starting point and a final point. Usually, as in stories, these points represent states of relative calm, particularly at the end. In between, various types of tension are built up and resolved in an idiosyncratic but pleasing visual rhythm. The calmer end states are usually orderly and visually simple, whereas the tenser intermediate states are usually more chaotic and visually confusing. If you replace "visual" by "aural," virtually the same can be said of music. I have been fascinated for many years by the idea of trying to capture the essence of the musical experience in visual form. I have my own ideas about how this can be done; in fact, I spent several years working out a form of visual music. By no means, however, do I think there is a unique or best way to carry out this task of "translation," and indeed I have often wondered how others might attempt to do it. I have seen a few such attempts, but most of them struck me as being unsuccessful. One striking counterexample is the set of "parquet deformations" meta-composed by William S. Huff, professor of architectural design at the State University of New York at Buffalo….

I say "meta-composed" for good reason. Huff himself has never executed a single parquet deformation. He has elicited hundreds of them, however, from his students, and in so doing he has brought this form of art to a high degree of refinement. He might be likened to the conductor of a fine orchestra. Although the conductor makes no sound in the course of a performance, we give much credit to the person doing the job for the quality of the sound. We can only guess at how much preparation and coaching went into the performance.

P. 15

Whereas Escher's tessellations are almost always based on animal forms, Huff decided to limit his scope to purely geometric forms. In a way that is like a decision by a composer to follow austere musical patterns and to totally eschew anything that might conjure up a "program" (that is, some kind of image or story behind the sounds). An effect of this decision is that the beauty and visual interest must come entirely from the complexity and subtlety of the interplay of abstract forms. There is nothing to "charm" the eye, as there is with pictures of animals. There is only the unembellished perceptual experience. Because of the linearity of this form of art, Huff has likened it to visual music. He writes: "Although I am spectacularly ignorant of music, tone-deaf and hated those piano lessons (yet can be enthralled by Bach, Vivaldi or Debussy), I have the students 'read' their designs as I suppose a musician might scan a work: the themes, the events, the intervals, the number of steps from one event to another, the rhythms, the repetitions (which can be destructive, if not totally controlled, as well as reinforcing). These are principally temporal, not spatial, compositions (although all predominantly temporal compositions have, of necessity, an element of the spatial and vice versa e.g., the single-frame picture is the basic element of the moving picture)."

P. 17

This piece also illustrates yet another way parquet deformations resemble music. A unit cell-or rather, a vertical cross section consisting of a stack of unit cells-is analogous to a measure in music. The regular pulse of a piece of music is given by the repetition of unit cells across the page. And the flow of a melodic line across measure boundaries is modeled by the flow of a visual line-such as the mountain-range lines-across many unit cells. Bach's music is always called up in discussions of the relation between mathematical patterns and music, and this occasion is no exception. I am reminded particularly of some of Bach's texturally more uniform pieces, such as certain preludes from "The Well-tempered Clavier," where in each measure there is a certain pattern executed once or twice and possibly more times. From measure to measure this pattern undergoes a slow metamorphosis, meandering in the course of many measures from one region of harmonic space to far-distant regions and then slowly returning by some circuitous route. For specific examples you might listen to (or look at the scores of) Book I, No. 1 and No. 2, and Book II, No. 3 and No. 15. Many of the other preludes have this feature in places, although not for their entirety. Bach seldom deliberately set out to play with the perceptual systems of his listeners. Artists of his century, although they occasionally played perceptual games, were considerably less sophisticated about, and less fascinated by, issues we now deem part of perceptual psychology. Such phenomena as regrouping would have intrigued Bach, and I sometimes wish he had known of certain effects and had been able to try them out, but then I remind myself that whatever time Bach might have spent playing with newfangled ideas would have had to be subtracted from his time for producing the masterpieces we know and love, and so why tamper with something that precious? On the other hand, I do not find this argument 100 percent compelling. Who says that if you are going to imagine playing with the past, you have to hold the lifetimes of famous people constant in length? If we can imagine telling Bach about perceptual psychology, why can't we also imagine adding a few extra years to his lifetime to let him explore it? After all, the only divinely imposed (that is, absolutely unslippable) constraint on Bach's years is that they and Mozart's years add up to 100, no? Hence if we give Bach five extra years, then we merely take five away from Mozart. It is painful, to be sure, but not all that bad. We could even let Bach live to 100! (Mozart would never have existed.) Although it is difficult to imagine and impossible to know what Bach's music would have been like if he had lived in the 20th century, it is certainly not impossible to know what Steve Reich's music would have been like if he had lived in this century. In fact, l am listening to a record of it right now. Now, Reich's music really is conscious of perceptual psychology. All the way through he plays with perceptual shifts and ambiguities, pivoting from one rhythm to another, from one harmonic origin to another, constantly keeping the listener on edge and tingling with nervous energy. Imagine a piece resembling Ravel's "Bolero," only with a much finer grain size, so that instead of its having roughly a one-minute unit cell it has a three-second unit cell. Its changes are so tiny that sometimes you can barely tell it is changing at all, whereas at other times the changes jump out at you. What Reich piece am I listening to? Well, it hardly matters, since most of his music satisfies this characterization, but for the sake of specificity you might try "Music for a Large Ensemble," "Octet" or "Violin Phase." 

P. 18

Perhaps irrelevantly, but I suspect not, the names of many of these studies remind me of pieces by Zez Confrey, a composer best known in the 1920's for his novelty piano pieces such as "Dizzy Fingers" and "Kitten on the Keys" and - my favorite - "Flutter By, Butterfly." Confrey specialized in pushing rag music to its limits without losing musical charm, and some of the results seem to me to have a saucy, dazzling appeal not unlike the jazzy appearance of this parquet deformation.

P. 18

Incidentally, I know of no piece of visual art that better captures the feeling of beauty and intricacy in a Steve Reich piece, created by slow "adiabatic" changes floating on top of the chaos and dynamism of the lower-level frenzy. Looking back, I see I began by describing this parquet deformation as "calm." Well, what do you know? Perhaps I would be a good candidate for one of The New Yorker's occasional notes titled "Our Forgetful Authors." More seriously, there is a reason for this inconsistency. One's emotional response to a given work of art, whether the work is visual or musical, is not static and unchanging. There is no way of knowing how you will respond the next time you hear or see one of your favorite pieces. It may leave you unmoved or it may thrill you to the bone. It depends on your mood, on what has recently happened, on what happens to strike you and on many other subtle intangibles. One's reaction can even change in the course of a few minutes. And so I won't apologize for this seeming lapse.

P. 20

Comparing the creativity that goes into parquet deformations with the creativity of a great musician, Huff writes: "I don't know about the consistency of the genius of Bach, but I did work with the great American architect Louis Kahn (1901-1974) and suppose it must have been somewhat the same with Bach. That is, Kahn, out of moral, spiritual and philosophical considerations, formulated ways he would and ways he would not do a thing in architecture. Students came to know many of his ways, and some of the best could imitate him rather well (although not perfectly). But as Kahn himself developed he constantly brought in new principles that brought new transformations to his work, and he even occasionally discarded an old rule. Consequently he was always several steps ahead of his imitators who knew what was but couldn't imagine what will be. And so it is that computer-generated 'original' Bach is an interesting exercise. But it isn't Bach-that unwritten work that Bach never got to, the day after he died." 

Writing lovely melodies is another one of those deceptive arts. To the mathematically inclined, notes seem like numbers and melodies like number patterns. Therefore all the beauty of a melody seems as if it ought to be describable in some simple mathematical way. So far, however, no formula has produced even a single good melody. Of course, you can look back at any melody and write a formula that will produce it and variations on it. But this is retrospective, not prospective. Lovely chess moves and lovely melodies (and lovely theorems in mathematics) have this in common: every one has idiosyncratic nuances that seem logical a posteriori but are not easy to anticipate. To the mathematical mind chess-playing skill and melody-writing skill and theorem-writing skill seem obviously formalizable, but the truth turns out to be more tantalizingly complex than that. Too many subtle balances are involved.

3. Anon. Science Digest, 1984, Vol. 98 Page 19, 25? Issues 7-9

A full bibliographic reference is not available, all that is known is on Google Books, as above. The issue month is not stated.

Although music is not mentioned as such, this is indeed implied, with words such as ‘composer’ and ‘composition’.

How to read a fylfot flipflop

A parquet deformation is not a warped apartment floor; it's an ingenious problem in design. The basic elements are called tiles: squares, hexagons or other polygons that form a grid, like floor tiles laid congruently in a repeating pattern. But for the students in William Huff’s design course at the State University of New York, Buffalo, such a design is only the beginning.

Their task is to subtly deform the tiles, step by step, so that they change as the design is read from left to right. “I look at it somewhat the way a composer might look at his composition”, says Huff. “I tell students to let their eye tell them whether it's flowing or not, then we look at the design analytically. What are the events? How long does it take to get from one to another? What are the rhythms?”

An event is an eye-catching configuration… [Missing text]

...return of the square, but with the swastika reversed-the final event.

There are other interesting discoveries to be made about vertical and horizontal lines. After 20 years, says Huff, “I come to these new each time.”

[Caption] HOW TO READ THIS FYLFOT FLIPFLOP. TURN IT COUNTERCLOCKWISE. A fylfot is a swastika. In this design, called a parquet deformation, the fylfot reverses at the right.

4. William S. Huff, ‘Students' work from the Basic Design Studios of William S. Huff’. In Intersight One. State University of New York at Buffalo, 1990. 10, pp. 8085.

Two mentions of music analogies.

The whole composition of a parquet deformation is not intended to be viewed spatially, but temporally -- as a kind of visual music. The Oriental scroll paintings are one of the great few temporal, visual compositions. Viewing one, then, is akin to the manner in which film is seen, poetry read, and music heard.

The text here borrows heavily from the text of the earlier  ‘The Parquet Deformation The Mirror-Rotation Symmetry’, 1979, of which for the sake of convenience I repeat below:

The total compositions are not intended to be viewed spatially, but temporally, as a sort of visual music. The Oriental scroll paintings are one of the great few temporal, visual compositions. Viewing them, then, is akin to the manner in which film is seen, poetry read, and music heard.

5. Charles Talley (Editor). Surface Design Journal - Volumes 16-17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.

NOT SEEN, GOOGLE BOOKS REFERENCE

Snippet view on Google Books:

P. 10. The incremental pace of change in a parquet deformation is rather like that of days moving one season to the next. Hofstadter notes its temporal character, equating a parquet deformation to visible music. The underlying principle seems to be …

One mention of music analogies. Referring Hofstadter’s article. Essentially inconsequential.

6. William S. Huff. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag 1996, pp. 307–314.

Seven mentions of music analogies.


7. William S. Huff. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010,.

One mention to music analogies, referencing back to ‘The Landscape Handscroll..’.

The Experience of Timing

On previous occasions, I gave oral and written accounts of a type of design, regularly assigned in my basic design studio—the parquet deformation—which disposes time to participate as an integral third dimension, thus dynamizing the two-dimensional spatial content of the design. Commentary on the aesthetic potential of the parquet deformation was presented at the Katachi 2 conference (Huff 1994: 219-222), and commentary on its geometric requisites was presented at the SEMA 4 conference (Huff 2003: 9). I liken the parquet deformation to a remarkable art form, the Chinese handscroll, which, in its most exceptional, but younger genre, the landscape handscroll, goes back a thousand years. Time unfolds as the scroll is synchronously unrolled and rolled—pleasurable frame by pleasurable frame—not dissimilarly to how music flows. Time is engaged, however, in a different manner in respect to compositions whose three dimensions are all spatial.

8. Laparidis, Stavros. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012,  P.  22. 

19 Example 5. Étude 9: Vertige, opening seemingly static but constantly changing type of music as “parquet deformation,” a very insightful term to describe this compositional design…

GOOGLE SCHOLAR REFERENCE, OSTENSIBLY ON PROQUEST. REQUESTED ON RESEARCHGATE

One mention of music analogies. Only a part-preview is available on ProQuest, of which just the first 13 pages are viewable. Although likely of a mention just in passing, of interest due to one of the few non Huff/Hofstadter music discussions.

References

[*] Anon. Science Digest, 1984, Vol. 98 Page 19, 25?

[*] Hofstadter, Douglas R. 'Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension'. ‘Metamagical Themas’, Scientific American 1983, pp. 14–20

[*] Huff, William S. The Parquet Deformation The Mirror-Rotation Symmetry, 1979

[*] Huff, William S. ‘Students' work from the Basic Design Studios of William S. Huff’. In Intersight One. State University of New York at Buffalo, 1990. 10, pp. 8085.

[*] Huff, William S. ‘The Landscape Handscroll and the Parquet Deformation’, In Katachi U Symmetry. Tohru Ogawa, ‎Koryo Miura, ‎and Takashi Masunari. Tokyo: Springer-Verlag 1996, pp. 307–314.

[*] Huff, William S. ‘Simulacra of Nonorientable Surfaces—Experienced through Timing’. In Spatial Lines, (Líneas espaciales) Patricia Muñoz, compiler. Buenos Aires: De la Forma, 2010, 128 pp.

[*] Laparidis, Stavros. ‘The Role of Allusion in Ligeti's Piano Music’. Dissertation, 2012,  P. 22.

[*] Talley, Charles (Editor). Surface Design Journal - Volumes 16-17. United States: Surface Design Association, pp. 8–10, 1991. Neither author nor article title is given.



11. Further Possibilities (Two versions, of 13 and 24 April 2021

New (24 April 2021)


Upon the completion of the parquet deformation, which in itself can be considered as serving as a finished work, in effect a first generation parquet deformation, it is then possible to use this as a framework for further possibilities. This involves subdividing, and symmetry operations involving superposing, with translation, reflection (both vertical and horizontal) and rotation. Typically, with all, the parquet deformation becomes more involved, with a broad doubling of lines. In effect, such additional aspects can be described as a second generation parquet deformation forming. The possibilities are just about endless, but the outcome is not aesthetic as another, as happens with first generation parquet deformations. Judgements must be made in the matter, otherwise the results become trivial. The broad aim here is to see any trends/tendencies, both favorable and unfavorable (i.e. aesthetic and non-aesthetic), and then apply the favorable instances to other parquet deformation of a broad like

nature. To this end, I use three different parquet deformations as exemplars, with the tiles being asymmetric, and one and two lines of mirror symmetry. The format adopted is two-fold: first, I show the first generation parquet deformation, and second, the various 'extra possibilities' (as outlined above) as a second generation parquet deformation (as such, there can be one or more such second generation instances). Such a format makes clear the 'before and after' aspect at-a-glance.

As alluded to above, the computer is a great aid here, and this is where it really comes into its own, with multiple use of a single image. Although each of the examples shown here are practical by hand, much more can be accomplished by computer, in both speed of execution and design.


SUBDIVIDING

By suitably subdividing the tiles, new parquet deformations can be formed. A variety of lies are used, including diagonals, from left to right and right to left and then both diagonals. A particular favorite is a double basket weave structure. This gives a very pleasing overlay effect at right angles. Other subdivisions are less well defined, selected as according to the parquet deformation. The outcome can depend on the nature of the parquet deformation. For instance, some parquet deformations have asymmetric tiles, of mirror symmetry, or order 4 rotation, all of which impinge on the process as to aesthetics. To this end, I show examples of all three instances, with typical subdivisions. As can be seen, only a few can be described as aesthetic.


Asymmetric Tile - Source (Tunisia - Sousse)


Fig. 1a. First Generation Parquet Deformation (Tunisia - Sousse)

Fig. 1b. Second Generation Parquet Deformation. One diagonal subdivided left to right( Tunisia - Sousse)

Fig. 1c. Second Generation Parquet Deformation. One diagonal subdivided right to left (Tunisia - Sousse)


Fig. 1d. Second Generation Parquet Deformation. Two diagonals subdivided, left to right and right to left (Tunisia - Sousse)

Fig. 1e. Second Generation Parquet Deformation. Alternate diagonals subdivided, left to right and right to left (Tunisia - Sousse)

Fig. 1f. Second Generation Parquet Deformation. Double Basketweave (Tunisia - Sousse)


Symmetrical Tile, One Axis of Reflection - Source (Argentina - Buenos Aires)


Fig. 2a. First Generation Parquet Deformation (Argentina - Buenos Aires)


Fig. 2b. Second Generation Parquet Deformation. One diagonal subdivided left to right (Argentina - Buenos Aires)


Fig. 2c. Second Generation Parquet Deformation. One diagonal subdivided right to left (Argentina - Buenos Aires)


Fig. 2d. Second Generation Parquet Deformation. Two diagonals subdivided, left to right and right to left (Argentina - Buenos Aires)


Fig. 2e. Second Generation Parquet Deformation. Double Basketweave (Argentina - Buenos Aires)


Symmetrical Tile, Two Axes of Reflection - Source (Rio De Janeiro)


Fig. 3a. First Generation Parquet Deformation (Brazil - Rio De Janeiro)


Fig. 3b. Second Generation Parquet Deformation.
One diagonal subdivided left to right
(Brazil - Rio De Janeiro)

Fig. 3c. Second Generation Parquet Deformation. One diagonal subdivided right to left (Brazil - Rio De Janeiro)


Fig. 3d. Second Generation Parquet Deformation. Two diagonals subdivided left to right and right to left 
(Brazil - Rio De Janeiro)

Fig. 3e. Second Generation Parquet Deformation. Basketweave 1 (Brazil - Rio De Janeiro)

A beautiful design, with the pleasing feature of overlapping blocks of four tiles at right angles, in the same manner as the famous Cairo tiling.


Fig. 3f. Second Generation Parquet Deformation. Basketweave 2 (Brazil - Rio De Janeiro)

Another beautiful design, with the pleasing feature of overlapping blocks of four tiles at right angles, in the same manner as the famous Cairo tiling.


TRANSLATION


Fig. 4a. First Generation Parquet Deformation (Tunisia - Sousse)


Fig. 4b. Second Generation Parquet Deformation. Translation half unit, vertically (Tunisia - Sousse)


Fig. 4c. Second Generation Parquet Deformation. Translation half unit, horizontally (Tunisia - Sousse)


Fig. 4d. Second Generation Parquet Deformation. Translation mid cell (Tunisia - Sousse)


Fig. 5a. First Generation Parquet Deformation (Argentina - Buenos Aires)



Fig. 5b. Second Generation Parquet Deformation. Translation half unit, horizontally (Argentina - Buenos Aires)

Fig. 5b. Second Generation Parquet Deformation. Translation half unit, vertically (Argentina - Buenos Aires)

Fig. 5c. Second Generation Parquet Deformation. Translation mid cell (Argentina - Buenos Aires)


Fig. 6a. First Generation Parquet Deformation (Brazil - Rio De Janeiro)

Fig. 6b. Second Generation Parquet Deformation. Translation horizontally, half unit (Brazil - Rio De Janeiro)

Fig. 6c. Second Generation Parquet Deformation. Translation vertically, half unit (Brazil - Rio De Janeiro)

Fig. 6d. Second Generation Parquet Deformation.  Translation mid cell (Brazil - Rio De Janeiro) N.B. The alignment is (naturally) not exact, masked at this small scale of diagram.


MIRROR OVERLAY - HORIZONTAL AXIS


Source (Tunisia - Sousse)


Fig. 4a. First Generation Parquet Deformation (Tunisia - Sousse)


Fig. 4b. Second Generation Parquet Deformation (Tunisia - Sousse)

N.B. Reflected about vertex. The same outcome arises if a midside cell is reflected


Argentina - Buenos Aires (Source)

Fig. 4a. First Generation Parquet Deformation (Argentina - Buenos Aires)

Fig. 4b. Second Generation Parquet Deformation (Argentina - Buenos Aires)

N.B. Reflected about vertex. The same outcome arises if a midside cell is reflected


Brazil - Rio De Janeiro


Fig. 5a. First Generation Parquet Deformation

N.B. The same outcome arises if a midside cell is reflected


Fig. 5b. Second Generation Parquet Deformation

N.B. The same outcome arises if a midside cell is reflected


MIRROR OVERLAY - VERTICAL AXIS

Given that this symmetry operation results in the second generation parquet deformation being the same at both ends, this is lacking aesthetically, and is not to be compared to the 'standard model', where the tiles differ at the ends (this negates instances where the same tile arises, but through part of its natural cycle, which is aesthetic)


Tunisia

Fig. 6a. First Generation Parquet Deformation (Tunisia - Sousse)


ADD

Fig. 6b. Second Generation Parquet Deformation

N.B. The same outcome arises if a midside cell is reflected


Fig. 7a. First Generation Parquet Deformation


Fig. 7a. Second Generation Parquet Deformation

Fig. 8a. First Generation Parquet Deformation

Fig. 8b. Second Generation Parquet Deformation

ROTATION OVERLAY - 180

Fig. 9a. First Generation Parquet Deformation (Tunisia - Sousse)

Fig. 9b. Second Generation Parquet Deformation - 180 around vertex (Tunisia - Sousse)

Fig. 9b. Second Generation Parquet Deformation -180 around midcell - same outcome! (Tunisia - Sousse)

Fig. 9c. Second Generation Parquet Deformation -180 around midcell (Argentina - Buenos Aires)


Fig. 9c. Second Generation Parquet Deformation -180 around midcell (Argentina - Buenos Aires)

Fig. 9d. Second Generation Parquet Deformation 180 about red vertex (Brazil - Rio De Janeiro)

Fig. 9e. Second Generation Parquet Deformation 180 about red midcell - Same as vertex! (Brazil - Rio De Janeiro)

Old 13 April 2021)

Upon the completion of the parquet deformation, which in itself can be considered as serving as a finished work, in effect a first generation parquet deformation, it is then possible to use this as a framework for further possibilities. This involves subdividing, and also superposing, using the three types of symmetry: translation, reflection and rotation. Typically, the parquet deformation becomes more involved, with a broad doubling of lines. In effect, such additional aspects can be described as second, third, and more generation parquet deformation forming. The possibilities are just about endless, but the outcomes are not aesthetic as another. Judgements must be made in the matter, otherwise the results become trivial. As alluded to above, the computer is a great aid here. Although each of the examples shown here are practical by hand, much more can be accomplished by computer, in both speed of execution and design.


Subdividing

By suitably dividing the tiles, new parquet deformations can be formed. Some are more obvious than others. A particular favorite is a double basket weave structure. This gives a very pleasing overlay effect at right angles. Fig. 1a shows a first generation parquet deformation, whilst Fig. 1b shows the second generation subdivision.


Fig. 1a. First Generation Parquet Deformation

Fig. 1b. Second Generation Parquet Deformation: Subdivided Double Basketweave

2. Translation - Superposition

Superposition is another effect with pleasing visual properties. A variety of designs are possible, with a variety of different effects, depending upon the selected parquet deformation. Typical translations include vertical or horizontal slides of a half or one unit. Other possibilities include midpoints of the sides, as well as the midpoint of the cell. Fig. 2a shows a first generation parquet deformation, whilst Fig. 2b shows the second generation midcell translation.


Fig. 2a. First Generation Parquet Deformation

Fig. 2b. Second Generation Parquet Deformation. Translated to midcell

Reflection



Rotation - Superimposed



1. Computer vs Handrawn Parquet Deformations


Since William Huff’s day, with archived hand-drawn parquet deformations dated 1963-1998, the computer has been used more and more in all manner of artistic endeavours. An obvious question to ask is whether the computer can improve, loosely defined, on the hand-drawn parquet deformations and perhaps take this even further, in new directions, and of which I now address. I now have experience of both procedures, although only latterly of computer drawing, of just the past few months, as against 34 years (at intervals) by hand. Even so, I now consider that I have sufficient knowledge to make a conscious choice as to advantages and disadvantages.


To begin, the de facto start is a drawing on graph paper, using the five types of lattice (as outlined by Huff [*]), namely a square, parallelogram, rhombic, rectangular, and hexagonal. Typically, a square is used. Huff outlines the pros and cons of the lattices; some are more suitable than others e.g. squares and parallelograms respectively. Sometimes the term ‘grids’ are used, although this appears to be incorrect. The core issue to address is to how such traditional media, graph paper, can be translated to the computer.  In short, this is very well, as might be expected for such a basic concept. Further, upon a basic square grid, typically of 2, 10, 20mm graph paper, of 10 units there is little other paper, aside from 1, 5, 10mm paper available. In contrast, the computer has a much more unit grid possible.


At its most basic, both procedures use a grid for drawing purposes, both easily available.


For computer software, my choice is Rhino 3D, a CAD program. Although this is arguably overkill, with the 3D features essentially of no application, it is the one program I have gotten along with. But likely a lot depends on one’s experience; I can easily imagine illustration programs e.g. Adobe Illustrator and geometry programs e.g. GeoGebra being used as well. However, CAD programs seem inherently better suited to the purpose. Whatever, this is just my personal viewpoint.  

In short, I consider the computer a near indispensable tool. Although the instances I show below are all feasible by hand, the advantage of the computer is immense, in a variety of ways, of both in the comparable drawing on (typically) squared paper, and perhaps even more so in the subsequent manipulations.

There are 5 main reasons for using the computer:

(1) At its most basic, repetition. With copy/paste, much more can be achieved than otherwise. For example, of my favoured 4-unit strip, detailed below, simply drawing a single row, and then repeating three times, obviously only requires a quarter of the time as by hand. By hand, the process is most laborious. This largely removes the tedium factor of drawing the same unit again and again. 

(2) More productive, with time saved. The time saved as above can be used to draw more works, using the example above, four times as much.

(3) Error-free work. With undo/redo, mistakes can easily be removed that a work with pen is otherwise impossible, of which with many lines can so easily occur, not to mention the additional fatigue factor. 

(4) It encourages experimentation that would otherwise be largely impractical by hand, with ‘superimposition’ in a variety of ways, discussed below. 

(5) It permits assembly into ‘super deformations’, discussed below. And further, other configurations, such as winding strips.

Some softer reasons include an unlimited supply of electronic materials and paper.

And further in the right hands, the computer can be used to expand on the Huff student-inspired instances. The advanced work of Kaplan [*] exemplifies this, and, to a lesser degree, at least in terms of the extent, Edmund Harriss [*]. However, Kaplan’s work, involving advanced algorithms, is somewhat of an outlier. Harriss’s work is on aperiodic tiling. Furthermore, there is also dedicated software that can assist, with the Parakeet plug-in, as shown by Esmael Mottaghi and Arman Khalli Beigi [*]. A major advantage here is in the swiftness of execution; a completed, intricate deformation once set up can be composed instantly that otherwise undertaken in Huff’s day would require many hours, if not days! However, this particular use of a computer can be said to be advanced, and likely very few design students will possess the knowledge.

An open question is whether such computer-drawn instances can be described as art, of which from the early days of its introduction being an age-old contention. Indeed, one can argue, given the perfection of the computer against the inevitable imperfection by hand that this is not art as such; anyone could have done this. Indeed, one can argue that perfection is soulless, obviously not done by a human, whereas when hand drawn, despite the inevitable imperfection, actually has more charm to it. Certainly, Huff did not seem to regard computer drawing as art. I am ambivalent on this. One can argue that the computer is simply another, better art tool. For instance, no mathematician calculates using a slide rule any more; there are simply more accurate and quicker electronic tools to use. They have served their purpose and are now in the past. A like comparison here can be made with traditional drawing tools, which lack the computer means of copy, paste, undo, redo etc. That said for sure, it is still possible to calculate this way and achieve great things. Indeed, I read that the Apollo astronauts took slide rules to the moon! But not their more recent successors. As above, there are better instruments, and so why cling to, for sentimental reasons, to outdated tools? However, a counter argument is that computer drawings lack the personal touch. Indeed, ever since the days of cave art, signatures have been left, of a hand, saying in effect a unique person made this. Both procedures have their advantages and disadvantages. Artists continue to work, or crossover, to both media. That said, there does seem to be a transition to more modern media. And in relation to parquet deformation, I have to say that I am strongly in the more modern-day camp. To me the advantages of modern media far outweigh any human factor, uniqueness by hand.


Page Created 11 March 2021

Essay 1 - Computer vs Handrawn Parquet Deformations

10 April 2021. Added Essays 1-7, with Essay 1 moved down.

11 April 2021. Added Essays 8-9

12 April 2021. Added Essay 'William Huff and Parquet Deformation Music Analogies'

13 April 2021. Added Essay 'Further Possibilities'

Comments