Cool Graffiti to Draw Easy Math

Street Math In Wildstyle Graffiti Art

© 1997 Josephine Noah

"Wildstyle" is a form of graffiti composed of complicated interlocking messages, arrows, and embellishment. Like all forms of graffiti fine art, it is spray painted on walls, trains, and other public surfaces, frequently illegally, and is intended to impose on public visual space, and to challenge viewers' ideas of who has the right to represent themselves publicly, and what art is. It is created both for, and in defiance of, the audience, which is fabricated upwards of other writers ¹ and both supportive and unsupportive members of the public. The reasons why people write are diverse and ever-evolving. Some motivations cited are resistance and rebellion, fame (literally making a name for oneself), and the desire to create beauty and share art with their community. Nigh writers autumn somewhere on a continuum blending these desires and more than. Wildstyle is intentionally difficult to decipher. Dondi, from New York, has said that when he writes for other writers he uses wildstyle, and when he writes for the public he uses straight letters (Chalfant, 1984, p.70). Part of the thrill of the creation of wild messages is the mental and artistic challenge presented both for the writer and the reader. The passion for patterns is one of the binding forces of the community. Copious amounts of fourth dimension are spent by writers in sketching, piecing, tagging, and bombing ², examining pictures in graffiti magazines, trading flix (photographs) of graffiti art, and meeting to pass around sketch books filled with ane's own and others' art to fill with more sketches. Another excitement of wildstyle is its subversive implications; information technology is a way of writing messages in huge letters on walls that is translatable only by a very small population of cohorts. Vulcan proposes, "The whole pregnant of the art is that it's a communication linguistic communication... My main affair is taking messages and distorting them, irresolute them, mutating them. It'southward nigh evolving the alphabet. Just because somebody said this is the way it's supposed to be, it doesn't mean it has to be; you can individualise the alphabet. You can make information technology your own" (Miller, 1993, p. 32). Usually, possibly eighty percentage of the time, what is written is the artist's proper noun; a mode of gaining fame and recognition within the community of graffiti writers and aficionados. Other letters are as well communicated, sometimes the proper name of a loved one, or a concise personal philosophy. The letters themselves, it is hypothesized, are a reworking of Arabic lettering incorporating African and Latin rhythms, signifying motility and flow (Miller, 1993). While these theories well-nigh graffiti'south roots and meaning are generally written by academically inclined graffiti artists and outsiders, any non-academic writer volition tell nigh the synonymous "funk" in wildstyle lettering, meaning motility, vibrance, spirit.

My intention in this paper is to discuss the forms of mathematics that take been developed in the design, painting, deciphering, and evaluation of wildstyle. The brief preceding background presents a basic summary of the driving purposes of this form of expression, from which the technical elements valued in the art take shape. Mathematical forms of thought accept been both appropriated and adapted from formal math, and, even more pervasive and significant, accept been invented to serve the functions of this community. This is what has been termed "street mathematics" (Nunes, 1993). Nunes, Schliemann, and Carraher convincingly summarize the relevance of street math as follows:

"Sociologists will exist interested in analyzing the social conditions under which street mathematics appears and what relationship it bears to variables ordinarily used to depict a society. Anthropologists will exist interested in street mathematics as cultural practices that have an organisation surpassing the level of the private and that are in some manner transmitted inside the culture. Educators volition exist interested in such questions as whether children at a given class level are probable to know particular mathematical concepts from their experiences outside schoolhouse, whether the new knowledge they gain in school can increase the power of their knowledge outside school, and whether classroom instruction of a novice and a street practiced should be different. Finally, psychologists volition be interested in the organization of knowledge in street mathematics, its forms of representation, its power to generate solutions to problems, and its conquering.
(Nunes, et al., 1993, p. half-dozen)"

The community of graffiti writers exhibit particularly rich, sophisticated, efficient, awarding-specific forms of street mathematics, from which educators tin can acquire much. Nunes et al. consider the significance of studying street mathematics to be in agreement the conditions nether which it arises, how educators tin can employ exterior math understandings in teaching of formal math, and how these knowledges are developed, used, and transmitted through communities and to novice members. All of these are extremely interesting phenomena which I will at some point examine relative to this community. At that place is an additional, and particularly important significance of street mathematics, though: what it implies about formal intelligence. Many graffiti writers are unsuccessful and uninterested in schoolhouse math; qualities which, when perceived past outsiders, may be interpreted as ignorance. Some artists are notable exceptions to this, and I will talk over them and their merging of street and school intelligences; but for the purpose of improving didactics it is critically important to await at the people, disturbingly the bulk, for whom school education fails. When people "fail" at schoolhouse math, withal apply street math in a sophisticated mode, nosotros must interrogate why school math is non reaching them. It may exist methods or content or educatee motivation, or some combination of these. Whatsoever the crusade of discontinuity, much is implied about the nature of formal and sanctioned cognition. School math is valued as a universal, generalizable set of tools to employ to any situation, yet for virtually people it is a source of disempowerment, equally they feel unable to think or apply formal algorithms in "real-world" situations. When this is then often the case, educators demand to question why this happens and what can be washed to value types of mathematical power that students already have, and not only relate "existent" math to street math to strengthen student'due south existent-life uses of math, but broaden school math to incorporate the strengths, flexibility, and creativity of street math. An analysis of math use in the graffiti community is peculiarly compelling because it is a counter-cultural group composed of people and an action that is by and large conceived of as criminal and unintellectual. The results, then, are particularly challenging to common conceptions of intelligence.

It is interesting to annotation the ways in which writers themselves speak of the mathematics of graffiti. It is mutual for there to exist discussion of residual, flow, and symmetry as mathematical elements, as well as perspective visualization (letters are often drawn iii-dimensionally). However, I have not, in my interviews or readings, heard whatever mention of the value of schoolhouse/formal mathematics in learning these skills. The informal mathematical elements used in the practice of their art seem to be conceived of as learned inside and specific to the application. Super LP Raven in Flop the Suburbs says, "[Wildstyle] is mathematical... graffiti is mathematically constructed... It's about proportion, balance, syllabic distribution... It should be, after you study someone's wildstyle once, you should be able to read anything they exercise in that style - if the mode makes sense" (Upski, 103-104). Giant has talked of his apply of "axonometric architectural renderings" ³ and the pyramidal course he uses to construct his pieces; at that place is "inherent balance, strength, and power associated with pyramids", he says. Delux and Eskae and members of their crew, the Aerosol Syndicate, study sacred geometry and contain the "natural" proportions, symmetries, and patterns prescribed by information technology to create their artwork. Delux, who studies mechanical engineering science, has also found that his applied science and graffiti skills symbiotically enhance each other, enriching his skills in both domains. Interestingly, the mathematically inclined artists that I have interviewed became interested in mathematics later on they began graffiti, and then began to incorporate these formal knowledges into their work. This intellectual and theoretical angle to their artwork seems to be highly respected by other community members, which may have powerful implications for motivation in school didactics.

Additionally, at that place are numerous breezy mathematical skills employed past writers that they practise not conceive of every bit mathematical. This may be considering it is uncommon for people to retrieve of skills that are learned and used contained of school as "existent" mathematics, or, equally Nunes, et al., say, "The mathematical skills involved in everyday activities go unrecognized. They are so embedded in other activities that subjects deny having whatever skills" (1993, p. eleven). Specifically, those in use here include pattern cosmos and deciphering, and tools and practices of measurement and proportional translation utilized in product of pieces. Subsumed in these categories are the specific talents of spacial visualization, symmetrical and geometrical blueprint and reasoning, and precise, consequent, and coherent application of pattern.

Encoding and decoding using patterning skills

Difficulty of deciphering by the uninitiated is a chief intent in the creation of wildstyles. To achieve the goal of being undecipherable to lay people while legible to other writers, at that place must exist coherence and commonalities within the domain that are transmitted to new members of the community. It is common for a writer to exist able to read a slice relatively hands that an outsider may not even realize has letters in it.

Writers utilise a common schemata in the deciphering of wildstyle pieces. When coming to a piece by an unfamiliar artist that is non hands read, the first step is ever to look for the signature ^iv mentioned before, a wildstyle slice will usually spell the creative person'south proper name, so if the signature is present and legible, the reader has a expert idea of what the slice may say. It is still oft no easy feat to run across the letters, though. The subsequent footstep is to expect for whatever relatively obvious messages in the piece. It is difficult to characterize the various directions this may accept, as it is dependent on the item codes of the piece and the strengths of the reader. Sometimes one or more messages can be establish relatively easily, and from there, information technology tin can be guessed that they will be of approximately the same size and evenly spaced, then it tin can exist guessed where other letters should autumn; features are and then looked for in those spots. Another frequently useful strategy that may follow or be concurrent with the same involves post-obit a line as it weaves above and below crossing lines and distractions, to come across if it is an embedded letter shape. This is useful in the frequent case that a alphabetic character is formed by simply 1 continuous line, just sometimes the shape is instead implied past several unconnected lines touching. This is observed in the comparison between the first and second E's in Figure ii ⁵.

It is of form central to know what shapes to wait for; this is function of the cognition of the practices of the domain. A knowledge of the standard shapes of upper and lower case Arabic messages is a basis, and from there writers become familiar with different common styles of letters employed and adapted by wildstyle writers. These are sometimes detail to regions, although regional variation is dissipating with the emergence of the internet, widely distributed international graffiti magazines, and writing on freight trains, which and so exhibit regional styles across the country. Also, many times a writer will be familiar with the styles of known artists, and may be able to recognize consistent patterns across pieces that help in deciphering. Post-obit Super LP Raven's comment cited earlier, stating that if the logic of a manner tin exist determined, it should exist like shooting fish in a barrel to afterwards read anything else in that manner.

Finding the letters in a piece becomes an obsession for writers; Delux calls it "obsessive-compulsive pattern disorder". It goes beyond wanting to know what a slice says; information technology is a game, an intellectual challenge, to detect the words. Ambiguity is adequate; that is, for there to be sections that look similar letters only actually aren't, or that may imply several letters. That is office of the complication and the "groundwork dissonance". An important component of deciphering is beingness able to sort betwixt letter and embellishment. Susan Farrell at Art Crimes ^vi sees wildstyle deciphering explicitly as a form of problem-solving: she speculates that the divergence between people who can "deal with" wildstyle and those who can't is due to their problem-solving ability. Do, every bit well, is a key component. Readers come to automatize the multifariousness of deciphering strategies they may try, and tin sense when to finish one line of analysis and try another, a typical quality of skilled mathematicians and trouble solvers.

Other factors helpful in reading wildstyles are patience and utilise of collaboration. Reading complex pieces may have twenty minutes, or fifty-fifty revisiting over several days. Information technology is frequently a collaborative procedure, where people verbally speculate about what letters sure shapes may signal, equally they jointly attempt to decipher. This is interesting in low-cal of Alan Schoenfeld's inquiry showing that it is a commonly held student belief near mathematics that if i is capable of doing it, it should be done in less than five minutes, and that it is a solitary activity. In schoolhouse mathematics, most students will quit chop-chop if they don't run across a known solution strategy, believing a trouble to be impossible for them. In this class of street mathematics, even so, multiple solution strategies are tried, and if they don't at first succeed, new ones may be invented. Collaboration is frequent also in deciphering, likewise every bit in aesthetic and technical evaluation.

Coherence of pattern within a piece is a very important factor in its evaluation. The patterns should exist consistent throughout a slice, and not random or done to look interesting or complicated without having a precise pattern or pattern in formation of letters throughout. It is unremarkably noted that when novices commencement come up into the graffiti earth, they usually want to do wildstyle, and they may get-go drawing designs that look intricate and tricky, merely really take no solid foundation. There should always be a strong "ghost" of a alphabetic character underneath the distracting extra lines, shapes, and fill-in (colorful designs which fill the letters in a piece, and may contribute to obscuring the lettering). What makes a coherent pattern and what doesn't is a complicated topic that I don't at this point take a solid plenty understanding to go very deep into. I will explore this more in time to come research. [ed. note: Meet especially Metamagical Themas: Questing for the Essence of Mind and Pattern by Douglas R. Hofstadter, which is one of the about entertaining and thought-provoking books I've ever picked upward.]

Informal "tools" used in production: measurement and proportional translation

Precision and cleanness are critical in respectable graffiti, both in design and in painting. I have already briefly discussed conventions of letter of the alphabet design; there is an equally strong emphasis on skill and technique in the actual painting. If 1 is an excellent sketcher just cannot transfer these to walls, a critical element of the art is lost. Enlarging a sketch onto a wall with authentic proportions is no piece of cake feat. Works may be in the range of ten to 25 anxiety across and 3 to eight anxiety tall, and may be extremely complex. Common measuring devices which could be applicable, such as rulers, tape measures, compasses, chalk line, and levels, are never used. The idea is considered quite preposterous; other tools specific to the domain have been invented to produce the precision that is and so valued in the community. Certain factors have contributed to the need to develop alternate measuring tools: one is that conservation of fourth dimension is ofttimes a gene, as many pieces are washed illegally; a second is that artists must deport a big amount of supplies (by and large spray cans) to the sites, and for economic system'due south sake, carrying boosted tools is undesirable. In response, writers have adapted the tools they have on hand to serve the functions needed: spray cans, their bodies, features of surfaces, and their mental pattern, mapping, and measurement skills, developed through extensive practice.

A spray can is one concrete measuring device used. The body of the can is slightly over six inches long, and three inches wide. In some designs, particularly large "directly" (non-wildstyle) letters, maintaining an even bar width is extremely important, and measuring this relative to tin can lengths or widths is ane method of assuring consistency. This is done mentally in many cases, but there are instances where bar width may be iii or more feet beyond, and mental estimations go increasingly imprecise. Another use of cans is in determining straightness of lines. A line may be intended to be straight for, say, fifteen feet, and this is notoriously hard to practice. Giant is reputed as being very skillful at this (he is 1 of few artists who even tries), and to practice it with precision he will hold the tin can vertically along a sketched bar, and detect if there are slight curves relative to the straight edges of the tin can, performing multiple mental (non-numerical) calculations of relative slopes.

Simultaneously, the trunk is used as measuring tool. A common concern is keeping lesser and top borders an fifty-fifty distance from the base of operations of the wall. This tin sometimes be quite easily washed using features of the surface, such as seams on cinder block walls, or bottom edges or lines of printed writing on freight or calorie-free-rails train cars. In other cases, where at that place are no such helping features, an creative person may begin a piece at the left edge, and annotation where the lesser border falls relative to her or his trunk, and then continue with the height of that trunk part as bottom edge throughout. The same technique can be used as a guide for top margin. Too, similar to the use of spraycan to mensurate bar width, hand span may exist used to evaluate changes in bar width.

At that place are many more ways that surface features of walls are used in the production of a piece. One practice applied in mapping a sketch onto a surface is similar to historically used perspective drawing tools discussed by Ferguson (1992, p. eighty), with the centre as "apex of the visual pyramid", and the flick existence fatigued on an intermediate screen between the eye and the prototype being represented. The graffiti author's utilise, notwithstanding, is changed. The intermediate prototype is the sketch, held at arm'due south length, and the artist mentally projects this image onto the surface behind it (see Effigy 3). South/he and so remembers where features of a sketch autumn relative to features of the surface (such as cracks, brick seams, and other paintings). This process will usually be repeated several times during a production. In this way, as well, right margins tin can exist approximated as a piece is begun, and so that if a slice is a collaboration (where 2 or more artists will simultaneously compose several pieces on a wall, frequently with edges touching), the next artist to the right knows where their left margin should be.

Some of the quantitative and proportional reasoning used past graffiti artists has been adapted from historically used art, perspective, and design practices, such as those ordinarily taught in high schoolhouse art classes. The act of imposing a grid onto a pic to be copied proportionally onto some other gridded surface is a standard and historically used representation that many of us are familiar with. While in about cases, this idea would exist scoffed at by graffiti artists, ane artist I spoke with is actually planning an extremely complicated slice that he would similar to put on a cinder block wall, precisely because he can section it into the 2-to-1 offset rectangularly patterned surface. This is certainly an exception.

Yet another awarding of mathematics in the product of graffiti art is in producing the desired book or menses rate of paint from the can. This is varied by switching the nozzle, or "cap". There are two types of caps nigh frequently used: fat caps and skinny caps, besides known equally phantom caps. Fat caps produce a wide, less dumbo line, while phantoms make a thinner, dense, well-baked line. The standard nozzles that come on spraycans have a quicker flow, which can crusade drips if it is non moved fast enough. Artists accept a very clear idea of how to produce wide and narrow lines, and opaque or translucent paint density, also as flares, where a line morphs from thin and dense to wide and scattered. Caps are of import, as well every bit technique with the spray can, including proximity to the wall and speed of hand motion. At that place are abiding calculations being performed to determine: the given book, width, and density of paint flow; what painting techniques will produce the desired outcome; and if it would exist preferable to use a different bachelor nozzle or seek out or invent a new one. Writers frequently experiment with caps from other kinds of aerosol products, testing its qualities, and sometimes even make their own past carving existing nozzles. I am unsure of whether they generally have an idea of what painting effect they desire and can predict how to modify a nozzle to make information technology happen, or whether they carve nozzles in various means without any predetermined desired outcome, merely to test possibilities.

Directions for further research

One topic that I haven't covered is the use of perspective in graffiti art. Writers commonly apply one-, two-, and multiple-indicate perspective, which I don't have an extensive understanding of myself, so noting and analyzing the complexities of its utilize are difficult at this signal. The majority of pieces are designed such that they announced three dimensional, for instance, by painting a shadow bandage onto the wall under the letters . Additionally, it is a relatively new phenomenon for some artists, notably Erni and Sleep, to portray letters equally though they are really three-dimensional figures, similar sculptures, weaving around each other (come across Figure half-dozen), whereas almost wildstyle appears to be two-dimensional letters weaving in a higher place and below each other, and casting a shadow.

Also, calculation of the amount of fourth dimension necessary for a slice and number of cans of paint needed must be performed, as one must residuum how long a piece will take with the reasonable amount of time information technology is possible to work at a site without existence caught (if it is an illegal spot). This is one of the more solidly numerical forms of mathematical reasoning, relative to the forms of mathematical idea I have mainly been addressing hither.

I would similar to further examine the strategies of problem solving within this domain, including what sorts of metacognition are enacted, and what other strategies are used that are like to or different from those productive in the solution of formal mathematics problems.

One approach I have considered using, and have done informally already, is request for think-aloud protocols equally graffiti writers decipher a piece. This begs for a comparing to "novices", all the same, and I'm skeptical about the validity of good-novice studies, given the extreme variations between subjects in addition to their experience with wildstyles. I practise recollect that inquiry of this sort would be extremely interesting, though, if it can be designed in a legitimate way.

Also, every bit I mentioned, I would similar to written report in more depth what qualities brand a coherent pattern, which is disquisitional in the quality and decipherability of styles. It is widely commented that being able to create a solid design is a skill that comes with extensive exercise and report. I am acquiring a basic feel for determining a piece's success in fulfilling that criteria, only in many ways it all the same defies caption for me. This has too been made difficult by the fact that the vast majority of pictures that are encountered in magazines, on the net, and in author's photograph collections, are of pieces that have been judged positively. I would similar to tour more than pieces in the streets and accept artists evaluate the pattern-coherence of works of more varied skill.

Symmetry, more oftentimes referred to past writers equally "balance", is extremely important likewise, and can involve quite complex geometric reasoning. Some artists cull to sometimes make their pieces precisely symmetrical, while usually it is sufficient for the piece to be generally symmetrical, meaning the height, width, and outline will be approximately equivalent around a vertical line of symmetry . Given that, writers take a deep knowledge of the construction of letters, including their reverses. This shows highly developed spacial visualization and, I would say, trouble-solving skills, every bit artists determine how to construct two messages so that they are reverses of each other, while maintaining the integrity of each letter. This is a complex topic that I'd similar to investigate.

Wildstyle artists, I have argued, have developed sophisticated forms of mathematical thought specific to the needs of their realm. Design ascertainment is now considered disquisitional in the development of functional and innovative formal mathematical idea, and it is apparent that wildstyle artists exhibit this talent flexibly and impressively in the practices of their community. Simultaneously, many forms of quantitative reasoning, primarily non-numerical, arise in situation-specific settings in the production of graffiti. This assay challenges what is often seen as a dichotomy between intellectual reasoning and creativity, with piffling overlap realized between the two. Not only is it apparent that in that location is far more than complex reasoning involved than may at offset be apparent in this fine art, but parallel to that, what has formally been conceived of as mathematical thought, particularly in the realm of problem-solving, can be a creative endeavor also.

Notes

1. "Writers" is the usual term used by graffiti artists to describe themselves.
2. These are forms of art production in public. "Piecing" is the cosmos of "masterpieces", tagging is chop-chop writing i'south name with marker, spraypaint, or other device, such as is frequently seen on mailboxes, phonebooths, desks, etc. "Bombing" is going out with the main intention of tagging many surfaces.
3. Giant describes this as techniques unremarkably learned in compages drafting classes, including utilize of 30-, 45-, and 60-degree angles, and one- or two-betoken perspective cartoon.
4. A signature is the same or like to the creative person's tag; if his usual tag is difficult to read, information technology will probably be simplified as a signature.
5. Translations and credits for all artwork are listed on the References.
6. Ms. Farrell is the curator of Art Crimes, a comprehensive web site which performs a powerful office of organization, education, and information dispersion inside and well-nigh the graffiti customs: http://www.graffiti.org

References

Art Crimes http://world wide web.graffiti.org.

Bukue. Personal Interviews. 20 November 1996-ongoing.

Chalfant, Henry and Cooper, Martha (1984). Subway Art.

Delux. Personal Interview. 26 November 1996 and xxx November 1996.

Eskae. Personal Interview. 30 November 1996.

Farrell, Susan. Personal Interview. 20 November 1996.

Ferguson, Eugene (1992). "The Tools of Visualization". Engineering and the Mind's Center. Cambridge: The MIT Press.

Giant. Personal Interview. 17 Nov 1996.

Miller, Ivor (1993). "Guerilla artists of New York City". Class, 35 Nunes,

T., Schliemann, A., & Carraher, D. (1993). Street mathematics and schoolhouse mathematics. Cambridge University Press.

Schoenfeld, Alan (1992). "Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics" (pp 334-369). In D. Grouws (ed), Handbook for Research on Mathematics Teaching and Learning MacMillan.

Sundance. Personal Interview. 30 November 1996.

Walsh, Michael (1996). Graffito. Berkeley, California: Northward Atlantic Books.

Wimsatt, William Upski (twelvemonth unknown). Bomb the Suburbs. Chicago: Subway and Elevated Press Co.

Delight contact Josephine Noah with comments and for reprinting information, or yo@graffiti.org

This article is archived at http://www.graffiti.org/faq/streetmath.html

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