•n.e nature of form in the dlgtt1I age is trapped in the invisible realm of code. Form+Code makes that world visible to the community that stands to gain the most from it: artists and designers." -John Maeda

•At tong last. here is a publication that looks comprehensively at the contemporary digital medium with clarity, at its recent past and into the future." -Greg Lynn

"Elegant as an algorithm, clear as a program, and as enthralling as a video game, Form+Code is a powerful tool, both as a tutorial and as an in-depth analysis of the aesthetics of the information age." -Domenico Quaranta

"This incredibly rich study of the history and possibilities of creating media through code is a must-have reference collection." -Karsten Schmidt

www.formandcode.com

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- - '. ·_ ~· - •. Once the exclusive domain of programmers, Form+Code in Design, Art, and Architecture fields of graphic design, typography, data code is now being used by a new generation of offers an in-depth look at the use of software mapping, art, digital fabrication, interactive designers, artists, and architects eager to in all creative disciplines. This stunning visual media, gaming, artificial intelligence, artificial explore how software can enable innovative survey introduces readers to more than 300 life, and all forms of new media and expression. ways of generating form and translating ideas. significant works of the past 60 years in the DESIGN BRIEFS --- RM . gN, ,. , -E Di -- ...\ ·• I

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fl -H9 Consider New York City's elaborate subway system. The New York City subway map organizes the com­ plexity of this transit system to help passengers navigate from one loca- °o tion to another. The visualization removes unnecessary geographic information ancTadtfs information related to train schedules and trans­ fers. The system is still difficult to traverse, but the map's visual clarity makes it manageable. Maps are an early form of visualization—maps of the stars were created before recorded history—but they are only one among a myriad of techniques available to designers. Visualization also helps communicate abstract LU information and complex processes. N < CO

These letters were created using a particle system. The particles are attracted to a unique position within a set of interrelated points and, over time, they move toward a single point. This software demonstrates the potential for data visualization to bring clarity to an otherwise chaotic system. tsualize Visualize -iSQ DATA INTO FORM lai

People have a remarkable ability to under­ In his book Semiology of Graphics: stand data when it's presented as an image. Diagrams, Networks, Maps, Bertin presents As researcher Stuart K. Card says, "To under­ another clear example of the communica­ stand something is called 'seeing' it. We try to tive power of visual representation. make our ideas 'clear,' to bring them into 1 Stuart K. Card, Jock 'focus,' to 'arrange' our thoughts."1 Like written Mackinlay, and Ben words, visual language is composed to con­ • l:: Shneiderman, Readings in Information Visualization: Using struct meaning. Our brains are wired to make "It!:::: Vision to Think (San Francisco: sense of visual images. In contrast, it can take Morgan Kaufmann, 1999), 1. years of education to develop the ability to read even the simplest article in a newspaper. The fundamentals of visual understanding, originally pursued by Gestalt psychologists in the early twentieth century, are now researched at a deeper level within the field The maps of France on the left and right of cognitive psychology. The findings of this both present the same sociographic data, research have been communicated within the divided by canton (a French territorial sub­ visual arts by educators including Gyorgy division). The representation on the right Kepes, Donis A. Dondis, and Rudolf Arnheim, replaces each number with a circle sized to as well as through the work of visualization correspond to the numerical value. We can pioneers such as William Playfair, John Tukey, spend time analyzing the left map to see and Jacques Bertin. Data presentation tech­ where there are concentrations of larger N niques that combine our innate knowledge numbers, but on the right map we instantly l-H with learned skills make data easier to under­ comprehend the increased density in the —I stand. In The Visual Display of Quantitative upper left. < Information, Edward Tufte presents a data set In the same book, Bertin introduces CO and representation that supports this claim. a series of variables that can be used to t-H Compare the tabular data to the scatterplot visually distinguish data elements: size, > representation to see how the patterns value, texture, color, orientation, and shape. become immediately clear when presented in For example, a bar chart distinguishes the second format. data through the height of each bar, and different train routes on a transit map are typically distinguished with color. For 10.0 8.04 8.0 6.95 visualizations using only one variable, each 13.0 7.58 9.0 8.81 element can be used in isolation. For multi­ 11.0 8.33 14.0 9.96 variate visualizations (containing more than 6.0 7.24 4.0 4.26 one variable) elements are combined. 12.0 10.84 7.0 4.82 When applying form to data, there are 5.0 5.68 always questions about goodness of fit, meaning how well the representation fits

10.0 the data. Visualizations can mislead as 8.0 13.0 8.74 well as enlighten. As Tufte warns in Visual 9.0 8.77 11 .0 9.26 Explanations: Images and Quantities, 14.0 8.10 6.0 6.13 Evidence and Narrative, "There are right 4.0 3.10 Edward R. Tufte, Visual 12.0 9.13 ways and wrong ways to show data; Ijxplanations: Images and 7.0 7.26 5.0 4.74 there are displays that reveal the truth |Quantities. Evidence and 2 Narrative (Cheshire, CT: and displays that do not." In Bertin's Graphics Press, 1997), 45. maps of France, the goodness of fit of the

isometricblocks, this visualization of people. It transitions relationship between by Ben Fry, 2003 human genome data. It fluidly between com­ each technique. Fry worked closely with visualizes single let­ mon representations for researchers at the ter changes (SNPs) of viewing the same data, Broad Institute of MIT the genome data for therefore revealing the and Harvard to create approximately 100 13

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Vinec, and Nijmegen in the vehicles and the ver­ blocking Diplomats, This visualization "by Catalogtree, 2005 Netherlands between tical axis shows the Catalogtree, 2008 shows each violation This graphic shows data 07:36 and 09:13 am. difference between the between 1998 and 2005, at its location within for 10,000 cars cross­ The horizontal axis measured speed and the jjipiomats in New York the city, with the ing a bridge between for each unit shows the speed limit. 1ty were responsible United Nations at the the cities of Arnhem distance between the or 143,703 parking epicenter. Vlolations. tZe Visualize -1-84 -1S5

search all. representations reveals information hidden refined as designers use them in diverse Harry Potter and Peace returns to the Half-Blood within the data. Because each piece of data contexts. Urumqi, but Uighurs China's Michael Jackson's Prince derives from a particular canton, associating A treemap is a visualization that utilizes and Han Chinese Harry Potter and the that data with its location on a map allows us nested rectangles to show the relations ethnic family won't bury Half-Blood Prince: the still lack trust critics' verdicts to see regional patterns. Presenting the data between one or more data elements. They in a table that is organized alphabetically are effective because they allow for easy tinderbox him without his brain Merchandise from Michael Jackson's 02 Arena would not reveal this pattern. By applying the 2-D size comparisons. The story of the first Obama broadens push for Cyberattacks Jam residency goes on sale Government and same visualization technique to a different treemaps, from their origin to the present, climate change pact Commercial Web feUnyKng jj^S Sa map—a map of Europe, for example—would is documented by the technique's origina­ Sites in US and ... Simon Katich and Ricky Prankster admits taking Google Swine flu Porting hit hundreds as Chrome OS screenshots death toll rises also not work as well. The Bertin map works tor, Ben Shneiderman, a professor at the G8 summit: UN Ousted Honduran Re-election raises 3 3 Ben Shneiderman and because each canton is roughly the same University of Maryland. The first treemaps accuses G8 of doing leader unlikely hope of bold Australia regain... Hardware STr™ Liner'like ffcgouamak working class hero Indonesian govt Catherine Plaisant, "Treemaps too little to tackle makers support SZm bpSPto' , passengers size, but the size differences among European were developed in 1991 as a way to show Indonesian Scores killed in Mitotan Russell unsure over rtvwwing'prom prison Snip retumhomo for space-constrained visual­ climate change Google OS SSL liiaeon^dw mem urine«u 'SSZm president ready lo Iraqi bombings — ization of hierarchies," countries would dilute the visual patterns the memory usage on a computer hard accommodate Ashes return Mb canlWkabout T"cf"nI**", Bank olEngland FSA to publish New 'cyber rivals'economic H2 WHOA'Australian newphore iKt-jng holds fire on QE complaint http://www.cs.umd.edu/hcil/ needed for interpretation. In this case, the drive. After subsequent applications and programs town bow mim Sturrldge targets Tim thunders S5 , claims, says Murdoch , and base rate statistics England call-up to stage joy data is tightly linked to a source (geography), further development, the public at-large attacks' hit S Alqhan blastkills EST"*""— Einntn JRitt 2 25, hall ol them IHL. FOTA pushing aheadwith M Korea breakaway —• SST* 2 but in other instances data can be more was introduced to treemaps by Map of the Children Atalwrikitan kllia 2T> * i abstract, such as when revealing patterns Market, an Internet application created by in language. The visualization techniques smartmoney.com in 1998. This applica­ that follow in the next section present other tion introduced the innovation of making options for revealing patterns in data. the tiles close to square, rather than using There are hundreds of distinct visualiza­ the thin tiles of previous treemaps, to G8- Berlusconi FRANCESCHINI, MESI DO. Del IUoOUI II, DIFFICILI MA NO Michael Jackson, Cina: Xinjiang, Hu tion techniques that can be organized into increase legibility. The circular treemap N impegno su crisi PAURACONGRESSO il giallo della esige stabilita' e categories,jncluding tables, charts, diagrams, technique explored by interface designer 1—1 PI INTD 9 CP, SarSandri;*chl0sli Chiesli 1414 II ddl sullo G8.G8, Michelle sepoltura e il invia uomo forte graphs, and maps. When creating a new visu­ Kai Wetzel in 2003 pushed the form of —I anniperagenteanni per agente, Sviluppo ora e Obama si < Obama: ce ZS*malumori per le legge commuove alization, one techniqueds^selected instead treemaps even further. Wetzel worked on ancora tempo per nttenuanti mistero della LSIESI Honduras , SSSSfEES 3 Scotti: Si trovi una of another based on the organization of the this representation as one of many ideas CO accordo SU C ima 00P0VER1ICECI .,J"' „ FolipoMebnOtarna soluzione di legalita vjvy out win to ,.....f.,,|W||UIWin ergastoloornaotnln in appclloannolln sawchiahmemto George Ctooneytrale s.'sr- condlvisa data and whalTbe-visualizatio.ni£jri£antJp for a Linux operating system interface. He w humab unor macerie "Gireremo gomoabwta convey. Data representations that commonly recognized that the approach wastes space > Sorpresa, Carla e giunta a I'Aquila Ma la sua appear in newspapers, such as bar charts, pie and the algorithm is slower, but the aspect agenda resta 'top... Boraii Mitaiu conrdida , Google, la grande G8; Greenpeace, BorsaMilano rimlMl/o (.mi IsiikJui, charts, and line graphs, were all developed ratio of each node is the same. The 2004 Infci biriiiiv) grande la 1 occasioneche attivisti ancora in chiude positiva. aspetta Wall Street Juvenilia Con I'uluII Juve, preso Felipe Milan InMBgeraio Linux non deve cima a 3 centrali Deciso rialzo per before people relied on software; in fact, most Newsmap application by Marcos Weskamp TuttoJuve perdere carbone Pirelli Melo commonly used data representation tech­ applied treemaps to the headlines of news Jum;, raduw e Fiat: IdV, non - Felipe nartsna per rraonnaoro en en pemietteremo niques are only useful for representing simple articles compiled from the Google News Pin/do Greenpeace.ua ;mmbl Chiusura di Termini Barcellonaedi doludente, reav* imerese data (1- and 2-D data sets). These techniques aggregator. The treemap representation Melo s'ha Alonso aetata ThorHlThor Hushovd! salgonoaS ""f"'" HB Ferrari to alia central! =Sr- es= air- «SSS_, 2SX&. S= are automated within frequently used soft­ makes is easy to see how many articles are rassa?Sotovoci' da fare occupate =3ess. £-• sT ~ -a—— — ware tools such as Microsoft Excel, Adobe published within each news category. For 1• nowsmap programs. Visualizing example, the visualization makes clear that, £ Ihu July9.2009 71)5924 Illustrator, and related information, once a specialized activity, is in England, the highest volume of published becoming a part of mass culture. articles is world news rather than national Writing new software is one approach to stories, while in Italy, the reverse is true. By move beyond common data representations. 2007, through the refinement of these and New visualization techniques emerge as other initiatives, the treemap technique had researchers and designers write software to become so ubiquitous that it was used in fulfill their growing needs. The treemap tech­ the New York Times with the expectation nique is a good example to demonstrate the that a general audience can understand it. origins and evolution of a new visualization. It also shows how techniques often arise The era of modern data analysis began with within a research group and are visually the 1890 U.S. Census. The Census Bureau

Newsmap, landscape of the Google countries and to view computer's hard drive "by large rectangles) Circular Treemaps, variation, the age of by Marcos Weskamp, News aggregator. The articles from seven that is shared hy four­ could be deleted to by Kai Wetzel, 2003 the file is shown with 2004-9 interface allows users categories. •®rian Johnson, 1991 teen people. It shows make space. Like the origi­ color. Red is applied The Newsmap visual­ to view the news from This visualization who was using the most nal Treemaps, this to new files and the izes the changing one or more of eleven ^ePiots the file con­ space and which large visualization also oldest files are a soft tents of a networked files (represented depicts file space on yellow. a hard drive. In this DYNAMIC FILTERS 127 realized that the population was growing so present. For example, by typing the name quickly that, using their existing analysis Deanna, we see this name originated in the method, the newly collected data would be 1920s, reached its peak in the late 1960s, out of date by the time it was evaluated. and has since become less common. The Herman Hollerith was commissioned to build interface begins with a stacked-graph a machine to automate the process. He suc­ representation of all names in the data set. ceeded by developing punch cards to store When a letter is typed, the search narrows data and a machine to read them. Since that to reveal only those names that begin with time, computing machines have enabled an the specified letter. For example, typing the unprecedented ability to acquire data. Today, letter C reveals the historic popularity of it's no longer possible to rely solely on static, Christopher and Charles. Further inputting paper representations. The deluge of data an A and T reveals that Catherine is the created by the information age has made most popular name that begins with Cat new forms of software analysis necessary. and also shows the relative obscurity of When there is more data than can be Catalina and Catina, among others. viewed at one time, it's necessary to limit the A group of photographs is also a data­ amount that is displayed. This process is base that may be filtered and navigated. called filtering or querying. An internet search The proliferation of online digital photo­ is an act of filtering. The internet is such a graphs has created a fascinating data set large data source that to get value from it, to be explored through image searching. search terms are used to limit what is seen at Jonathan Harris's The Whale Hunt is an ele­ any given time. A tool for filtering can provide gant example of navigating a large series of J*{

different levefsjjf control often correspond­ images. He travelled to Alaska to participate w ing to its use at a basic or expert level. For in a whaling expedition with a family of _l instance, when searching the web, it's pos­ Inupiat Eskimos. He took 3,214 photos from ^ sible to make a simple search where only the time he left New York City to returning keywords are input, but it's also possible to home nine days later. By default, the images l—l select a broad range of criteria such as file are presented sequentially, but he also ^ type and date to further refine the results. allows viewers to navigate in other ways. It's A real estate database is a good example of possible to jump to any image in the time­ a large data set that becomes more useful line, pause, and change the pace. But more with a filter. It doesn't make sense to look for interestingly, it's possible to select a subset all available listings for apartments, houses, of images based on categories. By using and condominiums if you're only looking for a fluid and clear interface, images can be one of the options. A tool like this becomes filtered according to a concept (e.g. blood, even more useful to search by a specific boats, buildings), context (e.g. New York price, size, or neighborhood. In fact, a 1992 City, Alaska, the Patkotak family house), or research project called the Dynamic Home a member of the cast (e.g. Abe, Ahmakak, Finder, developed by Christopher Williamson Andrew). After one or more selections are at the University of Maryland, was an early made, the image sequence is automati­ prototype for such a system. cally edited and the story told through the Another example is the NameVoyager images is changed to reflect the filters. by Laura and Martin Wattenberg. It's a clear example of a continuous visualization that is accessed through a dynamic filter. The project presents a simple way to discover the popularity of nearly 5,000 baby names used in the United States from the 1880s to the

NameVoyager, States from the 1880s each year. Names are ' with that letter. Type by Laura and Martin to the present. The selected by clicking on an additional letter Wattenberg, 2005 thickness of each its band or by typing. to further narrow the The NameVoyager shows name's color band Type a single letter search. the popularity of baby shows how many babies to refine the search to names in the United were given that name only names beginning —i?,g

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The Whale Hunt, Ssjecret liwa David Becker, 2002 Viewers may rearrange places, topics, and ^umbers, web pages. The interface as 212, 486, 911, 1040, tax forms, computer "by Jonathan Harris, the photographic ele­ other variables. This web-based project allows for exploration 1492, 1776, 68040, chips, famous dates, G°lan Levin w 2007 ments of a story to reveals the relative of this massive data set or 90210, occur more or television programs rt The Whale Hunt is an extract multiple sub- 7 in Watte,,i„.r popularity of every and provides a novel frequently than their that figure prominently °nathan Jeinter experimental inter- stories focused around integer between zero and lens for viewing social neighbors because they in our culture. " face for storytelling. different people, SfHy Wynecoop, one million according to patterns. Levin states, are used to denominate Pfefilashoff, their frequency on "Certain numbers, such the phone numbers, -430 NAVIGATION 151

Some early forms of data navigation might The sci-fi novels of William Gibson concupiscence have included flipping through clay tablets, introduced intriguing concepts for spatial physical attraction! moving through a room painted with hiero­ \l lo data navigation. In Neuromancer, published sexual desire —# glyphs, and rolling and unrolling a scroll. in 1984, he wrote about "rich fields of data" concupiscence Early books improved upon scrolls because and described a vision of cyberspace: "A

physical attraction they allowed the reader to move quickly graphic representation of data abstracted between sections in the text and could from the banks of every computer in the 4 William Gibson, be smaller and therefore easier to carry. human system."4 Although Gibson's world Neuromancer (New York: Ace, Book conventions such as the index, page was fictional, a related real-world concept 1984)751. numbers, and table of contents developed was developed by designer Lisa Strausfeld slowly. Despite thousands of years of refine­ in 1995. She describes her software, ment and the widespread proliferation of Financial Viewpoints, as follows: passionateness the Internet, we're still scrolling and viewing data on pages. The unique tool for looking Imagine yourself without size or weight. at and navigating pages on the web is the You are in a zero-gravity space and you hyperlink, a link from one page to another. see an object in the distance. As you turbulence Sturm una Dranj Ted Nelson coined the phrase hypertext in fly towards it, you are able to recognize the 1960s to describe this concept. Since that Eumenides Erinyes the object as a financial portfolio. From upheaval time, designers and researchers have pushed this distance the form of the object con­ forward this and other innovative navigation veys that the portfolio is doing well. You concepts by writing software. move closer. As you near the object, you As an example, imagine the data inside pass through an atmosphere of informa­ a thesaurus. There's a list of thousands of N tion about net assets and overall return n words in addition to all of the relations from statistics. You continue moving closer. _l each word to others. To explore this data, you Suddenly you stop and look around. < look up one word, which you may then follow The financial portfolio is no longer an CO to another, and so on. Even the small amount object, but a space that you now inhabit. HH Lisa Strausfeld, "Financial of time needed to hunt for the next word Information surrounds you.5 > madness Viewpoints: Using point-of- can break the flow. The Visual Thesaurus violence view to enable understanding of information," http://sigchi. software, written byThinkmap, makes At that time, Strausfeld was a research wildness org/chi95/Electronic/documnts/ navigating language relations a more fluid assistant in the Visible Language Workshop |8hortppr/lss_bdy.htrn. experience. The software shows a network (VLW) at the MIT Media Lab. The research vehemence rage of words related to the currently selected group was directed by Muriel Cooper, word. Clicking on one of the outlying words who set out to discover what graphic makes it the center, and new words appear design could mean in the new era of furiousness that relate to it, while the former relations communications, through the use of soft­ disappear. The interface allows the user to ware applications. David Small, another fierceness see the context around the current selection, researcher in the group, used software but avoids overwhelming the senses with to present large bodies of text within a ferocity additional layers of nonrelevant information. single navigable environment. His Virtual Spatial navigation is an emerging tech­ Shakespeare presents the entire works of nique for exploring data, but it has roots William Shakespeare within one continu­ delirium that are thousands of years old. The ancient ously navigable space. From the long view, memorization technique Method of Loci, only the names of individual plays, such as frenzy craze sometimes called a Memory Palace, places Hamlet and Henry V, are visible, but as you hysteria information inside imagined rooms within-the zoom closer, the acts come into view as mind to enhanceTecall by associating data rectangular textures, and finally it's possible fury with a mentally navigable space. to read the dialog and stage directions. ferocity j Visual Thesaurus, from love to passion parts of speech (verbs, by Thinkmap, to rage to fury to vio­ nouns, etc.) are color- 1998-present lence. Related words coded. Try it at fierceness When a word is select­ are connected with gray www.visualthesaurus. ed, a new set of related lines and antonyms are com. words emerges. In these connected with red- images, follow the path dashed lines. Different A short comic drim theseus .»•<»>• P°. PhilostraK, ween moram) w P| rLi'"'|w c, mystery play*- BOTTOM » *21 ,h,aa Turn melancholy forth to funerals^mirtl1' »pmnt. * *«;»d.opo.w The pale companion is nDt for our pomp. 20QLINCE M»rrMatn.uurpUyu)-.uurp|jy,j UExit Philostrate]] Mi's: Lamentable Comedy) Jnti [pi5«ij H'PPolyta 1 wooed thee with my sword, and W°KMost Cruel Death ul"ofPyrjr Pyramut and Thid*. PW^^Tp5N|THR0UeH^^j|J|gJ And won thy bye doing thee injuries. BOTTOM But 1 will wed thee in another key Avtiygoodpiete()fwofk,ltouit»ollim|1 WfrSoKj With pomp, with triumph, and with revelling. m«ry. Now good Peter Quince, call tunh vour aci.m by the scroll. Masicrs. spread yourselves. MHEnter Egeus and his daughter Hermia, and Lysanderand Demetrius] |{]E^ET]JU^JPAKI^AN|HE^^^ 30QLTNCE Answer as I call you. Nick Bottom,the weaver? egeus "TinHNffSfWffHfflKNOwl Happy be Theseus, our renowne d Duke. BOTTOM Ready. Name what pari I am lor. and proceed. theseus THINK SUREBECAUSE|BILLI0N| QUINCE Thanks, good Egeus. What s the news with thee.' UW You, Nick Bottom, arc set down for Pyramus. SENATOR[eJafiS egeus , .. BOHOM Full of vexation come I, with complaint 40 What is Pyramus.' A lover or a tyrant 40 Against my child, my daughter Herma Stand forth Demetrius. My noble lord, "a"K o. that killshitmeh mew* gdla" forCsw- WITH SENATOR MCCAIN THIS NOTION BY NOT TALKING TO PEOPLE WE ARE «r

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in the information to Obama and John McCain visualize the way lan­ within a navigable Financial Viewpoints, spatially and volu- ReConstitution, This software was allow users to view Algorithms were guage was used during environment. Prom far by Lisa Strausfeld, metrically represents by Sosolimited (Eric written for use with multiple representa­ Gunther, Justin Manor live performances dur­ applied to the live the debates. Utilizing software's away, each play looks 1995 a portfolio of seven mutual funds. A 3-D tions of the informa­ and John Rothenberg) , ing three presidential images and closed cap­ ability to dynamically like a column of lines. Strausfeld defines her point of view is used tion in a continuous 2008 debates between Barack tions to dynamically scale typography, As you navigate clos­ project as "an experi­ Small presents all of er, each character's mental interactive 3-D to represent context, environment." Shakespeare's plays dialog is revealed. information space that and context shifts 139 VISUALIZATION TECHNIQUE NETWORKS

As social, political, and country, or computer) and technical networks become connections show relation­ denser and more complex, ships between the nodes. widespread interest in visual­ Visualizations help us to see ization is growing. Provocative different types of networks: visualizations help us to bet­ centralized (star), decentral­ ter understand the sometimes ized (hybrid), and distributed invisible relationships that (grid or mesh). These different affect our world. Network organizations were elegantly diagrams frequently include diagramed in 1962 by Paul two types of elements: nodes Baran, one of the conceptual and connections. A node is an architects of the Internet. individual element (a person, wife

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The Internet Mapping form to the Internet. the network address, Power Structures, visual networks. It is a Bjinitasking. Minitasking to reveal visualization as the Project, They captured the pub­ colored by the top-level by Aaron Siegel, 2008 relational database ar.l toy Schoenerwissen/ the ad hoc networks transactions occurred, by Bill Cheswick and lic's imagination; from domain (the black areas These drawings build mapping tool that alloWS [OfCD, 2002 created through the revealing the struc­ Hal Burch, 1998 left: color is applied are .mil sites) and by on the work of Mark users to contribute data ®ith the rise of Gnutella network, a ture, filenames, and These images were the in relation to the dis­ the Internet service Lombardi, an artist who and draw relationships internet file sharing, peer-to-peer proto­ rhythm. first attempts to assign tance from the test provider. depicted crime and con­ |the duo of Anne Pascual col for sharing files. an appropriate visual host, as a function of spiracy information as and Marcus Hauer built Data fed into the 1-41 VISUALIZATION TECHNIQUE DYNAMIC MAPS

Most maps show many layers of maps are so familiar, they of information within a single provide a good foundation for surface. For example, a single additional layers of informa­ map might show the locations tion. Adding changes in time of roads, landmarks, topo­ and geometric distortion are graphy, and political borders. effective ways to push the Because the sophisticated conventions further. language and representation

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(middle) and descent Travel Time Tube Map, time between stations, are organized into con­ Worldmapper.org, 2006 "being mapped. For exam­ produced there. Because amount. This type of in the year 1 CE, fruit gipressing Velocity, r (bottom) from the moun- by Tom Carden, 2005 rather than simply centric rings showing In these cartograms, ple , in the map rep­ map helps the viewer exports, and child Masaki Fujihata, the United States pro­ tain. The decreased This map re imagines the their order. When a travel times from that information is com­ resenting Coal Power, duces a high amount of see differences imme­ labor. >94 climbing speed near the draftsman Henry Beck's station is selected, place. municated through the territory size energy from coal, its diately; clockwise from A 3-D map of Mount summit is reflected in classic Underground Map it becomes the center deformations in the shows the proportion of size is proportionally top, the maps show: Fuji was distorted by extreme distortion at as a malleable space. of the diagram and all size of each territory worldwide electricity larger than countries tourist expenditure, the GPS data gathered It warps to show the of the other stations represented in the data generated from the coal that produce a smaller coal power, population from Fujihata's ascent the peak. Visualize 143 VISUALIZATION TECHNIQUE MATHEMATICS VISUALIZATION

Images were created to objects, and machines to think about mathematics demystify basic mathematical long before computers were principles. Mathematica is invented to calculate and also the name of a powerful visualize. For instance, Euclid program used within the (circa 300 BCE) constructed sciences for calculations and diagrams to show relation­ visualizations. This program, ships between geometric along with other software elements and physical development projects, cleared models. A paper model of the path to new categories a Mobius strip and a glass of mathematics visualization, model of a Klein bottle can including the popular fractal make these intriguing sur­ images of the Mandelbrot set. faces approachable to a Mathematicians, artists, and wider audience, beyond those architects are actively mining who understand the equa­ the structures of numbers and tions behind them. Before the equations to produce visual era of the personal computer, images for pleasure and the Mathematics exhibition, insight. created by the Eames Office in 1961, presented diagrams,

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The superformula was first values for the parameters described by Johan Gielis in named m, n1, n2, and n3. The m 2003 as a way to mathemati­ parameter changes the num­ cally generate a wide variety ber of petals on the final form, of forms found in nature. The and the n parameters affect the form generated by the equation shape and size of the petals. can be controlled by setting The equation for the super- the values of a few key param­ formula is based on a circle. eters. The verdict is still out as Finding the position of each to whether the superformula point in the final form requires actually describes processes iterating around the degrees in nature or simply produces a of a circle, from 0 to 359, and good imitation of them. plugging the angle and param­ The first step to create a eters into the equation. basic 2-D form based on the superformula is to set the

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