Fatfonts: Combining the Symbolic and Visual Aspects of Numbers
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FatFonts: Combining the Symbolic and Visual Aspects of Numbers Miguel Nacenta Uta Hinrichs Sheelagh Carpendale School of Computer Science Dept. of Computer Science Dept. of Computer Science SACHI Group InnoVis Group InnoVis Group University of St Andrews, UK University of Calgary, Canada University of Calgary, Canada [email protected] [email protected] [email protected] ABSTRACT (including zero), and utilizes a positional system to allow In this paper we explore numeric typeface design for visu- the representation of higher orders of magnitude. alization purposes. We introduce FatFonts, a technique for Numeral systems have not, however, always been so flex- visualizing quantitative data that bridges the gap between ible and sophisticated; more simple systems exist. In the numeric and visual representations. FatFonts are based on unary numeral system (see Fig. 1(a), top), for instance, each Arabic numerals but, unlike regular numeric typefaces, the counted object is represented by a mark. Unary numeral sys- amount of ink (dark pixels) used for each digit is propor- tems are still used by, e.g., bartenders or prisoners to count tional to its quantitative value. This enables accurate read- beers on credit and days spent in jail, but they have the ing of the numerical data while preserving an overall visual obvious disadvantage that large numbers become difficult to context. We discuss the challenges of this approach that identify and manipulate. Fig. 1(a) shows how representing we identified through our design process and propose a set the number 34 (still relatively small) in the unary system is of design goals that include legibility, familiarity, readabil- tedious to write, difficult to read, and space consuming. This ity, spatial precision, dynamic range, and resolution. We might be why the Babylonians and many other civilizations contribute four FatFont typefaces that are derived from our developed more abstract symbols that support the repre- exploration of the design space that these goals introduce. sentation of large numbers without correspondingly larger Finally, we discuss three example scenarios that show how numeral combinations (see Fig. 1(a)). FatFonts can be used for visualization purposes as valuable representation alternatives. Categories and Subject Descriptors H.5.2 [Information Interfaces and Presentation]: Misc. General Terms Design Figure 1: (a) The unary, Babylonian, Roman, and Keywords Hindu-Arabic numerals (top to bottom). (b) U.S. education and military spending represented by Information Visualization, Typography, Numerals blocks and pie sectors. 1. INTRODUCTION However, abstraction also removes the direct relationship between the visual and the quantitative: we do not anymore In this paper we introduce the concept, design and soft- see a certain quantity, but have to learn to interpret a sym- ware implementation of FatFonts, a visualization technique bol that represents the quantity. In fact, the discipline of that integrates the symbolic and visual aspects of numbers. information visualization [25] is often concerned with pro- A numeral system is \a writing system for expressing num- viding visual representations that facilitate the comparison, bers" [27]. Although generally taken for granted, current perception, and comprehension of quantities. For example, numeral systems are sophisticated tools that result from Fig. 1(b), shows two simple visualizations of military and millennia of development. For instance, the Hindu-Arabic education spending in the 2011 U.S. federal budget. Both numeral system, that we use every day, is based on ten sep- visualizations can be regarded as numbers expressed in a arate symbols to represent the first ten numbers in base-10 unary system: the visualization on the left uses rectangles as the basic unit, and the visualization on the right uses area. However, such visualizations suffer from similar prob- Permission to make digital or hard copies of all or part of this work for lems as the unary numerals in Fig. 1(a): it is difficult to personal or classroom use is granted without fee provided that copies are identify exact numbers and operate with them. not made or distributed for profit or commercial advantage and that copies This paper describes our explorations in combining the bear this notice and the full citation on the first page. To copy otherwise, to symbolic and the visual aspects of numbers in a single, hy- republish, to post on servers or to redistribute to lists, requires prior specific brid technique: FatFonts (see Fig. 2). FatFonts are glyphs permission and/or a fee. AVI 2012 Capri Island (Naples), Italy shaped according to Hindu-Arabic numerals (the symbolic Copyright 2012 ACM 978-1-4503-1287-5/12/05 ...$10.00. aspect) that cover an area proportional to the represented Figure 2: A scalar field represented with FatFonts. value (the visual aspect). In other words, FatFonts are nu- 19]. This work and FatFonts share the dual representation merals that retain the recognizable shape of Hindu-Arabic of information (symbolic and visual) but FatFonts focus on numerals while their area (or amount of 'ink') is proportional the representation of quantitative data. to the represented number: number two's ink area is double Other related artistic works include visual poetry [7] (e.g., number one's, number three's is triple number one's, and so Apollinaire's calligrams), and Islamic calligraphic art. More on. In this way, FatFonts provide simultaneously a symbolic recently, kinetic typography videos (e.g., [20]) have become and visual quantitative reading of data, contributing to the popular where typography is animated to highlight the con- set of existing visual representation techniques in static, dy- tent, tone, and attitudes of spoken dialogue or song lyrics. namic, and interactive information systems. FatFonts lend As with the previous examples, FatFonts differs from these themselves to the visualization of large data sets where both in its goal of representing quantitative information. overview and numerical detail of data is important. The fol- lowing sections describe the FatFonts technique, our design 2.2 Font Manipulation in Visualization choices and alternative FatFont designs, their implementa- Early visualizations that required printing on paper through tion and algorithms, a set of examples of their use, and a character-based dot-matrix printers or typewriters made use discussion on how and when FatFonts can be beneficial com- of fixed letters and numbers to create shapes useful to un- pared to existing alternatives. derstand the data (e.g., Stem and Leaf plots [23] and re- lated techniques [17]). We take these ideas further by mod- 2. RELATED WORK ifying the glyphs themselves to create a meaningful visual Previous work from art and information visualization has overview. Text and numbers are also part of modern visual- made use of typography and related graphical techniques. In izations, but they are usually separate elements (e.g., labels), this section we discuss how these approaches are related to and their typeface is influenced by legibility or space effi- FatFonts. For clarity, other related work (e.g., information ciency, not the image. Examples of typography directly ap- visualization techniques comparable to FatFonts) is cited in plied in information visualization are tag- and word-clouds [3, our discussion of example application scenarios. 11] and more recently Wordtree [26], that vary the font size 2.1 Art, Typography, and Screening and/or weight to represent information such as the word frequency in a text. These techniques convey relative quan- Many artistic examples exist in which letters and digits tities, rather than explicit numerical data. Finally, typo- have been used to create pictures. One well-known exam- graphic maps make exclusive use of letters and typography ple is ASCII art, where a limited character set is creatively to form city maps [2]. These maps are similar to FatFonts in used to reproduce shapes and, taking the darkness of ASCII that the outline and texture of the text both convey mean- characters into account, greyscale images. In ASCII art tex- ing, but the goal here is to relate city shapes and their names, tual and numeric characters are only the means to build an not to communicate quantities as in FatFonts. image; that is, single characters are not meant to convey meaning but to be experienced as a whole. In effect, the 3. FATFONTS ASCII characters are used like pixels, not for the meaning FatFonts is a technique designed to bridge the gap between they symbolize but to build up an image. With FatFonts our symbolic and visual representations through the manipula- intention is to combine meaning in the individual characters tion of the shape of Hindu-Arabic numerals. In this section with the capability of building images as a whole. we describe the fundamentals, goals, and design decisions Artistic screening [21] is a development of the ASCII art that constitute this novel technique. idea. It allows halftoning through the use of any shape, in- cluding text and numbers. The primary purpose of artistic 3.1 FatFont Fundamentals screening is quality halftoning where individual glyphs are Glyphs as Symbols. Many of the advantages of modern beautiful in themselves. Intensity levels are predefined via a numeral systems over unary systems stem from the abstract dot contour and, for a given shading, a chosen glyph modi- symbolic nature of the glyphs used. While unary systems fied by these predefined dot contours is utilized. In contrast enable a more literal and direct perception of a quantity (as to FatFonts, the shape alone is used for artistic purposes shown in Fig. 1), Hindu-Arabic numerals can represent much while the symbolic meaning is not relevant. larger numbers using less space and enable mathematical There are other artistic techniques that, similarly to Fat- operations as well as comparisons. Importantly, modern nu- Fonts, make use of text to convey meaning through images merals are less error prone because each numeral is visually and words simultaneously, often in close relationship to each distinct from its siblings.