Bill Wake
5-30-95

This is intended to be a catalog of intellectual tools: various graphs, maps, charts, and other external memory aids. The categorization is rough; when I get enough tools to be interesting I’ll taxonomize them.

Textual Tools

• Outline
• Table
  • Table of elements
• Grammar [ASU]
• Ordered list
• Table of Contents
• Index
• Code (e.g., C++)
• Long division, canceling fractions
• Tableaux (solution for logic problems or OR problems)
• Stem & leaf plot [Tufte VDQI], back-to-back stem-and-leaf
  [Tukey EDA]
• Knitting patterns
• Math expressions
• Typography (??)
• Codes & ciphers e.g., Morse code
• Crossword puzzles
• Parallel texts
• Hinges and 5-number summary [Tukey EDA]

Graphical Tools

Scatterplots and variations

• Scatterplot [Tufte VDQI]
• Graph (x-y plot)
  • Variety of scales
  • Variety of grids (polar, triangular, etc.)
  • “Hedgehog” graph (lines show 3d)
• Box plot, bar chart, histogram, dot-dash plot [Tufte VDQI]
• Box-and-whisker plot [Tukey EDA]
• Circle graphs e.g., Boehm spiral model
• Two-way plot [Tukey EDA, p. 381]
• Bar chart (time series – organized vertically with time on x
  axis; qualitative – attribute or spatial – bars horizontal with
  value on y axis) [Smart and Arnold]
• Pie chart [Smart and Arnold]
• Area chart or band chart (area adds up to 100%) [Smart &
  Arnold]
• Line diagram (e.g., stock prices)
• Pictorial chart (e.g., 3-1/2 objects to represent 3500 real
  ones) [Smart & Arnold]
• Cartogram (map plot) [Smart & Arnold]; chart-map [Bertin
  1983]

Trees

• Sentence diagram / parse tree. May contain elided subtrees,
  parallel structures with dotted lines, dependencies among
  items.
• Competition tree (e.g., tennis tournament)
• Von Neumann – game theory – any ideas? Game tree
• Tree diagram of boards (AI) [GEB]
• Pedigree (genealogy)

Other Node/Arc Graphs

• Flow diagram (capacities on nodes or arcs)
• Finite state machine (specially labeled)
• Flow chart
• DAGs in general
• Concept graph (nodes are concepts, arcs are relationships)
• Class/object diagram (ala Rumbaugh or Booch)
• Entity-relationship diagram
• Data flow diagram
• Work-flow diagram
• Electronic circuit
• Category diagram
• Feynman diagrams
• PERT diagram

Maps

The location is important.

• Map
  2-1/2 D map (looks like a
  photograph)

• Weather map
• Exploded diagram
• T-diagrams (for self-compiling compilers). [Aho/Sethi/Ullman,
  p. 726]
• Geometry diagrams (angles, etc) (Sometimes a map)
• Data maps [Tufte VDQI]
• Blueprint
• Topographical map
• Level trace (rings of influence based on distance) [Tukey EDA,
  p. 469]

Abstract Pictures

Actual location isn’t important, relationship is.

• Picture, possibly with annotations, possibly abstract
• Venn diagram
• Harel statechart
• Abstract picture (Not sure how to describe this one). Example:
  picture of buffer in Aho/Sethi/Ullman “Compilers”, p. 91. Box/link
  diagram? Often used for data structures with pointers.
• Box diagram e.g., Aho/Sethi/Ullman chapter 7.
• T-diagrams (for self-compiling compilers). Aho/Sethi/Ullman p.
  726.
• Palette (of tools – ala Macintosh)
• Bongard problems [GEB]
• Icons
• Geometry diagrams (angles, etc)
• Maze
• Phillips curve [Tufte VDQI]
• Chernoff faces [Tufte VDQI]
• Kiviat Diagrams
• Dot tallies [Tukey EDA p. 18]

Time-Based Diagrams

• Musical score
• Time line
• Object interaction diagram (sort of a combination timeline and
  graph)
• Schedule chart (tracks for difft people, blocks for
  duration)
• Gantt chart
• Timing diagram
• Multiples / animations [Tufte VDQI]
• Graph with time on x axis, possibly multiple functions.
• EEG [Tufte VDQI]
• Time series graphs [Tufte VDQI]
• Railroad timetable [Tufte VDQI, Tufte EI]
• Data maps [Tufte VDQI]
• Minkowski space-time diagram (??)
• Seismograph
• Labanotation [Tufte EI]

Other Techniques

• Stereoscopic views [Tufte EI]
• Small multiples of images [Tufte EI]
• Micro-macro readings [Tufte EI]: multiple levels of detail
• Layering & separation [Tufte EI]
• Types of shading & texture (“retinal variables”) [Bertin
  1983]: size, value (gray scale), texture (variations of fineness
  & coarseness), color, orientation (of fill pattern), shape (of
  mark).

People & Ideas to Explore

• Anything from music, poetry, sonification?
• Tukey – EDA
• M. E. Spear – Charting Statistics, 1952
• Bertin
• Maps – physical vs. abstract. Does changing the location of an
  entity affect the information it represents?
• Parallelism and annotation. Text streams might support parallel
  structures (e.g., synoptic gospels). Annotation often takes the
  form of pointers between matching parts, or shadowed copies of the
  main item.
• Hierarchies and trees. There are many representations of
  hierarchies eg., trees and outlines. Are there other structures
  that share this notion?
• Tables vs. graphs. Some tables can take an almost graph-like
  form.
• Book on concept maps and hypertext – what was it?
• Scott Kim [GEB]

References

• Aho, Sethi, and Ullman. Compilers: Principles, Techniques,
  and Tools, Addison-Wesley, 1986.
• [Bertin 1983] Jacques Bertin. Semiology of Graphics,
  University of Wisconsin Press, 1983. QA90 B47513 1983.
• Gamma, Helm, Johnson, and Vlissides. Design Patterns:
  Elements of Reusable Object-Oriented Software, Addison-Wesley,
  1995.
• Goodman. The Complete HyperCard Handbook, Bantam,
  1987.
• L. E. Smart and S. Arnold. Practical Rules for Graphic
  Presentation of Business Statistics, Ohio State University:
  Columbus, OH, 1951. HA31 S6 1951.
• Tufte. The Visual Display of Quantitative Information,
  Graphics Press, 1983. QA90 T83 1983.
• Tufte, Edward R. Envisioning Information, Graphics
  Press: Cheshire, CT, 1990. QA90 T82 1990.
• Tukey, John W. Exploratory Data Analysis,
  Addison-Wesley: Reading, MA, 1977. HA29 T783.
• Waters. Categories and Computer Science, Cambridge
  Computer Science Texts, Vol. 27, 1991.