Related articles on the IMaGe website:
Animaps, II
Animaps III:  Color Straws, Color Voxels, and Color Ramps.
Animaps IV:  Of Time and Place

Sandra Lach Arlinghaus

The University of Michigan
Community Systems Foundation

"The people along the sand
All turn and look one way;
They turn their backs on the land
They look at the sea all day.

They cannot look out far,
They cannot look in deep;
But when was that ever a bar
To any watch they keep."

Robert Frost, Neither out far nor in deep.

Animated maps offer exciting possibilities for tracking spatial change over time.  In earlier work in this journal (see links above), animated maps (or "animaps") were used to track changes, across the globe, in bee mite population over time.  They were also used as analytic tools that could employ surrogate variables to mimic change over time in variables that were difficult to learn about.  The introduction of time, through animation, into the mapping process allows the user to participate "with" the map in more than a purely passive manner; two examples are offered below that allow the reader some degree of interaction with the process.  In the first, the reader experiences emotional involvement only and a downloadable interaction, only; in the second the reader can actually drag elements of the map around on the screen, as an instantaneous interaction achieved directly through the browser.

Mount Everest:  Landing and Take-off

Maps showing mountain ranges are often some of the most difficult to read.  Tightly spaced contours look like a jumble of spaghetti that communicate effectively only at quite a local scale.  The broad picture can be difficult to grasp.  Consider the following sequence of maps of the India/Nepal/China region surrounding Mount Everest.  Here the Himalayas come right up against the Gangetic Plain; tightly spaced contours give way sharply to no contours at all. 

All the maps in the table below are made from files from the Digital Chart of the World.  The contour interval is 1000 feet.  The red dot on the map was placed there at 28 degrees north latitude and 86.95 degrees east longitude, the coordinates of Mount Everest given in Goode's World Atlas.  That dot appears in all images in this section.

Click to see a larger image.  The only layers used in this map are those for contours from 1000 to 26000 feet along with the country boundary file.  Note the vertical separation line between tiles and the gaps in contours at higher elevations.  These suggest a lack of information. 
Scale:  1:5,000,000.
Click to see a larger image. When the layer for glaciers is added some of the missing information is added. 
Scale:  1:5,000,000.
Click to see a larger image. When the layer for perennial streams is added the remaining missing information is not filled in.  Extra information and extra clutter are added. 
Scale:  1:5,000,000.
Click to see a larger image. Taking a closer look (1:2,500,000) one can separate some of the contours; others still are clumped.
Click to see a larger image. Taking an even closer look (1:1,000,000) permits visual separation of all contours but at the expense of any broad view of the mountain range.

Triangulated irregular networks (TINs) are one way to bring some degree of visual order into maps with tightly spaced contours.  The table below shows a TIN for each of the maps in the table above.  They were made in ArcView 3.2 with both Spatial Analyst and 3D Analyst Extensions loaded.  The shading ramp employed was one of the default hypsometric set of hues.  (The reader should note that even though these are "standard" in some sense, green does not necessarily mean that there is lush vegetation nor does brown necessarily mean that there is dry, barren land.)

Click to see larger image. TIN based on the contours; the gaps in the contours appear as unusually steep slopes in the associated TIN (as at the right of the map).
Scale:  1:5,000,000.
Click to see larger image. Glacier pattern covers some of the contour gaps and unusually steep slopes. 
Scale:  1:5,000,000.
Click to see larger image. Streams added to the TIN cover it up a bit too much at this scale.
Scale:  1:5,000,000.
Click to see larger image. A closer view shows streams filling swales, as one might expect.
Scale:  1:2,500,000.
Click to see larger image. In an even closer view some of the finer triangular facets forming the TIN become evident.
Scale:  1:1,000,000.

At a broad scale these have the advantage of offering some order where little was discernible with contours alone or with contours and other layers. 

To get both Frost's close-up and far-out view--to look both out far and in deep--animate the TINs. 

Click to see a larger animation.

The animation above is formed from a sequence of 100 TINs of this region.  The single images range in scale from 1:5,000,000 to 1:100,000 with images captured at intervals of 100,000 change in the scale.  There are 50 images in the landing on Mount Everest sequence and 50 images in blasting off from Mount Everest sequence.  The red dot is fixed; it appears to move because, with scale change, the glacier background pattern is changing size and the pattern within it is changing position in relation to the fixed red dot.

In previous animaps, change was displayed on a base map.  Thus, clustering of regions on the map became apparent over a number of time periods.  What did not become apparent was clustering of events in time.  Such clustering can be important if one is looking for ways to intervene in the diffusion process; choke-points provide an opportunity to introduce innovations that can control or enhance the diffusion process.  A relatively new graphical device, a Java applet (Java is a trademark of Sun Microsystems), offers an exciting way to display change over time and reveals clusters of information in a graphically dynamic manner, much as one might imagine in watching the accelerated growth pattern of grape clusters on a vine.
Thus, the "Mapplet" below offers a different perspective on the varroa mite data set. That data set shows easily that there is one country reporting the mite in 1904; in 1912 there is a siting in one other country.  This sort of sporadic siting, one country at a time, occurs until 1963.  Post-1963 there are multiple countries that come in on a yearly basis:  sometimes 3 new additions, sometimes 7 new additions.  The pattern of new receptors may show cycles; indeed, experts on the mites might reflect on whether or not the graphical pattern on number of new countries by year corresponds in any way to various biological cycles associated with the mite or its host.  If it does, then choke-points in the pattern offer possible timing opportunities to intervene (Arlinghaus and Nystuen).  If it does not, then one might consider the extent to which there is cyclical pattern in reporting error or in shipping ( travel patterns.  A glance at the maps suggests that those who live in as yet unaffected regions might find such observations of particular interest.
In the Mapplet below, the pattern of reported sitings from multiple national sources starts just after 1963:  hence, the red color of 1963, as the pattern initiator.  The next siting of the mites occurred in 1967, in four different countries:  hence the entries of 67a, 67b, 67c, and 67d.  In 1968 there were also four sitings; thus, another four boxes, 68a, 68b, 68c, 68d.  The 1963 box is joined to each of 67a, 67b, 67c, and 67d using a length of line segment four times as long as the lengths from each of 67a, 67b, 67c, and 67d to each of 68a, 68b, 68c, and 68d.  Variation in time between sitings is represented by varying the length of line joining them.  All sitings in year X are joined to all sitings in year X+1 (or the next year in which sitings occurred).  The rationale for joining all from one year to all in the next year is that one does not know how the diffusion is taking place.  What is interesting here, perhaps, is that even when there are years with relatively large numbers of countries reporting sitings, still the pattern settles back to a small number eventually even though one might expect it simply to spread even more.  Two obvious directions to interpret this involve reporting error or some sort of saturation of the diffusion, perhaps related to forces such as human travel patterns or mite biology, that are outside the simple mechanics of diffusion (Hagerstrand).  The Mapplet can suggest directions for research questions.

Mapplet:  Structural model of varroa mite diffusion through time.  Pull the red year-box for 1963 all the way across to the right (use the scroll bar) and then drag and drop various pieces of the left side of the mapplet to unravel it and see the pattern of possible time points of opportunity at various stages in the diffusion process.  If a box "sticks" on another, pull it in a bit of a different direction.  Generally it is possible to move beyond the obstacle.  Mapplets seem to offer a wide array of possibilities for description, interpretation, and analysis of complex spatial systems.

  • Agriculture Western Australia, Entomology Web Site, links:
  • Arlinghaus, Sandra L.; Drake, William D.; and, Nystuen, John D. with data and other input from:  Laug, Audra; Oswalt,  Kris S.; and, Sammataro, Diana.  Animaps.Solstice:  An Electronic Journal of Geography and Mathematics.  Volume IX, Number 1, 1998.  Institute of Mathematical Geography.
  • Arlinghaus, Sandra Lach.  Animaps, II.  Solstice:  An Electronic Journal of Geography and Mathematics.  Volume IX, Number 2, 1998.  Institute of Mathematical Geography.
  • Arlinghaus, Sandra L. and Arlinghaus, William C.  Animaps III: Color Straws, Color Voxels, and Color Ramps, Solstice:  An Electronic Journal of Geography and Mathematics, Volume X, No. 1, Summer 1999, Institute of Mathematical Geography.
  • Arlinghaus, Sandra L., and Nystuen, John D.  "A cartographic perspective on the security of an urban water supply network," Perspectives in Biology and Medicine, University of Chicago Press; Vol. 32, No. 1, Autumn, 1988; pp. 91-102. 
  • Digital Chart of the World, 1993.  Strategic Mapping.
  • Environmental Systems Research Institute (ESRI), ArcView 3.2; ArcView Spatial Analyst Extension; ArcView 3D Analyst Extension.
  • Hagerstrand, Torsten.  Innovation Diffusion as a Spatial Process.  University of Chicago Press, 1967.
  • Liang, Y. Daniel.  Introduction to Java Programming, Second Edition.  Indianapolis:  Que Education and Training, 1999.
  • Schlossberg, Marc, personal communication.