1. An analog model built in 1941 to validate the “bouncing bomb” ideas of Dr. Barnes Wallis, in preparation for the successful Royal Air Force assault on German dams in 1943 (Reproduced by permission of Royal Air Force Museum)

2. A “live” table constructed by Antonio Câmara and his group as a tool for examining alternative planning scenarios The image on the table is projected from a computer, and users are able to “move” objects around on the image representing sources of pollution by interacting directly with the display Each new position results in the calculation of a hydrologic model of the impacts of the sources and the display of the resulting pattern of impacts on the table (Reproduced by permission of Antonio Camara/Ydreams)

3. The results of using the DRASTIC groundwater vulnerability model in an area of Ohio. The model combines GIS layers representing factors important in determining groundwater vulnerability and displays the results as a map of vulnerability ratings (Reproduced by permission of Hamilton to New Baltimore Grand Water Consortium Pollution Potential (DRASTIC) map reproduced by permission of Ohio Department of Natural Resources)

4. Graphic representation of the groundwater protection model developed by Rhonda Pfaff and Alan Glennon for analysis of groundwater vulnerability in the Mammoth Cave watershed, Kentucky

5. Results of the groundwater protection model Highlighted areas are farmed for crops, on relatively steep slopes and within 300 m of streams. Such areas are particularly likely to generate runoff contaminated by agricultural chemicals and soil erosion, and to impact adversely the cave environment into which the area drains.

6. Simulation of land-cover transition in part of the Amazon Basin (Courtesy: Gilberto Câmara, Director, INPE, the Brazilian remote sensing agency) (A)Predictions of a model based on eight years of transitions of individual cells starting with the observed pattern in 1997, using rules that include proximity to roads, changing agricultural conditions, and so on (B)Observed pattern after eight years of transitions

7. Massive crowds congregate in Mecca during the annual Hajj. On February 1, 2004, 244 pilgrims were trampled when panic stampeded the crowd. This was a unique but unfortunately not a freak occurrence: 50 pilgrims were killed in 2002, 35 in 2001, 107 in 1998, and 1425 were killed in a pedestrian tunnel in 1990. (© Kazuyoshi Nomachi/© Corbis)

8. (B) break through into the parade Simulation of the movement of individuals during a parade. Parade walkers are in white, watchers in red The watchers (A) build up pressure on restraining barriers and crowd control personnel (Reproduced by permission of Michael Batty) AB

9. Dan Brown (UM Photo Services, Scott R. Galvin)

10. Brown’s agent-based models represent the actions of multiple actors, including farmers who sell land, townships that buy properties to preserve and set zoning policies, developers who use different subdivision designs, and residents who are looking for a place to live that meets their needs. The models are being used to understand the ecological consequences of land-use change and to evaluate policy interventions

11. (A)the starting configuration (B) the pattern after one time-step (C) the pattern after 14 time-steps At this point all features in the pattern remain stable Three stages in an execution of the Game of Life

12. Simulation of future urban growth patterns in Santa Barbara, California. (Upper) Growth limited by current urban growth boundary. (Lower) growth limited only by existing parks (Courtesy Keith Clarke)

13. (red) the step function used to assess slope in Figure 16.4; (blue) a decreasing linear function; and (black) a function showing impact rising to a maximum and then decreasing Three possible impact functions

14. Screenshot of an AHP application using Idrisi (www.clarklabs.org) (Courtesy Clark Labs) The five layers in the upper left part of the screen represent five factors important to the decision. In the lower left the image shows the table of relative weights compiled by one stakeholder All of the weights’ matrices are combined and analyzed to obtain the consensus weights shown in the lower right, together with measures to evaluate consistency among the stakeholders