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Spatial Modeling with isee Spatial Map

April 15th, 2009 11 comments

Editor’s Note: This is part 3 of a 3-part series on spatial modeling in iThink and STELLA. Part 1 is available here. Part 2 is available here.



Last time, we explored a two dimensional diffusion problem by looking at a metal plate with constant heat applied to the center. The model is available here: 2d-diffusion. The results, using isee Spatial Map, of the start (left) and end (right) of a six-minute simulation are shown below.

2d-element-results

I am frequently asked how to set up Spatial Map. isee Spatial Map is a simple program that can be used to display any dataset as a two dimensional grid with specific colors assigned to data ranges. Since it is stand-alone, iThink and STELLA communicate with it through the Export Data functionality. If you wish to plot simulation results in Spatial Map, you must first set up a persistent link to a CSV file. This persistent link is always going to be from a table that contains just one element of the array you wish to view in Spatial Map.

In this example, a table named “Temp Export Table” was created to export the temperature data. The first element, temperature[1, 1], was placed in the table. There is a subtlety here that cannot be overlooked. I wish to plot the values of the stock T as it varies over time. Yet I export a different variable named “temperature”. Why is this?

This is necessary because although stocks can be exported in the format Spatial Map expects, the export settings that are compatible with Spatial Map only export their initial values no matter where the simulation is. If we export T, we will only ever see the initial conditions in Spatial Map. Thus, when displaying a stock in Spatial Map, and we almost always do display stocks, it is necessary to create a converter that is set identically equal to the stock. The converter will export its current values, and since it is equal to the stock, the stock’s current values will be exported. The converter used for this purpose in this sample model is named “temperature”.

Next it is necessary to set up the persistent link. Choose Export Data… from the Edit menu. The Export Type should already be set to Persistent and Dynamic. Under Export Data Source, select “Export variables in table” and choose the table with the array element in it from the pop-up menu. In this case, that table is called “Temp Export Table”. Also select “One set of values” under Interval. This forces the data to be export in the format required by Spatial Map. These settings are shown below.

spatial-export

To finish setting up the export, choose the CSV file to export to and press OK. For this model, the file is named “2D Diffusion.csv”. Note that all of this has already been set up in the attached sample, so you will not be able to set it up again. You can examine the settings, though, by choosing Manage Persistent Links in the Edit menu and then pressing the Edit link at the end of the “Temp Export Data” line in the Export block.

The value of “temperature” will now be exported once at the start of each run and once at the end. If you wish to see the simulation unfold in Spatial Map, it will be necessary to set a Pause interval, as dynamic links are also exported every time the simulation pauses. Under Runs Specs… in the Run menu, you can see that I have set the Pause Interval to 20. This forces the Spatial Map to update every 20 seconds during the simulation run. This also forces the user to keep pressing Run to advance the simulation.

Read more…

Spatial Modeling in Two Dimensions

April 7th, 2009 10 comments

Editor’s Note:  This is part 2 of a 3-part series on spatial modeling in iThink and STELLA.  Part 1 is available here.  Part 3 is available here.



Last time, we explored spatial modeling using the one-dimensional diffusion problem as an example.  Many spatial applications, however, require two dimensional formulations.  As an extension, we will now explore the two-dimensional diffusion problem.  Instead of a one-meter metal bar with constant heat applied at its ends, the two-dimensional diffusion problem looks at the response of a one-meter by one-meter metal plate with constant heat applied to its center.  We then watch the heat diffuse across the plate.

At first blush, one might think the two-dimensional case is much more difficult than the one-dimensional case.  In particular, if a grid is superimposed over the plate, each finite element on the plate has eight neighbors, as shown below.  It is tempting, therefore, to consider radiating heat in each of these eight directions.

2d-radiation

However, without looking at the two-dimensional diffusion equations, if we consider just the physical layout of this system, the four corners of the finite element only touch the four corner neighbors (1, 3, 5, and 7) at one point.  In contrast, the four sides of the finite element are shared with each of its four immediate neighbors (2, 4, 6, and 8).  This suggests that heat only radiates to (and from) these four neighbors, not all eight.  In fact, if we examine the two-dimensional diffusion equation, we find that there are only component contributions in the x– and the y-directions.  There are no contributions on the diagonal (which would appear in the equation as ∂2u/∂xy and ∂2u/∂yx terms).

Intuitively, then, we have a finite element that is very similar to the one-dimensional case.  We only need to add corresponding flows in the y-direction.  This leads to the following model with the individual finite elements arrayed.

2d-element-model

The array T is now two-dimensional, in x and in y.  In addition, dx can differ from dy, so the diffusion constant C must be broken down into its constituent parts Cx = k/dx2 and Cy = k/dy2.  This leads to the following set of equations for the radiant flows through the plate:

in left = Cx*T[X – 1, Y]                               in top = Cy*T[X, Y – 1]
out left
= Cx*T[X, Y]                                  out top = Cy*T[X, Y]
out right
= Cx*T[X, Y]                              out bottom = Cy*T[X, Y]
in right
= Cx*T[X + 1, Y]                          in right = Cy*T[X, Y + 1]

X and Y are dimension names for the elements in the x– and ­y-directions, respectively.

Using isee Spatial Map, it is possible to view the results of this diffusion across two dimensions.  Spatial Map displays an array as a one-dimensional or two-dimensional grid (depending on the array).  Each cell in the grid is filled with a color corresponding to the value in the corresponding cell of the array.  Below are two spatial maps.  The one on the left shows the initial conditions of the metal plate.  Note that heat only appears in the center of the plate, where it is being externally applied.  The map on the right shows the distribution of heat across the plate at the end of a six-minute simulation.

2d-element-results

The model is available here:  2d-diffusion.  It is already configured to use isee Spatial Map.  In the final installment of this 3-part series, I will describe how to set up isee Spatial Map.

Published Papers that Feature Models

April 6th, 2009 5 comments

sd-review-006One of our customers suggested we compile a list of articles after being asked to submit a paper about his STELLA model. We thought a list of published papers about STELLA and iThink models was a great idea. The information would not only be useful to people writing papers, it would be a wonderful resource for folks wanting to learn about other modeling projects.

It occurred to us that the blog would make a good home for the list because others could help keep it current by posting comments with links to newly published papers or papers we may have missed.

To get the ball rolling, we compiled a list from journals we are familiar with – System Dynamics Review and Journal of the Operational Research Society. The result is by no means exhaustive. It is simply a way to get things started. We need your help to expand this list and to include other journals that you’re reading.

If you know of a published paper about a STELLA or iThink application that does not appear on this list, please let us know about it by submitting a comment. It would be helpful if you included citation information so that we can quickly verify it and update our list.

Thanks for your help!

Click here to see the list

Medici’s Lever – An Online Cultural Policy Game

April 2nd, 2009 No comments
Medici's Lever consists of educational games and a freestyle laboratory that enables users to set game parameters

Medici's Lever consists of educational games and a freestyle policy laboratory

A couple of months ago, Steve Peterson came by the office and showed me an online game created with iThink and isee NetSim called Medici’s Lever.  I was really impressed.

The game begins in San Jose, California.  Dr. Lilia Maria Delgado, a legend of Silicon Valley’s rise to high-tech super power, has died and left a half-billion dollars to establish the “Delgado Arts Endowment”.  In her will, Dr. Delgado simply states that the mission of the Endowment is to advance the cultural life of San Jose.

Your job is to fulfill the mission by experimenting with the various approaches of five different CEO candidates over a 40 year period.  Each candidate personifies a different theory of arts and cultural development and provides you with different investment levers that impact overall “cultural vitality”.

The San Jose Rennaissance is one of two educational games that are a part of Medici’s Lever.  The other game is very similar but takes place in a different region — this time a fictitious European city dubbed the Capital of Culture.

The final module of Medici’s Lever is an interactive Policy Laboratory that lets the user “dial in” initial parameters to define the region in which they want to experiment.

The 3 elements of the "logic model" are displayed as a pyramid in the games

The 3 elements of the "logic model" are displayed as a pyramid in the games

Medici’s Lever is powered by an underlying iThink model (although users are unaware of this).  The games inform the player that it is driven by a “logic model” they must keep in mind when experimenting.

The premise of the logic model is: In order to maintain a healthy cultural ecology a region must strike a balance between three elements — cultural literacy, participation in cultural expression, and consumption of professional cultural goods and services.

In the games, the three elements are visualized as a pyramid.  What I found out after a couple of runs is that investing in the bottom of the pyramid pays off in the long-term.  The insight I gained was that a community needs to have people who appreciate art and culture and actively participate in it from a young age to be successful supporting the professional artists. In other words, it does not make sense to invest in a state-of-the-art performance hall if no one wants to attend the performances.

I think Medici’s Lever is an excellent example of how you can get folks thinking about a systemic issue in an easy and engaging way.

Background and Development

Medici’s Lever is the final project of Cultural Initiatives Silicon Valley, an organization that worked to implement a ten-year cultural plan for Silicon Valley from 1996 to 2006.  John Kreidler, Cultural Initiatives’ retired Executive Director, is responsible for the model concept and design.  The iThink model and web interfaces were developed by Steve and published online with isee NetSim.

CISV Logo

It is important to note that at its inception, Cultural Initiatives planned to operate for one decade only.  As the end of that decade approached, John and Steve began working on bringing all of the ideas of the foundation together in a model that could be played as a game.  It was key that the game live online so others could benefit from the insights of the foundation long after it had sunset.

When Steve started developing the iThink model for the game, isee NetSim was in its beta cycle.  We worked together to see if at this beta stage isee NetSim was up to snuff for creating the type of online game that he envisioned. During the process, Steve gave me a lot of valuable feedback on isee NetSim (and rooted out quite a few bugs too).

isee NetSim turned out to be a good fit.  Steve has been using iThink for a long time so he knows it well.  isee NetSim enabled Steve to do all of the interface design inside iThink itself and let isee NetSim take care of converting it to run over the web.  Since the games could now be run in the browser, players would not need to download and install software to play the game.

Steve told me that the game is intended for policy makers, community leaders, educators, artists, business leaders — anyone who should be thinking about the role of arts and culture within a community.  I asked him how he thought Medici’s Lever would be used.


From my perspective, a game like this provides an excellent vehicle for focused discussion about arts & culture policy.  Medici’s Lever surfaces a host of questions about what is necessary to build a rich, sustainable cultural landscape.  It provides a rich context for informed discussion. Models like this are not “true” in an objective sense, but they have great potential utility.”


Freestyle allows the user to "dial up" conditions for real metropolitan regions anywhere in the world.

Freestyle allows the user to "dial up" conditions for real metropolitan regions anywhere in the world.

This is an interesting point about models in general.  This game is fictitious, but the dynamics are useful.  By allowing players to dial in different initial parameters (population size, immigration, birth and death rates, social cohesiveness and several cultural factors), users can create conditions for real metropolitan regions anywhere in the world.

Another important point is that the model runs over the web.  This makes it easy for people who are thinking about these issues to interact with the games and lab and have an informed discussion.  Players do not need a background in modeling and system dynamics. And they don’t need to download and install software.

If you want to experience Medici’s Lever for yourself, click here to play the game now.

Video Demonstrates Modeling with Modules

April 1st, 2009 No comments

One of our recent webinars, What’s New in STELLA and iThink Version 9.1, highlights some of the new features added in last summer’s v9.1 release.  Karim Chichakly, Director of Product Development, guides you though the model building steps to create a supply and demand model that investigates the current housing crisis.

Among other topics, Karim covers how to organize your model with modules, draw causal loop diagrams and import data from multiple spread sheets.  Preview the 40 minute presentation with this 1.5 minute video clip.

>> Download the sample model files used in the presentation.

>> View complete webinar presentation.