verywhere we look, we see regularities, patterns, order. Many of these patterns have a kind of haunting beauty: the growth of a snowflake crystal, the perimeter pattern of a maple leaf, the advent of a summer squall. Other patterns, such as the dynamics of the Dow Jones or of a fourth grade classroom, seem messier, inchoate, yet still exhibit a familiar and recognizable general "shape." The characteristic shape can unfold in space or in time, sometimes striking and unmistakable and sometimes more hidden, needing probing observation or ingenious experiment to uncover it.

Why is there so much pattern in the world? While grappling with this question in full would take us far afield, we can start with a simple observation: large- scale patterns in the world are usually the result of the interactions of many smaller pieces that somehow combine in surprising ways to create the large-scale pattern. Such large-scale (macro-) patterns that arise out of the interactions of numerous interacting (micro-) "agents" are called "emergent phenomena" - that is, phenomena that emerge from interactions at a lower level or scale.

Visualize a flock of birds winging in the autumn sky or the amazing synchronized fireflies that blink in unison lighting up whole trees in the Far East. How do these patterns come about? All of these patterns are emergent; there is no leader bird which other birds follow, no conductor firefly leading the band - these patterns emerge out of the behavior of individuals and the adjustment of that behavior in interaction with other individuals.

The study of emergent phenomena is the principal occupation of a developing field of science, the study of complex dynamic systems. This broad new field seeks to understand how systems of interacting components evolve over time. In the minds of many, however, complex systems theory is not a new branch of science, but rather a new framework, a new perspective that allows us to see old scientific content in new ways. This new perspective and the methods it brings to bear have been adopted across a wide array of natural and social sciences. An understanding of complex systems is becoming an essential part of every scientist's knowledge and skills. The time has come for these ideas and methods to become a central part of every student's learning.

Despite its adoption by practicing scientists, the complex systems perspective is largely absent from the K-16 curriculum. One reason for the slow transfer to schools is the heavy reliance of complex systems methodologies on the use of powerful computational technologies. By enabling the rendering, simulation and visualization of the evolution of complex systems over time, the computer has proved an indispensable tool for making sense of complex systems and emergent phenomena.

Most of the tools used by experts to explore complexity in their domain of interest are highly domain specific - designed for use by experts to study a particular class of phenomena. Until very recently, no general purpose tools existed for students to render and explore systems of many interacting parts that can exhibit emergent behavior.

At the Center for Connected Learning and Computer-Based Modeling at Tufts University, our goal is to create computer-based tools and curricula to enable students to make sense of complexity and emergent phenomena. I will now describe a set of tools developed with the support of the National Science Foundation that enable typical secondary students to engage and make sense of complexity and emergent phenomena.

A major project accomplishment was the development of a computer modeling language (and associated materials) that would enable learners, teachers and students to create dynamic models of complex phenomena. The language we developed, called StarLogoT¹, is now in use by thousands of students, teachers and researchers worldwide. StarLogoT is one of a class of new so-called multi-agent modeling languages (a.k.a. object-based parallel modeling languages or agent-based modeling languages) that have emerged from the complex systems community.

StarLogoT (and its mother language StarLogo²) is an extension of the computer language Logo in which a user "drives" a graphical turtle on a computer screen by issuing commands such as "forward," "back," "right" and "left." In Logo, typically, the turtle is thought to carry a "pen" and, thus, draws a line when it moves. In this way, children can create geometric shapes by giving motion instructions to the turtle. In StarLogoT, however, instead of driving a single turtle, the user can drive (or, perhaps better to say, orchestrate) thousands of turtles. Instead of drawing with pens, turtles "draw" with their bodies. By that, I mean that the emergent shape of all the turtles' positions constitutes a drawing in StarLogoT³.

Allow me to illustrate with a simple example in which turtles take the shape of little squares or points. If we initiate a StarLogoT session with the command "create-turtles 1000" then 1000 little squares will appear in the graphics screen. However, because they are initialized to start in the middle of the screen, they all pile on top of each other and appear as a single point (see Fig. 1).

If we then type the command "forward 40" all of the turtles move forward 40 screen units (see Fig. 2). Note that because the turtles were initialized with different "headings," (they faced in different directions) they made the shape of a circle. This is already a simple example of emergent behavior. The fact that there were enough turtles so that by random chance they were likely to fill the holes ensured that a coherent circle emerged from the motions of independent turtles.

At first glance, the reader might wonder how the turtles can do anything different and interesting if they all follow the same commands. The power of StarLogoT comes from the fact that each turtle is an independent agent. Because each turtle had an independent heading, they all moved in different directions when we typed "fd 40." Since it is possible for turtles to have as many states as the user likes, the response of turtles to the same commands can vary markedly.

In addition to this difference amongst turtles, each turtle does its own separate computation. To see how this makes a difference, we can type the command "back 40" to get all of the turtles back to the middle of the screen, then invoke the command, "forward random 40." The function "random" computes a random value between 0 and 40. Because each turtle does its own computation, each one gets a different value for "random 40" and thus will move forward a different amount (see Fig. 3).

(Beginning students often want to reverse this operation and try the command "back random 40." However, this has unexpected results. Try it.)

In addition to turtles, StarLogoT has a second kind of agent that we call a "patch." Patches are very much like turtles except that they are always around and do not move. The screen is initialized to a user resizable grid of patches. In other words, even though the graphics screen looks like empty black where there are no turtles, in reality the patches are invisibly lurking there waiting for commands.

If we type the command, "setpatchcolor green," all the patches will change their color to green (see Fig. 4).

Finally, if we type the command "if xcor < 0 [setpatchcolor black]" then all the turtles to the left of the origin turn black (see Fig. 5). The key point to keep in mind is that they do not do this because they are "told" to do it by a leader. They each examine their own position on the screen, determine if they are to the left of the origin and, if so, they turn themselves black.

With these basic tools, we can now create models and dynamic simulations of many different kinds of complex systems. There is a saying that goes: "If all you have is a hammer, the whole world looks like a nail." With the powerful hammer of the StarLogoT language, it becomes easier to see emergent phenomena every- where. Not only the classic emergent phenomena described in the complex systems literature, but many everyday and scientific phenomena can be viewed through the lens of emergent phenomena. While, at first glance, emergent phenomena seems like an exotic add-on to the curriculum, we see it as a powerful amplifier of understanding for virtually all scientific topics. By enabling us to make cogent and testable connections between the micro and macro, the individual and the collective, the element and the system, the new lens makes them easier to understand for novice and for expert learners alike.

Uri Wilensky is Director of the Center for Connected Learning and Computer-Based Modeling at Tufts University.
oas@ccl.tufts.edu

FOOTNOTES

¹ StarLogoT currently runs only on Macintosh computers. A multi-platform version, which we call N-Logo, will be available in early 2000.

² StarLogo was originally developed at MIT. StarLogoT is an extension and superset of MIT's MacStarLogo.

³ StarLogoT "turtles" do not typically look like turtles. They are general purpose "agents" that can take on any shape.

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