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This model is inspired by the aggregation behavior of slime-mold cells. The slime mold spends much of its life as thousands of distinct single-celled units, each moving separately. Under the right conditions, those many cells will coalesce into a single, larger organism. When the environment is less hospitable, the slime mold acts as a single organism; when the weather turns cooler and the mold enjoys a large food supply, "it" becomes a "they." The slime mold oscillates between being a single creature and a swarm.
This model shows how creatures can aggregate into clusters without the control of a "leader" or "pacemaker" cell. This finding was first described by Evelyn Fox Keller and Lee Segel in a paper in 1970.
Before Keller began her investigations, the conventional belief had been that slime mold swarms formed at the command of "pacemaker" cells that ordered the other cells to begin aggregating. In 1962, Shafer showed how the pacemakers could use cyclic AMP as a signal of sorts to rally the troops; the slime mold generals would release the compounds at the appropriate moments, triggering waves of cyclic AMP that washed through the entire community, as each isolated cell relayed the signal to its neighbors. Slime mold aggregation, in effect, was a giant game of Telephone — but only a few elite cells placed the original call.
For the twenty years that followed the publication of Shafer's original essay, mycologists assumed that the missing pacemaker cells were a sign of insufficient data, or poorly designed experiments. But Keller and Segel took another, more radical approach. They shows that Shafer had it wrong -- that the community of slime mold cells were organizing themselves without any need for pacemakers. This was one of the first examples of emergence and self-organization in biology.
Initially, biologists did not accept this explanation. Indeed, the pacemaker hypothesis would continue as the reigning model for another decade. Now, slime mold aggregation is recognized as a classic case study in bottom-up self-organizing behavior.
In this model, each turtle drops a chemical pheromone (shown in green). The turtles also "sniff" ahead, trying to follow the gradient of other turtles' chemicals. Meanwhile, the patches diffuse and evaporate the pheromone. Following these simple, decentralized rules, the turtles aggregate into clusters.
Click the SETUP button to set up a collection of slime-mold cells. Click the GO button to start the simulation.
The POPULATION slider controls the number of slime mold cells in the simulation. Changes in the POPULATION slider do not have any effect until the next SETUP command.
The other sliders affect the way turtles move. Changes to them will immediately affect the model run.
SNIFF-THRESHHOLD -- The minimum amount of chemical that must be present in a turtle's patch before the turtle will look for a chemical gradient to follow. This parameter causes the turtles to aggregate only when there are enough other cells nearby. The default value is 1.0.
SNIFF-ANGLE -- The amount, in degrees, that a turtle turns to the left and right to check for greater chemical concentrations. The default value is 45.
WIGGLE-ANGLE -- The maximum amount, in degrees, that a turtle will turn left or right in its random movements. When WIGGLE-ANGLE is set to zero, the turtle will remain at the same heading until it finds a chemical gradient to follow. The default value is 40.
WIGGLE-BIAS -- The bias of a turtle's average wiggle. When WIGGLE-BIAS = 0, the turtle's average movement is straight ahead. When WIGGLE-BIAS > 0, the turtle will tend to move more right than left. When BIAS < 0, the turtle will tend to move more left than right. The default value is 0.
There are several other critical parameters in the model that are not accessible by sliders. They can be changed by modifying the code in the procedures window. They are: - the evaporation rate of the chemical -- set to 0.9 - the diffusion rate of the chemical -- set to 1 - the amount of chemical deposited at each step -- set to 2
With 100 turtles, not much happens. The turtles wander around dropping chemical, but the chemical evaporates and diffuses too quickly for the turtles to aggregate.
With 400 turtles, the result is quite different. When a few turtles happen (by chance) to wander near one another, they create a small "puddle" of chemical that can attract any number of other turtles in the vicinity. The puddle then becomes larger and more attractive as more turtles enter it and deposit their own chemicals. This process is a good example of positive feedback: the more turtles, the larger the puddle; and the larger the puddle, the more likely it is to attract more turtles.
Try different values for the SNIFF-THRESHOLD, SNIFF-ANGLE, WIGGLE-ANGLE, and WIGGLE-BIAS sliders. How do they affect the turtles' movement and the formation of clumps?
Change the SNIFF-ANGLE and WIGGLE-ANGLE sliders after some clumps have formed. What happens to the clumps? Try the same with SNIFF-THRESHOLD and WIGGLE-BIAS.
Modify the program so that the turtles aggregate into a single large cluster.
How do the results change if there is more (or less) randomness in the turtles' motion?
Notice that the turtles only sniff for chemical in three places: forward, SNIFF-ANGLE to the left, and SNIFF-ANGLE to the right. Modify the model so that the turtles sniff all around. How does their clustering behavior change? Modify the model so that the turtles sniff in even fewer places. How does their clustering behavior change?
What "critical number" of turtles is needed for the clusters to form? How does the critical number change if you modify the evaporation or diffusion rate?
Can you find an algorithm that will let you plot the number of distinct clusters over time?
Note the use of the
patch-right-and-ahead primitives to do the "sniffing".
Ants uses a similar idea of creatures that both drop chemical and follow the gradient of the chemical.
Keller, E & Segel, L. (1970). Initiation of slime mold aggregation viewed as an instability. Journal of Theoretical Biology, Volume 26, Issue 3, March 1970, Pages 399–415.
Wilensky, U., & Resnick, M. (1999). Thinking in levels: A dynamic systems approach to making sense of the world. Journal of Science Education and Technology, 8(1), 3-19.
Johnson, S. (2001). Emergence: The Connected Lives of Ants, Brains, Cities, and Software. New York: Scribner.
Resnick, M. (1996). Beyond the centralized mindset. Journal of the Learning Sciences, 5(1), 1-22.
See also http://www.creepinggarden.com for video of slime mold.
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For the model itself:
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Copyright 1997 Uri Wilensky.
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at email@example.com.
This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.
This model was developed at the MIT Media Lab using CM StarLogo. See Resnick, M. (1994) "Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds." Cambridge, MA: MIT Press. Adapted to StarLogoT, 1997, as part of the Connected Mathematics Project.
This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2000.