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If you download the NetLogo application, this model is included. You can also Try running it in NetLogo Web 
This is a new kind of mathematical investigation — we are investigating the emergent shape created by the movement of many turtles moving independently in simple ways. Each turtle is moving so as to create a circle of a fixed radius (set by the RADIUS slider). What happens if the radius they are all circling at is changed in midaction? Guess before you try it.
The turtles create their circles by moving forward a little and turning right a little so as to end up with a circle of the specified radius. We start all the turtles on a circle of that radius so they move around the circle.
The NUMBER slider determines the number of turtles circling.
The RADIUS slider determines the size of the circle each turtle moves on.
The SPEED slider determines how large a step each turtle take at each clock tick  it determines the speed of circling.
The SETUP button creates NUMBER turtles on a circle of radius RADIUS centered at the point (0 0). The turtles are all headed so as to move around the circle.
The ALLCIRCLE button starts the turtles circling. They are each drawing their own circle of radius RADIUS.
Change the value of the RADIUS slider while the turtles are circling. Before you do it, what is your guess as to what will happen when you change the RADIUS?
What is happening to the shape described by the turtles?
How far out do the turtles go?
How far in do they come?
Try different values of both starting radius and changed radius.
You can also do further investigations with the following controls:
The ZEROCIRCLE button lets you just focus on turtle zero's movement  all the rest are stopped.
The DRAWCIRCLE button lets you draw a circle on the patches with a radius equal to DRAWRAD. This way you can track the movement of the turtles.
If the PLOT? switch is on, the plot will show a plot of turtle zero's distance from the origin as the turtles circle.
Try the command lt 50
while the turtles are circling. Is this the same behavior as you observed when changing the radius?
In the Command Center, get a single (or several) turtles to trace their path using the command pendown
(pd
). This may help to show the relationship between the circles of individual turtles and the circle you see as they all move together.
What tools can you build to help visualize what is going on?
The display
command is used for smooth animation.
If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.
For the model itself:
Please cite the NetLogo software as:
Copyright 1997 Uri Wilensky.
This work is licensed under the Creative Commons AttributionNonCommercialShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/byncsa/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 uri@northwestern.edu.
This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECTBASED 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 converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORKBASED 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 REC0126227. Converted from StarLogoT to NetLogo, 2001.
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