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# Turtles Circling

 If you download the NetLogo application, this model is included. You can also Try running it in NetLogo Web

## WHAT IS IT?

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 mid-action? Guess before you try it.

## HOW IT WORKS

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.

## HOW TO USE IT

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 ALL-CIRCLE 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?

## THINGS TO NOTICE

What is happening to the shape described by the turtles?

How far out do the turtles go?

How far in do they come?

## THINGS TO TRY

You can also do further investigations with the following controls:

The ZERO-CIRCLE button lets you just focus on turtle zero's movement -- all the rest are stopped.

The DRAW-CIRCLE button lets you draw a circle on the patches with a radius equal to DRAW-RAD. 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 `pen-down` (`pd`). This may help to show the relationship between the circles of individual turtles and the circle you see as they all move together.

## EXTENDING THE MODEL

What tools can you build to help visualize what is going on?

## NETLOGO FEATURES

The `display` command is used for smooth animation.

## HOW TO CITE

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: