NetLogo Mystery Pattern
Contents
1. check the color of the patch on which the turtle lands set the patch color to white only if it is not already white Refer to the the NetLogo user manual for more information if necessary Questions for Reflection on Further Modifications l Your model uses an equilateral triangle the dimensions we set for the NetLogo canvas at the start of the activity were chosen specifically to give us such a triangle What do you think would happen if we used a triangle with different proportions Is there any easy way to test your hypothesis What do think would happen if we were to start with a shape that wasn t triangular i e with more than three target vertices to choose from For example what if we chopped the top off of our triangle and started with a trapezoid How difficult do you think it would be to modify your program to answer that question NetLogo Mystery Pattern 152. same result as that obtained by cutting holes out of triangles Aside from the fact that the turtles were always moving halfway toward one of the vertices of a triangle there was little if any hint that the final pattern produced would have anything to do with triangles at all NetLogo Mystery Pattern 14 Additional Exercises Modifying the Model l There are a number of ways to change a turtle s location So far we have used the forward procedure which moves the turtle forward in the direction it is already facing Another approach is to use the jump procedure which works in exactly the same manner as forward except that NetLogo doesn t try to animate the entire path of the turtle Modify your draw procedure to use jump instead of forward What is the result If the model uses jump it might not be that important for the turtles to appear at all In NetLogo each turtle has a hidden variable which we can modify to control whether a turtle is visible alternatively we can use the hide turtle and show turtle procedures Modify your setup corner procedure so that all turtles are invisible Currently each turtle modifies the color of the patch on which it lands setting it to white it does this whether the patch color has already been turned white by another turtle or not However a turtle can condition its behavior on the color of the patch it is on using an if statement Modify your draw procedure using an if statement to
3. NetLogo Mystery Pattern Introduction Sometimes we may observe that very simple behaviors when repeated by many agents or even by a smaller number of agents acting over a long period of time can produce very rich interesting patterns In this activity we ll be building a NetLogo model that has agents with a very simple behavior At each step a turtle will perform the following steps 1 Select one of three target points these points make up the vertices of a triangle at random 2 Move half the distance toward the selected target point 3 Mark its new location with a white dot on a black background To begin each turtle will be located on one of the three target points Alternatively we could start with each agent midway between two of the target points since those midpoints are where all of the agents will move to in the first step anyway What pattern if any will result from the turtles following their programmed behaviors How many repetitions of the above steps will it take before any such pattern emerges We could try to answer the questions above by doing the exercise on paper but it would probably become very tedious very quickly possible long before the mystery pattern is clear NetLogo Tutorials The NetLogo Coordinate System In setting up the vertices of our triangle the three target points that will be used by the agents it will be useful to know a little bit about the coordinate
4. Set the turtles per vertex slider to a value of 1 Click the Setup button Click the Draw button If you get any errors try and fix them by yourself or with the instructor s help Assuming your program is running correctly what pattern do you notice Change the value of turtles per vertex to a higher value and repeat steps 2 and 3 Has anything changed Repeat step 2 then slow your turtle movement down using the slider at the top of the NetLogo world Now repeat step 3 and watch how the turtles move How would you describe this movement in general terms NetLogo Mystery Pattern 13 What is the Mystery Pattern The pattern drawn by the turtles is called Sierpinski s Triangle or Sierpinski s Gasket The best known recipe for creating this figure is as follows 1 Start with a triangle 2 From the original triangle cut out the triangle formed by connecting the midpoints of all three sides of the original triangle 3 Continue the process with the smaller triangles created treating each one as if it were the original triangle The first few iterations of this process are illustrated below In this activity we ve used an entirely different method to draw the same figure in fact there are several methods for producing Sierpinski s Gasket In this approach the participants not just the turtles but probably the programmers as well had no idea that the rules being followed would give the
5. at ends the setup corner procedure type the following code to draw let target one of corners face target forward 0 5 distance target set pcolor white end 3 Use the Check button to make sure you don t have spelling or space errors 4 Let s review this procedure a First the turtle uses one of to select at random one of the set of patches stored in the variable corners b Now that the turtle has selected one of the vertices and stored it in the variable target it changes direction to turn towards the selected vertex There are a couple of ways to do this in this case we use the procedure face which turns the turtle to face some other turtle or patch c Then the turtle moves forward by half the distance between the turtle and the target vertex d Finally when the turtle comes to rest it changes the color of the patch on which it is standing using set pcolor making it white NetLogo Mystery Pattern 10 5 Review the contents of your Procedures window it should look something like this globals corners iO SSicwys clear all set corners patch set parca 0 wex pyeexr 10 parce waepx qpexeos 110 min obycor F 10 paca uma j xeeu 3 10 uon pyeo 10 ask corners BESTU 6 0ieimese end t9 SXetuupo 6o e set pcolor white Sprout turtles per vertex set color blue set size 2 0 end to draw let target one of corners face target forward 0 5 distance
6. button on the toolbar near the top of the window 13 Click somewhere in the white space to the left of the canvas the Button configuration window will appear 14 This button will be used to run the setup procedure you just wrote to set it up correctly set the following configuration values a Type the word setup leave out the quotes when you type it into the Commands text box b If you want you can give this button a different display name by typing something in the Display name field and or a shortcut key by typing a letter in the Action key field as have done in the example Your Button window should look something like this Button observer E 15 Click the OK button 16 Click the Setup button you just created If your program is working correctly you should see three blue dots forming a triangle on the canvas Why are they blue Didn t we ask those three patches to set their colors to white Yes we did However each of those three patches also created turtles which are all standing stacked up on top of each other if there is more than one turtle per vertex on those patches each of those turtles is blue When the turtles start moving they will uncover the white potches 17 If you got an error message at any point e g when you clicked the Check button in the procedures window or when you clicked your Setup button read the message displayed and look at the highlighted code Did you l
7. eave necessary spaces out Did you misspell a NetLogo command Did you spell one of your own procedure or variable names inconsistently If you can find the error correct it and try again if not ask for help from the instructor NetLogo Mystery Pattern 9 Making the Turtles Move As described earlier the turtles in this model will follow a very simple set of rules At each step a turtle will pick one of the three vertices at random and move towards the selected vertex stopping after moving half of the original distance between the turtle and the vertex then the turtle will change the color of the patch it is on to white then it will repeat the same process again and again and again ad infinitum at least until we tell them to stop In our setup procedure we put the patches that will be the vertices of our triangle in the corners variable they are still in that variable even after setup is complete so the turtles can use that variable when they need to select one of the vertices as a target point NetLogo has built in statements that allow a turtle to change its direction so that it is headed towards a patch or another turtle It also has statements for calculating the distance from one agent a turtle or patch and another We ll be using both of these facilities in writing the procedure for our turtle behavior 1 Click on the Procedures tab so that you can resume typing your NetLogo program 2 After the end statement th
8. extension of nlogo 7 After the end of the setup procedure again give yourself some blank lines write the setup corner procedure eO Serup Corner set pcolor white sprout turtles per vertex set color blue set size 2 0 end 8 Again use the Check button to check your typing There might be logical errors in the code that you don t catch until you try to run your program but using Check will help you catch typing problems early 9 Reviewing setup corner a We begin by setting the color of the patch to white that way all three vertices of our triangle start out white b Then we use the sprout command which you might not have seen before sprout is the command a patch uses to create turtles right on that patch and then to ask those turtles to do something Here the patch is creating as many turtles as are specified with the turtles per vertex slider that we created at the start c Finally the patch asks each of those turtles to set its color to blue and to set itself to twice the normal size Normally turtles are as large as the patches since the patches in this model are so small the turtles will be small as well Setting the size to 2 0 will make them a bit easier to see 10 Save your program again by using the File Save menu option or by typing Ctrl S 11 Click on the Interface tab to switch back to the window that shows the NetLogo canvas NetLogo Mystery Pattern 8 12 Click on the Button
9. f course NetLogo Mystery Pattern 6 Writing the Model Setting up the Target Points the Vertices of the Triangle Imagine drawing a triangle on the NetLogo canvas with its base stretching all the way across the bottom with a little space left over so we can see things more easily and with the top vertex centered almost at the top of the canvas As it turns out the three corners vertices of that triangle are pretty easy to describe in NetLogo if we leave a margin ten patches wide on all four sides of the canvas then coordinates of the top lower left and lower right vertices are respectively 0 max pycor 10 min pxcor 10 min pycor 10 and max pxcor 10 min pycor 10 Ofcourse we just set the dimensions of the screen ourselves in fact we set them so that the resulting triangle would be equilateral so we could just use the numbers we typed into the World amp View settings window but to be on the safe side let s assume we don t know the specific dimensions For the next few minutes we will be writing NetLogo code So do the following 1 Click on the Procedures tab near the top of the NetLogo window 2 Type the following at the top of the code editing area to tell NetLogo that we will be using a variable called corners to keep track of the three vertices of the triangle globals corners 3 Immediately below what you just typed I recommend giving yourself a blank line or two first type
10. is considered to be the patch on which the turtle is standing 5 The user can change the width or height of the NetLogo world at any time in fact we will do that very thing in this activity however a NetLogo program can use world width and world height to get the current values at any time 6 The patches on the extreme right hand side of the NetLogo world have an X coordinate of max pxcor those on the top of the canvas have a Y coordinate of max pycor Similarly min pxcor and min pycor are the X and Y coordinates respectively of the patches on the extreme left hand side and bottom respectively of the NetLogo world These variables are related to the overall size of the canvas by the formulas world width max pxcor min pxcor and world height max pycor min pycor 1 NetLogo Mystery Pattern 3 Getting Started Start NetLogo amp Configure Canvas 1 From the Macintosh Applications folder or from the Windows Start All Program NetLogo menu launch the NetLogo v4 0 2 application not NetLogo 3D 2 Because we want the marks made by the agents to be placed very precisely and because NetLogo colors and entire patch at once we will need to set up the NetLogo canvas with a large number of very small patches To do this click the Edit button at the top of the canvas and make these changes a Leave Location of origin set to center b Set the max pxcor value to 288 c Set the max pycor value to 251 d Unchec
11. k the World wraps horizontally checkbox e Uncheck the World wraps vertically checkbox f Set the Patch size value to 1 0 g Uncheck the Turtle shapes checkbox h Uncheck the Show tick counter checkbox NetLogo Mystery Pattern The World amp View window should now look like this cone d 3 Click the OK button we now have a canvas that is 503 patches tall and 577 patches wide with each patch being 1 pixel X 1 pixel in size NetLogo Mystery Pattern Controlling the Number of Turtles One experiment we will do is to see if the results are any different when we use a small number of turtles vs a large number Since all of the turtles will begin on one of the three vertices of a triangle we ll use a slider to control the number of turtles per vertex 1 2 Click the Slider button in the toolbar at the top of the screen Click somewhere in the white space to the left of the canvas this will display the Slider configuration window Make the following changes a Set the Global variable value to turtles per vertex leave the quotes out when you type it b Set the Minimum to 1 c Set the Increment to 1 d Set the Maximum to 100 The Slider configuration window should now look something like this Click the OK button Now we need to write the code that will use the value from this slide to create the specified number of turtles and make them follow the behavioral rules described previously o
12. system used by NetLogo The following diagram illustrates some important points to remember y max pxcor max pycor A world height turtle at 4 6 8 gsm min pycor Y world width F NetLogo Mystery Pattern 2 1 Like the Cartesian coordinate system used in Algebra Analytic Geometry and Calculus the NetLogo world has an X and a Y axis The center of the coordinate system is the origin which is usually located in the physical center of the NetLogo world as well where both X and Y have values of zero 0 2 Overlaid on the coordinate system is a grid of patches Each patch has a color and an optional label a NetLogo program can also define additional variables for a patch 3 The center of a patch is a point in the coordinate system where the X and Y values are integers these coordinates are used to refer to the patch For example patch 3 2 in the diagram is a square with its center at 3 2 this square is the region where 2 5 X 3 5 and 1 5 e Y 2 5 4 A patch s coordinates are always integer values but that is not necessarily true for a turtle on a patch In the diagram there is a turtle located at 4 6 8 3 which is on the patch centered at 5 8 Though a turtle may be drawn so that it looks like it is on two or more patches at once the turtle s center point is what matters the center point will be at the coordinate location of the turtle and the patch in which the center point falls
13. target set pcolor white end Save your program Click the Button button in the toolbar UE S gt appear NetLogo Mystery Pattern Click in the white space to the left of the canvas the Button configuration window will Click the Interface tab to return to the window showing the buttons sliders and canvas 11 10 This button will be used to set the turtles into motion running the draw procedure you wrote So set the configuration as follows a Select Turtles from the Agent s pull down menu b Puta check mark in the Forever checkbox c In the Commands text box type draw without the quotes d If desired type a Display name and Action key When you are done the Button configuration window should like something like this 11 Click the OK button 12 Save your program NetLogo Mystery Pattern Running the Program The Moment of Truth If you ve managed to catch your typing errors as you go your program should be ready to run Have you formulated a hypothesis about the type of pattern if any that will result when the turtles start moving around and turning the patches they land on white What do you think will happen Will it make a difference if you start with one turtle per vertex vs 100 turtles per vertex Do the turtles interact directly in any way Do they interact indirectly e g by contending for space or other constrained resources Let s try it l 2 3
14. the following setup procedure remember spaces spelling and square brackets are very important UO SSeS clear all set corners patch set pacca 0 wnscx iweous 10 pacca uumexx e cow 10 mim pycor 10 pacca min pxeot sr 10 mim poycor r 110 ask corners SST CORNS end 4 After typing the code use the Check button at the top of the window to verify that you typed the code without spelling or spacing errors In fact there will be an error message indicating that NetLogo doesn t know what we mean by setup corner don t worry about that error since we will fix that next However if there are other others NetLogo Mystery Pattern 7 5 Let s review what the setup procedure is doing a We begin by using clear al11 to clear the canvas any turtles and any variable values b Then we tell NetLogo that the global variable corners will hold the set of patches located on the three vertices of our triangle c Finally we ask each of those patches that we put into the corners variable to execute the setup corner procedure What does setup corner do Nothing yet we haven t written it But we will do so in a moment 6 Now would be a good time to save your program In the File menu select Save and navigate to a folder where you can save files the Desktop folder or the folder assigned to you on a network file server for example You can give your program any name you like as long as you use an
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