# Random Walk Left Right

### 1 collaborator

Uri Wilensky (Author)

### Tags

mathematics

Tagged by Reuven M. Lerner over 9 years ago

Model group CCL | Visible to everyone | Changeable by group members (CCL)
Model was written in NetLogo 5.0.4 • Viewed 1166 times • Downloaded 38 times • Run 0 times

## WHAT IS IT?

This is a model to simulate a random walk. In this simulation, all turtles walk to the left and forward or they walk to the right and forward. The turtles randomly choose between either direction each time they move.

The path traced out by the turtles moving in this pattern is called a lattice.

## HOW IT WORKS

As the simulation continues, one can expect the turtles to become more spread out. Observe the kinds of patterns that develop as the turtles move.

Shading of turtles is representative of how many turtles share that location. Dark shades imply more turtles. Light shades imply fewer turtles.

For purposes of this simulation, "forward" will mean moving toward the top of the view, "left" will mean moving toward the left edge of the view, and "right" will mean moving toward the right edge of the view.

## HOW TO USE IT

Use the NUMBER-OF-TURTLES slider to select how many turtles will participate in the random walk.

Use the NUMBER-OF-STEPS slider to decide how many steps a turtle will take on each turn.

How steps are implemented:

• If NUMBER-OF-STEPS is set to 1 and a turtle is going left, it will go left one step and then go forward one step. (Imagine a turtle walking along the bottom and left edge of a 1 x 1 square.)
• If NUMBER-OF-STEPS is set to 4 and a turtle is going left, it will go left four steps and then go forward four steps. (Imagine a turtle walking along the bottom and left edge of a 4 x 4 square.)
• Each of the above movements would be considered a single "pace."

Use the TURTLE-TRAILS? switch to have the turtles put their pens down to trace their paths and show the part of the lattice they are covering. This switch must be set before the SETUP button is pressed.

All sliders except NUMBER-OF-TURTLES may be changed during a simulation.

Press the SETUP when all of the above selections have been made. This will create the selected number of turtles at the bottom center of the world.

Press GO ONCE button to make the turtles move one pace.

Press the GO button to make the turtles move until one of the turtles cannot complete its number of steps. When one turtle reaches this point, all the other turtles will stop even if they can complete the step.

To stop the simulation while it is running, press the GO button again.

The gray bar in the middle of the world is at xcor = 0. This is where all the turtles start.

## THINGS TO TRY

Try to answer the questions below before running the simulations.

• What reasoning led you to correct predictions?
• What assumptions that you made need to be revised?

Try different numbers of turtles while keeping all other slider values the same.

Try different numbers of steps while keeping all other slider values the same.

## THINGS TO NOTICE

Think about how you would define an "average" turtle and an "average" walk.

Where would you expect an average turtle to end up at the end of the simulation? Why?

How many paces would you expect there to be in an average walk? Why?

What kinds of calculations or measurements would you use in trying to answer these questions?

How do your answers to the above questions compare to the average of the x coordinates of all the turtles?

## EXTENDING THE MODEL

As the model stands, it plots two lines (right and left) over time. Another way to look at this simulation is to plot the distribution of turtles. Create a histogram to show this type of data.

The turtles will stop if they come up to an obstacle (cannot move forward or to the right/left), give the turtles the ability to think ahead and choose a different step/direction.

Give the turtles the ability to walk backwards.

Create a three dimensional lattice.

## NETLOGO FEATURES

Since turtles in this model only move in the positive direction and they start at the bottom the origin is relocated to be at the bottom of the view also, so there are no patches with negative pycor.

## RELATED MODELS

Random Walk 360, Galton Box, Binomial Rabbits

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

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 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, 2002.

Click to Run Model

```;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; variable declarations ;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;

globals
[
num-turtles-right  ;; how many turned right this tick
num-turtles-left   ;; how many turned left this tick
sum-right-turns  ;; the sum of turtles that turned right for the entire run
sum-left-turns   ;; the sum of turtles that turned left for the entire run
]

;;;;;;;;;;;;;;;;;;;;;;
;; setup procedures ;;
;;;;;;;;;;;;;;;;;;;;;;

;; sets up the patches and creates turtles

to setup
clear-all
ask patches [ set pcolor gray + 3 ]
draw-line-up-middle
setup-turtles
init-vars
reset-ticks
end

;; draw a line up the middle

to draw-line-up-middle
crt 1
[
set pen-size 3
set pcolor 8
pd
fd world-height
die
]
end

;; determines the number of turtles and their color
;; if turtle-trails? is on, the turtles' pens should be down,
;; otherwise they should be up

to setup-turtles
;; the origin is at the bottom of the view so there is no need
;; to relocate the turtles upon creation
crt number-of-turtles
[
set color black
set pen-size 3
ifelse turtle-trails?
[ pd ]  ;; have the turtles put down their pens
[ pu ]  ;; have the turtles pick up their pens
]
end

;; counts the number of right and left turns and paces of the turtles

to init-vars
set sum-right-turns 0
set sum-left-turns 0
end

;;;;;;;;;;;;;;;;;;;;;;;;
;; runtime procedures ;;
;;;;;;;;;;;;;;;;;;;;;;;;

;; have the turtles randomly pick either right or left and
;; have them move in that direction
;; if one turtle cannot move, then stop

to go

set num-turtles-right 0  ;; the number of turtles turning right currently
set num-turtles-left 0   ;; the number of turtles turning left currently

;; if one turtles cannot move because it is at the edge of the world, then stop
if any? turtles with
[ patch-at 0 number-of-steps = nobody or
patch-at (- number-of-steps) 0 = nobody or
patch-at number-of-steps 0 = nobody ]
[ stop ]

[
ifelse ((random 2) = 0)
[
go-left
set num-turtles-left (num-turtles-left + 1)
]
[
go-right
set num-turtles-right (num-turtles-right + 1)
]

;; set the color of the turtles to give a rough idea of how many turtles
;; are at each location -- the lighter the color, the greater the number
;; of turtles
set color scale-color blue (count turtles-here) (number-of-turtles / 5) 0
]
;; update the sums of right and left turns
set sum-right-turns (sum-right-turns + num-turtles-right)
set sum-left-turns (sum-left-turns + num-turtles-left)
tick
end

;; turn left and go one-pace

to go-left  ;; turtle procedure
lt 90
one-pace
end

;; go forward number-of-steps, turn upwards and go forward number-of-steps

to one-pace  ;; turtle procedure
fd number-of-steps
fd number-of-steps
end

;; turn right and go one-pace

to go-right  ;; turtle procedure
rt 90
one-pace
end

```

There are 10 versions of this model.

Uri Wilensky over 9 years ago Updated to NetLogo 5.0.4 Download this version
Uri Wilensky over 10 years ago Updated version tag Download this version
Uri Wilensky over 10 years ago Updated to version from NetLogo 5.0.3 distribution Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Updated from NetLogo 4.1 Download this version
Uri Wilensky over 12 years ago Model from NetLogo distribution Download this version
Uri Wilensky over 12 years ago Random Walk Left Right Download this version

## Attached files

File Type Description Last updated
Random Walk Left Right.png preview Preview for 'Random Walk Left Right' almost 10 years ago, by Uri Wilensky Download

This model does not have any ancestors.

This model does not have any descendants.