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How to apply Random walks ?

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ahmed elnashar
ahmed elnashar on 11 May 2012
Commented: Image Analyst on 6 Oct 2022
If I'ave axes (x,y) and i want to apply random walk on there a function in matlab stands for this .

Answers (3)

John D'Errico
John D'Errico on 11 May 2012
xy = cumsum(-1 + 2*round(rand(1000,2)),1);
Why do you need a function?

Image Analyst
Image Analyst on 11 May 2012
Edited: Image Analyst on 22 Jan 2020
Try this nice graphical demo:
% Demo to do a random walk in 2 dimensions.
% User is asked for the number of steps to take.
% By Image Analyst
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
workspace; % Make sure the workspace panel is showing.
fontSize = 20;
format compact;
% Ask user for a number of steps to take.
defaultValue = 15;
titleBar = 'Enter an integer value';
userPrompt = 'Enter the number of steps to take: ';
caUserInput = inputdlg(userPrompt, userPrompt, 1, {num2str(defaultValue)});
if isempty(caUserInput),return,end; % Bail out if they clicked Cancel.
integerValue = round(str2num(cell2mat(caUserInput)));
% Check for a valid integer.
if isnan(integerValue)
% They didn't enter a number.
% They clicked Cancel, or entered a character, symbols, or something else not allowed.
integerValue = defaultValue;
message = sprintf('I said it had to be an integer.\nI will use %d and continue.', integerValue);
numberOfSteps = integerValue;
deltax = rand(numberOfSteps) - 0.5;
deltay = rand(numberOfSteps) - 0.5;
xy = zeros(numberOfSteps,2);
for step = 2 : numberOfSteps
% Walk in the x direction.
xy(step, 1) = xy(step, 1) + deltax(step);
% Walk in the y direction.
xy(step, 2) = xy(step, 2) + deltay(step);
% Now plot the walk so far.
xCoords = xy(1:step, 1);
yCoords = xy(1:step, 2);
plot(xCoords, yCoords, 'bo-', 'LineWidth', 2);
hold on;
textLabel = sprintf('%d', step);
text(xCoords(end), yCoords(end), textLabel, 'fontSize', fontSize);
% Mark the first point in red.
hold on;
plot(xy(1,1), xy(1,2), 'rs', 'LineWidth', 2, 'MarkerSize', 25);
textLabel = '1';
text(xy(1,1), xy(1,2), textLabel, 'fontSize', fontSize);
grid on;
% Mark the last point in red.
plot(xCoords(end), yCoords(end), 'rs', 'LineWidth', 2, 'MarkerSize', 25);
title('Random Walk', 'FontSize', fontSize);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Calculate the distance from the origin.
distanceFromOrigin = hypot(xCoords(end), yCoords(end));
message = sprintf('Done with demo!\nDistance of endpoint from origin = %.3f', distanceFromOrigin);
0000 Screenshot.png
Stelios Fanourakis
Stelios Fanourakis on 28 Jul 2019
Is this automatic or semi automatic? I guess it needs the user to define seeds. Is there an option for this to be automated?
Image Analyst
Image Analyst on 29 Jul 2019
My code does not ask the user for any "seeds". My code asks the user for the number of steps. From then it's automatic, though of course you could alter any of the variables you want.

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Richard Willey
Richard Willey on 11 May 2012
MATLAB includes a wide variety of functions that can be used to simulate a random walk. Depending on what precisely you want to do you can use anything from the "rand" function in base MATLAB to bm (a function in Econometric Toolbox to model Brownian motion).
The following file exchange submission includes some good examples that a MathWorks Application Engineer developed to illustrate random walks.
Lucio Biondaro
Lucio Biondaro on 6 Oct 2022
There is actually no reason to choose 1 or 0.5. I had imagined that the randn function could be used with average value the average distance of the displacement. But I believe such a model would no longer be a random walk.
Image Analyst
Image Analyst on 6 Oct 2022
You could use randn instead of rand if you want. It's still random. It's just however you want to define your experiment.

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