Plotting a random walk step by step

Hello!

I'm trying to plot a random walk in 2D on a circle with the plot being updated every time the particle takes a step (not just when an entire particle walk iteration is complete). It has 2 particles with 20 steps each. It runs fine with the first particle, then the drawing lines become crossed. I know it has something to do with the drawing command, but I am new to Matlab and am clueless. This is not MY code, I am just trying to modify it for my own practice. Run it and you'll see what I mean. Any help will assist in my learning. Thank you!

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
clc;
clearvars;
stepsPerWalk = 20; % Length of the x-axis, also known as the length of the random walks.
numberOfWalks = 2; % The amount of random walks.
x_t(1) = 0;
y_t(1) = 0;
% Plot a circle
radius = 20;
pos = [-radius, -radius, 2*radius, 2*radius]; 
rectangle('Position',pos,'Curvature',[1 1], 'LineWidth', 3)
axis equal;
ax = gca;
ax.FontWeight = 'bold';
ax.FontSize = 20;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
hold on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
% Do the random walk.
for m = 1 : numberOfWalks
  for n = 1 : stepsPerWalk % Looping all values of N into x_t(n).
    distance = radius + 1;
    while distance > radius
      % Get new trial x_t and y_t
      A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
      if rand > 0.5
        % Change only x.
        x_t(n+1) = x_t(n) + A;
        y_t(n+1) = y_t(n);
      else
        % Change only y.
        x_t(n+1) = x_t(n);
        y_t(n+1) = y_t(n) + A;
      end
      % Compute distance again with new values.
      distance = sqrt(x_t(n+1)^2 + y_t(n+1)^2);
    end
    plot(x_t, y_t, 'LineWidth', 2);
  caption = sprintf('Walk #%d of %d', m, numberOfWalks);
  title(caption, 'FontSize', 25, 'FontWeight', 'bold');
  hold on;
  drawnow;
  end
end
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
axis square;

[Hyohun]

is this using Markov chain?

Answer 1

[Mathieu NOE]

hello

IMHO, the problem comes that x and y are not reinitialized (put to zero) when you start the next walk

so I changed this and now every new walk will start from the origin and previous walk values of x and y are flushed.

you could also change the code so that the second walk starts where the first stopped

hope it helped :

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
clc;
clearvars;
stepsPerWalk = 50; % Length of the x-axis, also known as the length of the random walks.
numberOfWalks = 5; % The amount of random walks.
% x_t(1) = 0;
% y_t(1) = 0;
% Plot a circle
radius = 20;
pos = [-radius, -radius, 2*radius, 2*radius]; 
rectangle('Position',pos,'Curvature',[1 1], 'LineWidth', 3)
axis equal;
ax = gca;
ax.FontWeight = 'bold';
ax.FontSize = 20;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
hold on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
% Do the random walk.
for m = 1 : numberOfWalks
    x_t = 0; % reset x and y at start of iteration 
    y_t = 0;
  for n = 1 : stepsPerWalk % Looping all values of N into x_t(n).
    distance = radius + 1;
    while distance > radius
      % Get new trial x_t and y_t
      A = sign(randn); % Generates either +1/-1 depending on the SIGN of RAND.
      if rand > 0.5
        % Change only x.
        x_t(n+1) = x_t(n) + A;
        y_t(n+1) = y_t(n);
      else
        % Change only y.
        x_t(n+1) = x_t(n);
        y_t(n+1) = y_t(n) + A;
      end
      % Compute distance again with new values.
      distance = sqrt(x_t(n+1)^2 + y_t(n+1)^2);
    end
    plot(x_t, y_t, 'LineWidth', 2);
  caption = sprintf('Walk #%d of %d', m, numberOfWalks);
  title(caption, 'FontSize', 25, 'FontWeight', 'bold');
  hold on;
  drawnow;
  end
end
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0.05, 1, 0.95]);
axis square;

[Christopher Schmiedl]

Thank you, but unfortunately it still behaves the same way, I even tried to put it in the next loop as well, I got the same outcome.

Answer 2

[Steven Lord]

You're adding a new line to the axes each time you want to put a new point down. That's numberOfWalks times stepsPerWalk different lines. Instead, I recommend creating an animatedline and calling addpoints inside the loop to add a new point to the existing line.

x = 0:5:360;
h = animatedline('LineStyle', ':', 'Marker', 'o');
axis([0 360 -1 1])
for k = 1:numel(x)
    addpoints(h, x(k), sind(x(k)));
    drawnow expose
end

If you execute this in your MATLAB session you'll see the plot being constructed one point at a time. In Answers all you'll see is the final result.