Self avoiding random walk help

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Argumanh
Argumanh on 11 Feb 2019
Commented: Image Analyst on 12 Feb 2020
Dear all,
I am trying to create SAW random walk in matlab. First I have written a code which it can have 6possible steps on a lattice(code is attached).
Now I want to create a self avoiding random walk, which after the first step, it can only have 5 possible steps (cannot go back on itself). Any idea that how may I change the code? should I write another code?
clear all
clc
a = 1 ; % Step size
N = 2 ; % Number of Random Walks
S = 100 ; % Number of steps
r=zeros(1,1);
for k = 1:N
for i = 1:S
t = randi(6);
% Every step in "x" and "y" and "z" directions:
if t == 1
x{i} = 1;
y{i} = 0;
z{i} = 0;
elseif t == 2
x{i} = -1;
y{i} = 0;
z{i} = 0;
elseif t == 3
x{i} = 0;
y{i} = 1;
z{i} = 0;
elseif t == 4
x{i} = 0;
y{i} = -1;
z{i} = 0;
elseif t == 5
x{i} = 0;
y{i} = 0;
z{i} = 1;
elseif t == 6
x{i} = 0;
y{i} = 0;
z{i} = -1;
end
X = cell2mat(x);
Y = cell2mat(y);
Z = cell2mat(z);
end
X1=[r,X];
Y1=[r,Y];
Z1=[r,Z];
% We sum the steps to get all the data in a new cell array:
X2{k}=cumsum(X1);
Y2{k}=cumsum(Y1);
Z2{k}=cumsum(Z1);
end
% Now we have the data for N number individual random seeds, and
% we have it for S number of steps:
x2=cell2mat(X2);
y2=cell2mat(Y2);
z2=cell2mat(Z2);
% we get N sets of data for S random steps:
x_final=reshape(x2,[S+1,N]);
y_final=reshape(y2,[S+1,N]);
z_final=reshape(z2,[S+1,N]);
% We plot the Random walk:
plot3(x_final,y_final,z_final,'x-')
grid on
axis equal
Best,
Argu
  4 Comments
DEBIDATTA BEHERA
DEBIDATTA BEHERA on 12 Feb 2020
What will be the scilab code for self avoiding random walk?
Image Analyst
Image Analyst on 12 Feb 2020
I'd copy the code to a scilab discussion forum and ask for help translating it into that language.

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Accepted Answer

Adam Danz
Adam Danz on 11 Feb 2019
Edited: Adam Danz on 12 Feb 2019
Working from the cleaner version of your code I provided in the comments under your question, here's an adapted version that avoids random steps that go back on the previous step.
Here are som key parts of the code
  • 'randWalkMat' is a matrix of random steps; rows are X,Y,Z
  • 'forbddenPairs': each row defines two columns of randWalkMat that would cancel out a step.
  • The for-loop and the nested while-loop are designed to choose a random column in randWalkMat but to check that the chosen column is not a forbidden pair with the previously chosen column. If so, it chooses another one.
  • Everything after that is just a cleaner version of your original code.
Feel free to ask followup questions!
clear all
clc
a = 1 ; % Step size
N = 2 ; % Number of Random Walks
S = 100 ; % Number of steps
randWalkMat = [...
1 -1 0 0 0 0;
0 0 1 -1 0 0;
0 0 0 0 1 -1;
];
% list columns of randWalkMat that shouldn't be neighbors
% * Each row needs to be in accending order
forbiddenPairs = [
1,2;
3,4;
5,6];
X = zeros(S,N);
Y = X;
Z = X;
t = randi(6);
for k = 1:N
% Choose random indices of randWalkMat
for i = 2:S
accepted = false; %reset flag
while ~accepted
t(i) = randi(6);
% Determine if current step goes back on previous step
if ~ismember(sort(t(i-1:i)), forbiddenPairs, 'rows')
accepted = true; %step is OK, move on.
end
end
end
randWalk = randWalkMat(:, t);
X(:,k) = randWalk(1,:);
Y(:,k) = randWalk(2,:);
Z(:,k) = randWalk(3,:);
end
% Now we have the data for N number individual random seeds, and
% we have it for S number of steps:
% we get N sets of data for S random steps:
x_final = [zeros(1,N);cumsum(X)]; % *
y_final = [zeros(1,N);cumsum(Y)]; % *
z_final = [zeros(1,N);cumsum(Z)]; % *
% We plot the Random walk:
plot3(x_final,y_final,z_final,'x-')
grid on
axis equal
  5 Comments
Argumanh
Argumanh on 10 Mar 2019
Hi Adam,
I want to change this code, in a sense to create a self avoiding random walk. And by self aboiding I mean that the steps would never cross previous steps that have been taken until now. If you wish, I can create a new question and put the link here.
I would highly appreciate
Argumanh
Argumanh on 11 Mar 2019
Hi Adam,
You can follow the question from here:
https://www.mathworks.com/matlabcentral/answers/449454-complete-self-avoiding-random-walk

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More Answers (1)

Argumanh
Argumanh on 12 Feb 2019
Hi Adam,
Thanks for your help, I was sonering when I change the number of random walks it is not working. For example I run this code for several random walks(and not just for 2). Also I would also appreciate if you explain how the accepting method is working. I am also eager to create a situation with only 4 possible moves(90 degrees). from the previous step
with my berst regards,
Argu
  1 Comment
Adam Danz
Adam Danz on 12 Feb 2019
See reply above. Please use comment section rather than proposing a solution unless that is your intent.

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