%%% Your task is to determine if the average length of a random walk varies

%%% as you vary the number of dimensions.

%%% Example: N=1 -- random walk on the line; N=3 Random walk in 3D space.

%-----------------------------------

% Create a simulation for computing random walks in N dimensions where N

% is to be specified by the user.

% In particular, the user will specify the number of steps to be taken,

% the number of times the simulation is repeated.

% In addition, the summary statistics will be returned: mean and standard

% deviation of the distance from the origin traveled over the e.g. 1000

% repetitions of the simulation.

% A step is taken +/- one unit along a single dimension -- it is a random

% walk on a lattice rather than on arbitrary directions in real space.

nSteps = input('Enter the number of steps in a single run: ')

nRepeats = input('Enter the number of simulation runs to do: ')

nDimensions = input('Enter the number of dimensions of the space: ')

distanceStats = zeros(1,nRepeats); % Contains distance traveled in each run.

currentParticlePosition = zeros(1, nDimensions); % Start at (0,0, ..., 0)

%----------------------------------------------------------------------------

% Fill in all the code details here (easy to do with nested for loops):

%--------------------------------------------------------------------------

distTraveled = sqrt(sum(currentParticlePosition.^2)); % Euclidean distance from origin.

distanceStats(1,i) = distTraveled;

fprintf('Final Position: %6.2f \n', currentParticlePosition);

fprintf('The distance from the origin is: %6.2f \n', distTraveled);

meanDist = mean(distStats);

stdDist = std(distStats);

fprintf('Mean: %6.2f and standard dev: %6.2f of distance traveled. \n', meadDist, stdDist);

% -------------------------------------------------------------------------

% 1. Do enough simulation runs for nDimensions = 1, 2, 3, 10

% to draw conclusions about whether the distance from the origin varies

% with the number of dimensions.

%

% 2. Plot the mean and standard deviation of distStats for 1, 2, 3, 10

% to demonstrate your conclusion.