Make Random Walk into 3D

I have a code set up for a randomwalk already, but how would I alter it to make a 3D Random Walk?

steplenght = .01;
positions = zeros(2,100000);
 
currentPosition = [0;0];
currentTimeStep = 2;
 
 
while currentPosition(1,1)^2 + currentPosition(2,1)^2 < 1
    randomDirection = 2*pi*rand(); 
    unitDisplacementVector = [cos(randomDirection); sin(randomDirection)]; 
    displacementVector = stepLength*unitDisplacementVector; 
    currentPosition = currentPosition + displacementVector; 
    positions(:,currentTimeStep) = currentPosition; 
    currentTimeStep = currentTimeStep + 1;
end
 
positions = positions(:,1:currentTimeStep-1);
 
hold on;
 
scatter(positions(1,:),positions(2,:),2,'filled');
 
 
theta = linspace(0,2*pi);
plot(cos(theta),sin(theta));

[Walter Roberson]

It is confusing that you have

steplenght = .01;

but your code refers to stepLength . Someone reading the code would be wondering whether there was the intention that the two different variables are related somehow.

Answer 1

[darova]

I do this

dt = .01;

[x, y, z] = deal( 0 );
[X,Y,Z] = sphere(30);
surf(X,Y,Z,'edgecolor',[1 1 1]*0.8,'Facecolor','none')
hold on
k = 0;
while norm([x y z])^2 < 1 && k < 1000
    t = 180*(rand-1);
    p = 180*(rand-1);
		% spherical system of coordinates
    x = x + dt*cosd(t)*cosd(p);
    y = y + dt*cosd(t)*sind(p);
    z = z + dt*sind(p);
    k = k + 1;
    pause(0.1)
    plot3(x,y,z,'.b')
end 
hold off

[ST]

Can you update the code for the Random Waypoint Mobility in 3D? I want to add different velocities, directions and pause times for each node within the boundaries of 3D cube.

[Bruno Luong]

The code by danova is flawed in the sense that create an anisotropic walk. The particle ends up systematcally near the pole. Generate direction with uniform spherical angle coordinates will condense the direction to north/south.

I call this climatic walk. ;-)