Lorenz Attractor Animation with Frame-by-Frame Plotting

I was trying to create an animation of Lorenz Attractor. I used the following code but it did not give me the result I want like https://en.wikipedia.org/wiki/Lorenz_system.

% Parameters
sigma = 10;
rho = 28;
beta = 8/3;

% Time span
tspan = [0 50];  % Adjusted for smooth animation

% Initial conditions
y0 = [1; 1; 1];

% Lorenz system of equations
lorenz = @(t, y) [sigma * (y(2) - y(1)); 
                  y(1) * (rho - y(3)) - y(2); 
                  y(1) * y(2) - beta * y(3)];

% Solve the system using ode45
[t, y] = ode45(lorenz, tspan, y0);

% Set up the figure for animation
figure;
h = plot3(y(1,1), y(1,2), y(1,3));
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Lorenz Attractor Animation');
grid on;
axis([-20 20 -30 30 0 50]);
view(3);
hold on;

% Animate the Lorenz attractor
for i = 2:length(t)
    % Update the plot data
    h.XData = y(1:i, 1);
    h.YData = y(1:i, 2);
    h.ZData = y(1:i, 3);
    
    % Refresh the figure
    drawnow;
    
    % Optional: Pause to slow down the animation if too fast
    pause(0.01); % Adjust the pause time as needed
end

Answer 1

[Walter Roberson]

% Parameters
sigma = 10;
rho = 28;
beta = 8/3;

% Time span
tspan = [0 50];  % Adjusted for smooth animation

% Initial conditions
y0 = [1; 1; 1];

% Lorenz system of equations
lorenz = @(t, y) [sigma * (y(2) - y(1)); 
                  y(1) * (rho - y(3)) - y(2); 
                  y(1) * y(2) - beta * y(3)];

% Solve the system using ode45
[t, y] = ode45(lorenz, tspan, y0);

% Set up the figure for animation
figure;
h = plot3(y(:,1), y(:,2), y(:,3));
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Lorenz Attractor Animation');
grid on;
axis([-20 20 -30 30 0 50]);
view(3);
hold on
h = plot3(y(1,1), y(1,2), y(1,3), 'k.', 'MarkerSize', 20);

% Animate the Lorenz attractor
for i = 2:length(t)
    % Update the plot data
    h.XData = y(i, 1);
    h.YData = y(i, 2);
    h.ZData = y(i, 3);
    
    % Refresh the figure
    drawnow;
    
    % Optional: Pause to slow down the animation if too fast
    pause(0.01); % Adjust the pause time as needed
end

[Walter Roberson]

It would probably be better to use something like

tspan = linspace(0, 50, 1000);

in order to avoid the issue that using a tspan with only two elements in it, results in outputs in which time is generally irregular.

[Athanasios Paraskevopoulos]

Thank you for your valuable answer. However, I can not see the motion on the plot

[Walter Roberson]

It works fine for me when I execute inside of MATLAB.

If you are running it under MATLAB Answers, then MATLAB Answers will show you only the final plot, not anything in-between.

[Athanasios Paraskevopoulos]

Oh understood! I tried to run it under MATLAB Answers. Thank you very much again