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
endI 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 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 ode45, differential equations, 3d plots MATLAB Answers — New Questions
