Make a movie of trajectories in MATLAB - matlab

Question

I want to create a movie in MATLAB which looks like this:
https://www.youtube.com/watch?v=8z_tSVeEFTA
Mathematically, I have the differential equations and the code to solve them numerically:
% lorenz - Program to compute the trajectories of the Lorenz
% equations using the adaptive Runge-Kutta method.
clear; help lorenz;
%* Set initial state x,y,z and parameters r,sigma,b
state = input('Enter the initial position [x y z]: ');
r = input('Enter the parameter r: ');
sigma = 10.; % Parameter sigma
b = 8./3.; % Parameter b
param = [r sigma b]; % Vector of parameters passed to rka
tau = 1; % Initial guess for the timestep
err = 1.e-3; % Error tolerance
%* Loop over the desired number of steps
time = 0;
nstep = input('Enter number of steps: ');
for istep=1:nstep
%* Record values for plotting
x = state(1); y = state(2); z = state(3);
tplot(istep) = time; tauplot(istep) = tau;
xplot(istep) = x; yplot(istep) = y; zplot(istep) = z;
if( rem(istep,50) < 1 )
fprintf('Finished %g steps out of %g\n',istep,nstep);
end
%* Find new state using adaptive Runge-Kutta
[state, time, tau] = rka(state,time,tau,err,'lorzrk',param);
end
%* Print max and min time step returned by rka
fprintf('Adaptive time step: Max = %g, Min = %g \n', ...
max(tauplot(2:nstep)), min(tauplot(2:nstep)));
%* Graph the time series x(t)
figure(1); clf; % Clear figure 1 window and bring forward
plot(tplot,xplot,'-')
xlabel('Time'); ylabel('x(t)')
title('Lorenz model time series')
pause(1) % Pause 1 second
%* Graph the x,y,z phase space trajectory
figure(2); clf; % Clear figure 2 window and bring forward
% Mark the location of the three steady states
x_ss(1) = 0; y_ss(1) = 0; z_ss(1) = 0;
x_ss(2) = sqrt(b*(r-1)); y_ss(2) = x_ss(2); z_ss(2) = r-1;
x_ss(3) = -sqrt(b*(r-1)); y_ss(3) = x_ss(3); z_ss(3) = r-1;
plot3(xplot,yplot,zplot,'-',x_ss,y_ss,z_ss,'*')
view([30 20]); % Rotate to get a better view
grid; % Add a grid to aid perspective
xlabel('x'); ylabel('y'); zlabel('z');
title('Lorenz model phase space');
But I don't know how to plot two different trajectories at once in different colors, and make a clip that looks like this (with the side plot that shows the X coordinate solutions in the same time).
Can anyone help me with this ?
Thank you!

Answer 1

In your example code, you already have a for loop, which goes through all time steps. Now, to generate such an animation, we'll want to plot the figure at each time step. This is done by
for istep=1:nstep
%* Record values for plotting
x = state(1); y = state(2); z = state(3);
tplot(istep) = time; tauplot(istep) = tau;
xplot(istep) = x; yplot(istep) = y; zplot(istep) = z;
%* Find new state using adaptive Runge-Kutta
[state, time, tau] = rka(state,time,tau,err,'lorzrk',param);
%* Create Plot
figure(2);
x_ss(1) = 0; y_ss(1) = 0; z_ss(1) = 0;
x_ss(2) = sqrt(b*(r-1)); y_ss(2) = x_ss(2); z_ss(2) = r-1;
x_ss(3) = -sqrt(b*(r-1)); y_ss(3) = x_ss(3); z_ss(3) = r-1;
plot3(xplot,yplot,zplot,'-',x_ss,y_ss,z_ss,'*')
view([30 20]); % Rotate to get a better view
grid; % Add a grid to aid perspective
xlabel('x'); ylabel('y'); zlabel('z');
title('Lorenz model phase space');
%* Save frame
output_video(istep) = getframe;
end
This will create an array of structs output_video, which is of size 1 x nstep and contains cdata (the image data) and colormap for each frame.
You can view this video in MATLAB with
implay(output_video)
or save it do disk using the VideoWriter class:
v = VideoWriter('my_trajectory_video.avi')
open(v)
writeVideo(v,output_video)
close(v)