clc;
clear;
close all;
warning off;
addpath(genpath(pwd));
global sigma rho beta
rho = 28;
sigma = 10;
beta = 8/3;
tf = 60;
[~,sol1] = ode45(@lorenz,[0 tf],[1;2;3]);
[~,sol2] = ode45(@lorenz,[0 tf],[1;2;3.0001]);
%The line making up the curve never intersected itself and never retraced its own path. Instead, it looped around forever and ever, sometimes spending time on one wing before switching to the other side. It was a picture of chaos, and while it showed randomness and unpredictability, it also showed a strange kind of order.
[C,h] = size(sol1);
angle = 0;
figure;
writerObj = VideoWriter('Lorenz.avi'); % Name it.
writerObj.FrameRate = 500000; % How many frames per second.
writerObj.Quality = 100;
open(writerObj);
for j = 1:C
p1(j,:)= sol1(j,:);
p2(j,:)= sol2(j,:);
% Plot
plot3(p1(:,1),p1(:,2),p1(:,3),'k', p2(:,1),p2(:,2),p2(:,3),'r')
hold on
plot3(p1(1,1),p1(1,2),p1(1,3),'ko','markerfacecolor','k')
plot3(p2(1,1),p2(1,2),p2(1,3),'rd','markerfacecolor','r')
plot3(p1(j,1),p1(j,2),p1(j,3),'ko','markerfacecolor','k')
plot3(p2(j,1),p2(j,2),p2(j,3),'rd','markerfacecolor','r')
hold off
axis([-20 20 -40 40 0 50])
axis off
set(gca,'color','none')
% Rotation
camorbit(angle,0,[p1(1,1),p1(1,2),p1(1,3)])
angle = angle + (360/C);
% Record
frame = getframe(gcf);
writeVideo(writerObj, frame);
end
close(writerObj)
clf; close;
disp('Done');
%% Function :
function ydot = lorenz(t,y)
global sigma rho beta
%LORENZ Equation of the Lorenz chaotic attractor.
% ydot = lorenz(t,y).
ydot(1) = sigma *(y(2) -y(1));
ydot(2) = y(1)*(rho -y(3)) -y(2);
ydot(3) = y(1)*y(2) -beta*y(3);
ydot =[ydot(1);ydot(2);ydot(3)];
end
