lorenz.m
%Equazione differenziale Ordinaria dell'attrattore di lorenz
%-----------------------------------------------------------
% dx/dt = -10 x - 10 y
% dy/dt = x - y - (sqrt(27)+x)z
% dz/dt = sqrt(27)*(x+y) - z + xy
function dy = lorenz(t,x)
dy = zeros(3,1);
dy(1) = -10*x(1) + 10 * x(2);
dy(2) = x(1) - x(2) -(sqrt(27)+x(1))*x(3);
dy(3) = sqrt(27)*(x(1)+x(2))-x(3)+x(1)*x(2);
end
draw_lorenz.m
function [t,x,y,out] = solve_lorenz(x_0,t_f,n)
y = [ ] ;
x = [ ] ;
plot3(0,0,0);
out = cell(n,1);
hold;
for i=1:n
x_i = rand(1,3)*0.1 + x_0;
x = [x x_i'];
[t,temp]=ode45(@lorenz,[0 t_f], x_i);
out{i} = temp;
y_len = length(temp);
y_f = temp(y_len,:);
y = [ y y_f'];
plot3(x_i(1),x_i(2),x_i(3),'ko');
plot3(y_f(1),y_f(2),y_f(3),'kx');
end
min_size = 1e10;
min_x = 1e10 ;
min_y = 1e10 ;
min_z = 1e10 ;
max_x = 0;
max_y = 0;
max_z = 0;
for i=1:n
s = size(out{i});
x_max = max(out{i}(:,1));
x_min = min(out{i}(:,1));
y_max = max(out{i}(:,2));
y_min = min(out{i}(:,2));
z_max = max(out{i}(:,3));
z_min = min(out{i}(:,3));
if s(1) < min_size
min_size = s(1);
end
if x_max > max_x
max_x = x_max;
end
if y_max > max_y
max_y = y_max;
end
if z_max > max_z
max_z = z_max;
end
if x_min < min_x
min_x = x_min;
end
if y_min < min_y
min_y = y_min;
end
if z_min < min_z
min_z = z_min;
end
end
for j = 1:min_size
clf;
axis([min_x max_x min_y max_y min_z max_z]);
plot3(out{n}(:,1),out{n}(:,2),out{n}(:,3),'c');
hold on;
for i=1:n
v = out{i}(j,:);
plot3(v(1),v(2),v(3),'ko');
end
pause(0.1);
drawnow;
hold off;
end
end