% We'll start with some random data:
title('Messy Random Data Plot');
plot(rand(100,1),"-*;;")
clg
pause(1)

% here's the solution of a system of differential equations:
% gradient:
function xdot = f (x, t)
r = 0.25;
k = 1.4;
a = 1.5;
b = 0.16;
c = 0.9;
d = 0.8;
xdot(1) = r*x(1)*(1 -x(1)/k) - a*x(1)*x(2)/(1 + b*x(1));
xdot(2) = c*a*x(1)*x(2)/(1 + b*x(1)) - d*x(2);
endfunction
               
% initial value:
x0 = [1; 2]
% set of times at which to solve:
t = linspace (0, 50, 200)';

% and the solution, using lsode:
x = lsode ("f", x0, t);

% time for a plot!
title('ODE solution');
plot (t, x)
clg
pause(1)

% note how it handles a vector, plotting both coordinates against time.
title('ODE solution: second coordinate');
plot (t, x(:,2))

clg
title('sines and cosines');
t = 0:0.1:6.3;
plot (t, cos(t), "-;cos(t);", t, sin(t), "+3;sin(t);");