> # chaos example; sfb 13 nov 01
> sigma:=10;r:=28;b:=8/3;
> Lorenz:=[diff(x(t),t)=-sigma*x(t)+sigma*y(t), diff(y(t),t)=r*x(t)-y(t)-x(t)*z(t), diff(z(t),t)=-b*z(t)+x(t)*y(t)];
> with(DEtools);
> p1:=DEplot(Lorenz, [x(t),y(t),z(t)], t=0..50, {[x(0)=5,y(0)=10,z(0)=10]}, scene=[t,x], stepsize=0.01, linecolor=red, thickness=0, axes=box):
> p1;
> p2:=DEplot(Lorenz, [x(t),y(t),z(t)], t=0..50, {[x(0)=5.01,y(0)=10,z(0)=10]}, scene=[t,x], stepsize=0.01, linecolor=black, thickness=0, axes=box):
> p2;
> with(plots);
> #The only difference is the 0.01 difference in the initial value for x(0), 5 vs 5.01, but note how eventually the curves are totally different
> display(p1,p2,title="sensitive dependence on initial conditions");
> p3:=DEplot(Lorenz, [x(t),y(t),z(t)], t=0..50, {[x(0)=5,y(0)=10,z(0)=10]}, scene=[x,z], stepsize=0.01, linecolor=red, thickness=0, axes=box, title="The Lorenz Strange Attractor"):p3;
> 
>