sig=10;b=8/3;r=29;tmax=50;
aa=NDSolve[{x'[t]==sig (-x[t]+y[t]),y'[t]==r x[t]-y[t]-x[t] z[t],
z'[t]==x[t] y[t]-b z[t],x[0]==5.,y[0]==10.,z[0]==25.},{x,y,z},
	{t,0,tmax},MaxSteps->40000,AccuracyGoal->8,PrecisionGoal->12];
pp=ParametricPlot3D[{(x[t]/.aa)[[1]],(y[t]/.aa)[[1]],(z[t]/.aa)[[1]]},
{t,0,tmax},AxesLabel->{"x","y","z"},PlotPoints->5000,PlotRange->All]