In[]:=
AttractorOfLorenz::usage="The geometric locus is the movement that follows a point in space, solution of the system of three non-linear differential equations that appears below. Where x represents the air speed, y is the temperature difference between the up and down currents and z is the distortion of the vertical temperature profile with respect to a straight line. Lorenz used the values of σ, ρ and β, which appear below. They are respectively the Prandtl number which is the ratio between the velocity of viscose diffusion and the speed of thermal diffusion, the Rayleigh number is the criterion for the relationship between buoyancy and inertia, the last number is of adjustment. If we change the initial value and one variable by one millionth, the trajectories will advance together at the beginning and then they will separate and make infinite turns in a finite space, orbiting between the two main foci, the eyes of the butterfly's wings. That's why it is said The fluttering of a butterfly in Brazil can produce a tornado in Texas. References: Internet; Personal. ";
In[]:=
Manipulateσ=10;ρ=28;β=;sol=NDSolve[{x'[t]==σ(y[t]-x[t]),y'[t]==x[t](ρ-z[t])-y[t],z'[t]==x[t]y[t]-βz[t],x[0]==0,y[0]==1,z[0]==0},{x,y,z},{t,0,50}];ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.sol],{t,0,t1},ColorFunction->"DarkRainbow",PerformanceGoal->"Quality",PlotRange{{-25,30},{-25,30},{0,50}}],{{t1,50},0.00001,50,0.00001},SaveDefinitions->True
8
3
Out[]=
