Three different starting points generate the green, blue and magenta paths. The starting points are very close together, and initially overlap, looking like a single blue path. The chaotic nature of the Lorenz attractor is evident as the paths diverge over time.
This animation runs 2000 iterations with a timestep of 0.01, with starting positions (1, 1, 1), (1, 1, 1.01), (1, 1.01, 1). The equations used are: