To explore sensitivity to initial conditions we perturb those conditions and watch for departure from the original calculation.
First we give the top particle with mass 3 a velocity to the right of 10–2.
At time t = 32 the images are just a few pixels off but by t=34 the dance has changed and by t=35 masses 3 and 4 have eloped:
Starting at t=32:
Starting mass 3 with vx = 10–3 the difference becomes visible at about t = 38. Here are the images starting at t = 32.
I don’t know if mass 3 escapes.
For mass 3 starting with vx = 10–4 we trace until t = 90.
Starting at about t = 40 differences begin to be visible.
The following is for 40 < t < 90.
For mass 3 starting with vx = 10–5 we trace until t = 88.
The difference appears at t = 46.
The following is for 40 < t < 88.
For mass 3 starting with vx = 10–6 we trace until t = 88.
The difference appears at about t = 52.
The real divergence follows a near expulsion and the final encounter is much changed.
Starting from t = 48:
For mass 3 starting with vx = 10–7 we trace until t = 88.
The difference appears at about t = 59.
Starting from t = 56: