The sim hereunder puts 100 test particles in the lagrangian point to Earth at 1Au , separated by 60° with a range of +/- 5% in Mean Anomaly to this 60° .  
Curious about the stability .  
The trojans seem remarkably stable as can be seen in the animation .  
However as all particles tend to settle towards the 60° point they seem to move in a weird way .  
The sim was run for about 500 years .

it's not so much a snake as a caterpillar really