Euler step count changes paths and endpoints

Drag the yellow start, then change step count. Both curves use the same field; Euler differs in how often it reevaluates the direction.

Fine-step reference trajectory 　 Euler trajectory; dots mark field evaluations 　 initial distribution

Target distribution Show initial distribution

Euler steps 4 steps

Step size h = 0.250 Endpoint error = —

A coarse Euler step follows one arrow over a long interval. More frequent field evaluations can track velocity changes better and approach the fine-step trajectory in a stable convergent regime.