Sorry I delete my question. Please delete this topic for me. Thanks!
What are you saying by 'the initial positions of the clusters'?
Did you mean to say 'which observations fall into which clusters'?
For example if you have 5 observations and decide to make k=2, allocate the observations randomly into 2 clusters, calculate the means and min distances to re-allocate.
The initial allocation won't have a bearing on the end result for a fixed k. Although it may change the number of iterations requird to reach the final clustering.