Even without the scaling by the length and dt , when changing the speed the
first point of the history is different.
A possible cause of this is that the random numbers aren't being
distributed along the time dimension last, and so altering the array length is
altering which numbers from the random sequence end up in the first time
slice of the history array.
A solution would be to permute the array to the dimension that is dealt to
last in the handing out of the numbers of the random sequence, which would
presumably be first (the current position) or last dimension, then permute it
back once the noise array is populated.