If at every step your vectors contain all of the values so far, you can just replace scatter! by plot.
And unless you are animating it, you probably want to put the plot command outside the loop.
Details
scatter!(...) is an alias for plot!(...; seriestype=:scatter), but you want the default seriestype, :line.
The version of these commands with a ! are updating, so they leave whatever was previously drawn in place. This is not what you want since you are adding all of the points every time.