plotting the starting and ending points in addition to coloring points to show their position along the walkit would be nice to see where each walk begins and ends to do sowe can plot the first and last points individually once the main series has been plotted we'll make the end points larger and color them differently to make them stand outas shown hererw_visual py --snip-while true--snip-plt scatter(rw x_valuesrw y_valuesc=point_numberscmap=plt cm bluesedgecolor='none' = emphasize the first and last points plt scatter( ='green'edgecolors='none' = plt scatter(rw x_values[- ]rw y_values[- ] ='red'edgecolors='none' = plt show(--snip-to show the starting pointwe plot point ( in green in larger size ( = than the rest of the points to mark the end pointwe plot the last xand -value in the walk in red with size of make sure you insert this code just before the call to plt show(so the starting and ending points are drawn on top of all the other points when you run this codeyou should be able to spot exactly where each walk begins and ends (if these end points don' stand out clearlyadjust their color and size until they do