Mad Robot

A mad robot sets off towards the North East on a journey from the origin. It travels in stages by moving forward and then rotating on the spot. It follows these pseudo-code instructions:

SUB JOURNEY

$\quad$DISTANCE = 1000

$\quad$WHILE (DISTANCE  > 0.001)
$\quad\quad$MOVE DISTANCE
$\quad\quad$STOP
$\quad\quad$ROTATE(90, DEGREES, CLOCKWISE)
$\quad\quad$DISTANCE = DISTANCE / 2
$\quad$END WHILE

$\quad$EXPLODE

END SUB

Where does the robot explode?

Extension: Write a program such that the angle rotated and other factors in the problem are variables. Explore where the robot might end up.