Play, notice, wonder.[br][br]Use the slider n to control the number of planets (2-6).[br]You can move the planets as you like.[br]You can move the starting point of the space ship.[br][br]Each round, the ship captain randomly chooses a planet, points the ship in that direction, and moves a certain distance (which you control by the slider a).[br][list][*]If a=.5, the ship moves to the midpoint between its current position and the chosen planet.[/*][*]If a=.2, the ship moves to a point that is 20% current position, 80% chosen planet.[/*][*]Experiment with a to see what else can happen.[/*][/list]The first 200 ship positions are shown.[br][br]Brad to do:[br]Increase number of points shown without breaking software :([br]Here's a way to do that: https://www.geogebra.org/m/nr5wzz2b[br]Include something about similarity transformations.

Click any blue point to move the ship half way to that point.[br]Land the ship in the shaded cell in the fewest possible moves. (Aim for d moves.)[br][br]To do:[br]Victory indicator[br]Larger click zones to move?