turn on turbo mode (shift+green flag) up and down arrows to control inner speed left and right arrows to control outer speed s to show lines h to hide lines L to turn off blue lines I to turn on blue lines O to toggle the black dot outlinesl green flag randomizes cool things: when the inner turn speed is either half or double the outer turn speed, it always creates a cardioid. when the inner turn speed and outer turn speed are the same, it always creates a circle. when the inner turn speed is -1 times the outer turn speed, it creates a weird eye shape when the inner turn speed is -2 time the outer turn speed, it creates a weird propeller thing It is mathematically impossible for to take more than 12 seconds to draw a shape (when both speeds are integers). this is because it moves __ degrees 30 times a second. using this, you can make an equation for how many full loops made, where S is the speed, and T is time, The equation is (30TS)/360, since it has to make 360 degrees to make a full turn. this equation can be simpified to TS/12. after 12 seconds, T would be 12, so the eqution for 12 seconds is (12s)/12, and the 12s cancel out, leaving it doing S circles. Since S is an integer, that means it has done S full circles, leaving it where it started. this proces would be done for the outer speed and inner speed, giving the same results, so they would both end up where they started, making sure that it will finish drawing after 12 seconds.
