Logarithmic spiral

Drag the red dot.[br]Can you figure out what happens to the red number as it loops around the spiral?[br][br](When you've had enough of that, click the checkbox in the bottom right and read on below.)
With the checkbox checked...[br]Click the [b]×[/b] button to multiply the red and blue numbers.[br]How does the position of the purple number (the result) relate to the positions of the red and blue numbers?[br][br]Some suggestions...[br][list][*]Set the blue number to 10. Perform any multiplication, so that the purple number shows. Then drag the red dot to calculate multiples of 10 (1×10, 2×10, etc.). In general, where is 10 times a number located on the spiral?[/*][*]Do similar for multiples of 2. (Or multiples of any number.)[/*][*]Calculate 2×0.5. Then 4×0.25. In general, where is the reciprocal of a number located on the spiral?[/*][*]What's the smallest purple number you can find?[/*][*]Where is 0 on the spiral?[/*][/list]

Information: Logarithmic spiral