Title. Inspirals

These spirals are called INSPIRALS (Kathleen Martin and Donna Bearden, "Mathematics and Logo. A Turtle Trip Through Geometry"). For these shapes the size in general procedure remains constant, while the size increment is equal to zero, and the variety of shapes is obtained by varying initial angle and angle increment. Unlike the POLYSPIRAL, where the angle increment is equal to zero, the inspiral brings us more complicated problem with defining a Stop Rule.

After some experiments with inputs for the procedure, one comes to the conclusion, that spiral usually makes several "arms" and then the Turtle returns to the initial position. The number of arms and their shapes depend on angle value and angle increment as well. A thorough investigation of this problem may be found in the book mentioned above.

Here we would like to present our findings organized in a chart form. The size varied between 5 and 10 in all our experiments, its value doesn't ifluence the shape of the spiral.

Number of "arms" Initial angle Angle increment Stop Rule
2 2 2 if :angle>360*2 [stop]
3 1 6 if :angle>360*3 [stop]
4 1 4 if :angle>360*4 [stop]
5 1 10 if :angle>360*5 [stop]
6 1 3 if :angle>360*6 [stop]
8 1 8 if :angle>360*8 [stop]
9 1 18 if :angle>360*9 [stop]
10 1 5 if :angle>360*10 [stop]
12 1 12 if :angle>360*12 [stop]
18 1 9 if :angle>360*18 [stop]
"staircase" 1 2 Turtle never returns "home"

Title. Inspirals