spirals are special snowflakes (wen 3D polar)

these are all root 5 spirals (of the original circle...meaning the segment i'm creating them from is 2.236 times the radius of the original circle)

not only does final placement and direction of rotation (clockwise or counterclockwise) matter, but the positioning of the original segment matters. for example all of these spirals have the same radius but they look wildly different because of the original angle of the segment i'm deriving them from. (remember from geometry class that every point on a circle is equidistant from the center - that's the beauty of circles)

perhaps something meaningful in drawing them at 0, 90, 180, and 270 degrees as the limits of differences in direction

ultimately i think the spirals can help visualize the chart in an axis or line of sight

(i spent way too long yesterday drawing circles with my finger in midair, in different directions and moving my head/perspective to try to understand sine waves...then thinking about what this all means for cycles)