In “First Whirled Warp”, I looked at the paths traced by the midpoint of two points moving at varying speeds around the perimeter of a circle or polygon. Now I wanted to look at the midpoint of two points moving on the perimeter of a star. Suppose the star looks like this:

Four-pointed star

If the two points start at the same vertex and one point is moving 1/2 as fast as the other, the midpoint traces a shape like the head of a fox:

Fox-head from midpoint of two points moving in speed-ratio 1/2 : 1 (or 1 : 2)

If one point is moving 1/3 as fast (or 3x faster), the trace looks like this:

Midpoint of two points moving in speed-ratio 1/3 : 1

And if the points are moving -1/3 : 1, that is, in opposite directions (one clockwise, one widdershins):

Speed-ratio -1/3 : 1

And you can adjust all pixels outward so that the outer vertices of the star lie on the perimeter of a circle:

Speed-ratio -1/3 : 1 (circular)

Here are more traces created by the midpoint of two points moving around the perimeter of a four-pointed star:

Speed-ratio 1/5 : 1

Speed-ratio 3/5 : 1

↓

Speed-ratio 3/5 : 1 (circular)

Speed-ratio -3/7 : 1/3

↓

Speed-ratio -3/7 : 1/3 (circular)

Speed-ratio 7/3 : 6/7

↓

Speed-ratio 7/3 : 6/7 (circular)

Speed-ratio -7/3 : 6/7

↓

Speed-ratio -7/3 : 6/7 (circular)

If the star is adjusted like this:

Variant on four-pointed star

You can get mid-traces like this:

Speed-ratio -1/7 : 1 (adjusted star)

↓

Speed-ratio -1/7 : 1 (adjusted star) (circular)

Here’s a three-pointed star:

Speed-ratio -4/5 : 1 (3p star)

↓

Speed-ratio -4/5 : 1 (3p star) (circular)

And some five-pointed stars:

Speed-ratio 2/7 : 1 (5p star)

↓

Speed-ratio 2/7 : 1 (5p star) (circular)

Speed-ratio -7/5 : 3/7 (5p star)

↓

Speed-ratio -7/5 : 3/7 (5p star) (circular)

Previously Pre-Posted

• First Whirled Warp — an earlier look at points performativizing on perimeters