## Bugs #24

Here is a look at the vertical spoke rising above the origin. Msets and Tricorns alternate here as well. The picture back in Bugs #18 show a mini-tricorn. The text describes an infinite grid of points covering the whole plane where the iteration of 0 falls into a 2-cycle. The hot spots in this picture are some of the points on that grid.

## Bugs #23

Zoom out by another factor of two. The two shapes alternate over the entire horizontal axis at a spacing of $a*\pi$.

Recall the formula, $bugR(x+yi) = a*sin(x/a) + yi$, and whatever you may remember about the sin() function. bugR() is periodic with period $2*a*\pi$. bugR(z) = 0 for all $z = a*n*\pi$, n an integer. For the even multiples, $bugR(z+2n*a\pi) \approx z$ and for old multiples, $bugR(z+(2n+1)*a\pi) \approx -\overline{z}$. While these observations do not constitute a full proof, it does strongly suggest why the two shapes alternate along the real axis.