Bugs #23

Bugs Fractal 97

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.

Bugs #20

Bugs Fractal 94

No posts for the last two days. I have no excuses, I simply did not make the time. I will try to make up with multiple posts today.

The next few pictures are success out-zooms of Bugs #16 to get an idea of what the neighborhood looks like.

Today’s image is a zoom out by a factor of two.

For a quick recap, this formula is bugR, defined back in Bugs #14 , with parameter a = 2.5.