fractal – Page 2 – Spyke Art

Bugs #23

Posted on 2019-08-182019-08-17 by Spyke

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 #22

Posted on 2019-08-172019-08-20 by Spyke

Bugs Fractal 96

This one has the same zoom factor as the previous, the center has been moved to $a*\pi/2$ . As with the bugI images, m-sets and tricorns alternate, this time along the real (horizontal) access. Compare with Bugs #10.

Bugs #21

Posted on 2019-08-172019-08-20 by Spyke

Bugs Fractal 95

Zoom out by another factor of 2.

Bugs #20

Posted on 2019-08-172019-08-17 by Spyke

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.

Bugs #19

Posted on 2019-08-142019-08-14 by Spyke

Bugs Fractal 93

At the next intersection to the east is a mini-tricorn. The minibrots and tricorns alternate.