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The Ragin' South Asian · Head Poncho

I don't really know what it means so I voted connected to feel less lonely.

The Potter · Feat of Clay

Hmmm 2 people supported connected. One of them was me. There were 6 in favor of disconnected.

So there is a theorem that says if the point 0+0i is trapped, the set will be connected. So instead of some arbitrary location, lets center the image at 0+0i and see if it is black.

It is pretty but hard to tell exactly what is going on in the exact center. So I can zoom in as far as Fractal Domains can really handle, 1e-11.

Clearly the center is non-black. But there is something funky going on.
This fractal was using 30 000 iterations. So what happens if the iteration count is reduced to 20 000?

20 000 iterations

Suddenly the center of the image is black.

As far as I can see, the change is a result of rounding errors. I believe the Julia point C= -0.7472241 -0.06128591i is connected...unless we rely on rounded calcualtions. Which the first image did. Felicitous

(When I posted this question, I didn't know the answer.)
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

extropalopakettle · No offense, but....

Lowering the number of iterations will show areas to be black that shouldn't be - areas very close to points in the set, but not in the set itself.

I tried checking C= -0.7472241 -0.06128591i, but I suspect there's some rounding there too, as what I got was a bit different.

The Potter · Feat of Clay

I believe that it is connected mostly because of the way it fills the space. Trailing lines that approach a point are normally connected. When there is just 5 or so of these finger it is pretty obvious. This image just has too many to easily count.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

Thok · Oh, foe, the cursed teeth!

Zag · Tired of his old title

I think his point, Thok, is that these are an expression of art and emotion, and he doesn't really care about the precise mathematics. It seems a valid way to think about it.

Thok · Oh, foe, the cursed teeth!

The Potter · Feat of Clay

While I have been exploring fractals primarily as art, I have a reasonable understanding of the math behind it. But I am not ever going to be part of the math community. And yes, I do believe my understanding of being connected is consistent with your posts.

I wasn't searching for anything. But when was looking at the image I was a little confused-- it comprised of patterns that I see with obviously connected sets but the appearance of being disconnected.

Also I should note that after about 25k iteration level, there is a very sharp transition in amount of coloration. This explained my confusion perfectly-- the set is connected but became disconnected by limitations of the software.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

The Potter · Feat of Clay

Oh, I see why the software is having trouble. The point is really close to -0.75 + 0i. This point is "neck" of the "bug" on the main Mandelbrot.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.