Locating the Centroid

[stardust4ever]

In my experience of really deep zooming with Fractal Extreme (Mandelbrot Z=Z^2+Z), I have found that minibrots get scarcer and scarcer the deeper you go. I have found that anytime I deviate from the centroid, the cycling starts over again and I go through many sequences similar to but slightly different than features I have already explored. With any of the higher order 'brots, finding the centroid of a feature is a no-brainer. Deviation from the centroid is like taking all the paths you've been through thus far, and reiterating them before landing at a periodic doubling of the point I deviated at. Well, I found a feature with an interesting spiral shape with some backfacing spikes, and thought it would be interesting to zoom in at the tip of the spike. Well, after cycling through all of the various formations, I arrive at the doubling point (at about 2^-314) and can't seem to find the exact location of the centroid. My intention is to continue zooming in until I find the minibrot, and later make a zoom movie out of it. When I try to zoom in on the line, I just see fragmented sameness without any indication of where to pinpoint the center. I want to try to reach a minibrot in as few zooms as possible from his location. but I'm afraid if I pick the wrong point, I'll just wind up going through countless repeated formations, only to arrive in the same situation much deeper in the zoom. Does it even really matter, or can I just pick a spot on the line close to the center?

Confused.

[ker2x]

(Mandelbrot Z=Z^2+Z)

+Z ?

Confused.

me too 

[klixon]

If you were to pick a random point that isn't the very centre of the structure you're looking at, you're going to have to do a lot more zooming then if you were to pick the one in the middle.

Try zooming in by making sure the sides of the zoombox cross the black x's i put in your picture. There's two small dents there that are almost certain to be at exactly the same distance from the centroid. Once that renders and you still don't see where to zoom in next, try fiddling with the gradient. Don't get discouraged... The closer you get to it, the faster those bounderies follow each other, so it should get easier every time you zoom in.

I'm very curious what you find down there. It's one of my favourite pastimes, deep-zooming

[reesej2]

I would suggest a gradual zoom. Instead of zooming in by a factor of fifty, try a factor of two or three. It'll take a lot longer, but you'll reach a minibrot sooner.

[klixon]

no zoom-box in fractal extreme?

[stardust4ever]

I go home from school this weekend and take a closer look at it on my primary render machine. I have a quad core phenom II 64 bits @3.6 Ghz. It renders fractals over 12 times as fast as my 2Ghz 32 bit core duo laptop. And I did try to zoom in a little bit closer up on the bar and just saw hundreds of mostly identical-looking bar-like islands all composed of smaller bars. I was just framing this zoom as a point of reference to show the symmetry, hence the slight zoom out. It will be slow-go zooming in because it requires a lot of time to make out the details. I suppose one of the little segments will be slightly fatter than the others, and that will indicate the path I need to zoom into. The feature surrounding this area is very beautiful and intricate. Problem is I zoomed inside the tip of the spike instead of outside, so there's no separation barrier like there normally is. Zooming in about twenty times before selecting a point probably didn't help, but it creates more dramatic zooms that way.There's some highly dense features and some low density ones you can see in the side ripples.

[Calcyman]

I just see fragmented sameness without any indication of where to pinpoint the center.

There might not be a minibrot at the centre of it. It could be a Misiurewicz point, in which case you'll never reach a minibrot, even after an infinite number of zooms. An example is the point near −0.1011 + 0.9563i.

[stigomaster]

It seems to be a Julia barrier, and there are always minbibrots inside them as far as I know.

[stardust4ever]

Sorry for the late reply.

Yeah, I eventually found it. The repeating features were consistantly smaller-sized closer to the middle. It took about 20 or so zooms before I found a division on the spike in the form of a cross shape. Everything beyond that point is fourfold or more, as expected. I'm probably going to zoom back out some and redo the zoom from an earlier point before my last deviation. Thanks for the comments and suggestions...