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I've seen some Mandelbrot zooms rival 1 billion iterations before.

Kai Wells even tried making a zoom with 1 billion iterations, but a glitch appeared. I request that you help Kai Wells if you have the chance: https://www.youtube.com/watch?v=7azfLq7DMTA&list=UUNxnO--5mIH8j5ZjhCo6gvQ&index=7

Has anyone completed a fractal zoom using 1,000,000,000 iterations? This number would be incredible, for it would be a whole new order of magnitude of iterations. Even though I've never personally used more than about 5,000,000 iterations (my computer is pretty old), I know that it would be impossible to get more than 4,294,967,295 iterations on Kalles Fraktaler. Sometimes, when selecting the formula on Kalles Fraktaler, the iteration statistics panel jumps to that and then decreases to what I was using.

I've seen a few non-Mandelbrot-based formulas at 1 billion or more iterations.

As I was writing this post, I found it is theoretically possible for my computer to render a 64x36 image at 1 billion in less than an hour. That is a rotten low resolution, and I'm guessing the image would have no zoom, but I would be the first to see the 1 billion iteration M-set.

I'm guessing a 1,000,000,000 iteration fractal zoom will exist before 2018.

This one has 750 million:
https://youtu.be/ModQ59muXmU

it has never been clear to me what you guys actually mean with these iteration counts.  it seems whenever iterations this high are mentioned it is always with regard to a [kalles fraktaler] zoom video and not a still image.  so what does this number represent exactly?  is it the maxIter for a render?  the maxIter for the last keyframe in a zoom video?  some kind of cumulative tally?  something else?


just no.   :snore:

see what youve started kalle?    ;D

The 1 billion is the maxiter for the last image- thats where the iterations are highest

That's the closest I've seen to 1,000,000,000.

And by the iteration counts, we often refer to a video unless noted. The iteration number is the maxIter for a render. However, these high numbers are uncommonly used for still images.

I tried rendering a 1,050,000,000 iteration image of the M-set. I had no luck: I estimated it would take five hours. When I checked on my computer, it said it was rendering for 7 hours and 0% of the image was done. So, I need a bigger image size. I may try again to create a 1,000,000,000 iteration still image. But I may not have enough time to do it, for the reason below:

I'm a fractal enthusiast, all right, but I'm only 12 years old. My parents say I can't have my computer running when I'm asleep, and I want to respect their wishes.

Good idea man! I personally never leave my computer run overnight, but I do leave it to render when I'm out of the house. Have you tried hybernating it? I usually use that when I want to turn it off.

I was gone for seven hours, so I left my computer rendering the 1.05 billion iteration M-set. Hibernating is also a nice idea. I've been thinking of doing that.

people, as quazor pointed out, we need to define a "term" for "max iteration", intuitively for me the max iteration is the bailout limit (not the abs(z) but the konkrete iter count bailout limit) for an image, so, how to prove? at least ONE pixel needs to be rendered with a bailout of { actualIterCount>maxIterCount-someDelta }

Here is a Mandelbrot zoom done with 100,000,000 iterations.  The red pixels are inside points that didn't escape.  Clearly, more iterations are needed to clean it up.  The location and zoom are:  center = -1.1136622993314711985069 + 0.25198222165777163072684i, 1.0868534E13.

Here's the same one done with 1,000,000,000 iterations.  Both were done in Ultra Fractal.  Here are the parameters.

2016-12-19-b {
; 1/2 x 1/3 x 1/4 x 1/5 x 1/6 z 1/7 x 1/8 x 1/9 x 1/10
fractal:
  title="2016-12-19-b" width=640 height=480 layers=1
  credits="Kerry Mitchell;12/19/2016"
layer:
  caption="Background" opacity=100
mapping:
  center=-1.1136622993314711985069/0.25198222165777163072684
  magn=1.0868534E13 angle=-121.6385
formula:
  maxiter=1000000000 percheck=off filename="Standard.ufm"
  entry="Mandelbrot" p_start=0/0 p_power=2/0 p_bailout=1000000
inside:
  transfer=none solid=4294901760
outside:
  density=0.25 transfer=linear filename="lkm3.ucl" entry="smooth-tanh"
  p_power=2/0 p_bailout=1000000 p_mode=log p_density=1 p_minskip=0
gradient:
  smooth=yes rotation=-100 index=100 color=16777215 index=-100 color=0
opacity:
  smooth=no index=0 opacity=255
}

You did it! (plays sound effect at 6:15 of https://www.youtube.com/watch?v=Z4Owtds9hNM) It would be utterly impossible for my computer to do that. Ultra Fractal isn't even as fast as Kalles Fraktaler. But that's only for an image. I'm guessing this may cause a bit of jealousy in the fractal community.

Yes I think the definition would be the pixel with the highest iteration count in an image.

KF stores all iteration values from the reference in an array, so theoretically it needs 2 x 8 x 1''' = 16GB of ram to render such image - if zoomed less than e600. But I think there would be some overhead.
One could perhaps not store the pixels that are skipped by series approximation and make such image with less ram.

It's a great thing you told us that the RAM needed for an image is 16 x the number of iterations. That's why, even with absurdly low resolution, I can't render an image with 1 billion iterations.

The theoretical maximum number of iterations I could use on any render is about 230,000,000. I rendered a 15,000,000 iteration image with very poor render quality. It took me 47 seconds to render the 15 million.

I figured the rendering time for a Mandelbrot image on my computer in seconds is about equal to iterations * length * height / 280 million.

I used a quality so low to render the Mandelbrot Set with 15,000,000 iterations, I guarantee you will be rolling on the floor laughing: 40x22!

To render a single good-quality 230,000,000 iteration image would require over a week of continuous rendering. This may not even be possible, because other programs may take part of my RAM.

Yes, with a resolution that low it wouldn't really be worth 'watching' imo. I find that locations that have high iterations count (at least 100k) could look really interesting / odd (at least compared to the more 'normal' fractals) if we are talking Mandelbrot. Also 3x3 super sampling and at least 1080p...

Here's another example requiring a high iteration count, with a twist.  The first image (red and white) uses 400,000 iterations.  At first glance, it looks like a standard inside/outside Mandelbrot zoom into the boundary of a cardioid, except that the baseline is curved, not straight.  Increasing the iterations to 1 million shows that the red solid area is really made up of fractal structure.  Taking them to 400 million (last image) almost cleans up all of the under-iterated regions.  There's still a small central red (inside) area that is cleaned up by 1 billion iterations.

I have noticed this phenomenon of distorted "Mandelbrot bulbs" when zooming into a dense spot while not using enough iterations. I also rendered a location using 800,000,000 iterations on Ultra Fractal a while ago. (It took 18 minutes to render.) As long as you aren't past roughly e13, Guessing is so amazingly faster than Perturbation!

My computer won't bother to render anything on Kalles Fraktaler using more than roughly 33,000,000 iterations, but it will probably use over one billion with Ultra Fractal.