Deepest known image

[LesPaul]

It seems like videos of "deep zooms" are common and the record for the current best appears to advance regularly.

But what about just the deepest known image?  It's a lot easier to create a single image than a zoom video.  I've seen zoom videos that get to a final zoom factor of over 10³⁰⁰.

I expect that making just a single image with much higher magnification than 10³⁰⁰ would be possible -- I'm planning to try right after posting this.

I did a little searching and didn't find anything resembling an "official" record for deepest image.  Surprising, given the popularity of deep zoom videos.

I think it's only fair to require that a candidate for "deepest image" would have to contain some of the set as well as some area outside the set.  Otherwise, you could just claim that a solid black image was an infinitely deep zoom into (0, 0).   

Or should their be even more strict requirements?  For example, a minimum image size is probably a good idea, to prevent 2x2 pixel images from being submitted.

Anyway, I think it would be a fun record to track, and it might produce some really amazing images.

[msltoe]

I'd be curious what kind of aesthetic improvements (or even notable differences) are there in the deep zoom realms vs. the typical double precision zoom world.
Dare to surprise me.

[LesPaul]

I'm finding that rendering starts to be painful, on my humble 3GHz system, when you venture into zooms greater than 10³⁰⁰.

I'm rendering a 320x200 image now in UltraFractal and the estimated render time is about 1.5 hours.  I'll post as soon as it's done, but it's hard to say how interesting it will be, as it's currently just a handful of giant pixels.   

I'm expecting, even hoping, that someone will immediately destroy this record by zooming to 10¹⁰⁰⁰ on their massive render farm.  The tricky part is actually zooming in that far.  Just picking a random point is extremely unlikely to find an area that isn't either completely outside or inside the set.  I used the brute-force method of essentially "zoom-in, zoom-in, zoom-in, oops went too far inside, zoom-out a little, zoom-in, zoom-in, zoom-in, oops went too far outside..."

[LesPaul]

Here's the result.




Re = -0.8243080375593406755222341347020768075802226306010194444627533013510679491245773355430
496573332321229868079855771897938309204960632350878439589569338757090459774866819555673666972
484326084859113186666639750370110332407666113759616770658543516775550238530919092607105781085
861853162741942859383071572242315572146282498903031032656212363269693461109044174140602342488
735619
Im = 0.19122477617848000790561241783933389388298142056743652808384657288772170393904362204635
458281246223313927396284135849192641412091081676953846267148464011263377690405196118057238535
635997101757564535491845530718199768171631582721365552205171908803093962517932218686359284504
294954105931838760720616847221500609621922270114152587646433316948187803352897036957079171418
27354

Magnification = 1.6E360


I guess it looks pretty similar to what you see in shallow zooms.  The "structure" of the spirals just appears to get gradually more chaotic, which is what I'd expect.

I've set a very low bar!  I am eager to see it shattered.

[cKleinhuis]

dont confuse more chaotic with missing-alias.... what happens down there is the spiral arm count in general increases,
nearly every part of the brots increase their spiral counts ... while retaining the minibrot shape .... and just dont forget
you can paddle with your boat from mini brot to minibrot and sometimes reaching the big sea ....

why hasnt anone done a game ? the game of the lonely paddler needing to find its way back to the big sea

[LesPaul]

I did some experimenting and found that chasing the highest possible zoom doesn't really encourage "interesting" images.  The best way that I found to zoom extremely deep is to choose a rational number known to lie on the set boundary as the image location, such as (0, 1).  Unfortunately, the image never changes significantly from the classic "lightning bolt" commonly found in that area.  Even at a zoom of 10²⁰⁰⁰, the maximum number of iterations required per pixel is under 6000.  The only limitation to how far I could zoom at this location is that UltraFractal's arbitrary precision eventually hits a limit somewhere around 10⁵⁰⁰⁰.

[fractower]

If you have gone to the trouble of implementing arbitrary precision then you can use a binary search to find an arbitrary small region that includes the boundary in O(log2) steps. There will be an infinite number of crossings between (almost) any point inside the set and outside the set.

[cKleinhuis]

watch the images by paudelbrot he finds interesting areas, mostly in the various valleys of the mandelbrot... hunt the minibrots ...

[msltoe]

I agree with cKleinhuis, the minibrots are areas of perturbations from standard Julia patterns.
I expect that with more levels of minibrots (minis within minis, etc), more variation.

[fractower]

How is the zoom depth measured? Does 10^5000 indicate the step size between sample points.

Also does someone have a rule of thumb for number of mantissa bits required for a given zoom depth? I assume it is something like log 2 of the depth with a few extra for loss of precision during iterations.

[Dinkydau]

If the unzoomed image has a size of 1, then the zoomed image will be 10^5000 times as large, which is pretty incredible btw. I've done a deep zoom in ultra fractal to somewhere around 10^1383:
http://dinkydauset.deviantart.com/art/Deepest-mandelbrot-zoom-E1383-177347085
Don't ask me how long this took to render, months it took, it was incredible.

Fractal extreme is limited to 2^7200, which would be around 2,6 * 10^2167 in the power-of-ten-notation, but it renders much faster than ultra fractal. I've rendered a very simply image with a magnification of the maximum 2^7200 at (-1,999999999~ ; 0), never posted it before because it's both predictable and boring. It took only minutes, and a minibrot at that depth would probaby take a few days (at a resolution like this).


Unfortunately this program doesn't allow further zooming, not really sure why exactly, but it doesn't work. I'd be interested to see some really deep zooms, even deeper than this.

Apart from going just... deep, there are interesting things to be found. It appears that almost every pattern in the mandelbrot set, "repeats" itself in a different form, by increasing in quantity or order, if you know what I mean.

[cKleinhuis]

jost for interest how large in bytes is that number ? on a first guess i would say something around a solid megabyte

[Dinkydau]

You mean to save the full number as a text file? That's just the number of digits. Since a zoom level is normally not a broken number (totally unnecessary), that would be the power in the 10^n notation. 10^5000 is only 5 kilobyte.

[plynch27]

A base-2 zoom level of 7200 would require a minimum of 7200 bits of precision plus extra bits to provide a range to render the image within. log[10](2^7200)~=2167, i.e. a base-2 zoom of 7200 would equate to a base-10 zoom of 2167. Fractal eXtreme uses a precision of 7456 bits at its maximum zoom level of 2^7200. This comes to a space of 932 bytes, which is 92 bytes short of an even KB.

[plynch27]

A base-2 zoom level of 7200 would require a minimum of 7200 bits of precision plus extra bits to provide a range to render the image within. log[10](2^7200)~=2167, i.e. a base-2 zoom of 7200 would equate to a base-10 zoom of 2167. Fractal eXtreme uses a precision of 7456 bits at its maximum zoom level of 2^7200. This comes to a space of 932 bytes, which is 92 bytes short of an even MB.

I meant that it's 92 bytes short of an even KB, not MB. My bad.