Highest Iteration Count for Escaping Point (Mandelbrot)

[apeirographer]

Greetings,

Can someone tell me what are some of the highest iteration counts for escaping points for (outside) the Mandelbrot set?

I found a point that escapes after 99,981,296 iterations.  Is that a lot?  Or are the deepest Mandelbrot zooms focused on areas with much higher iteration counts?

Thank you in advance!

Apeirographer

[PieMan597]

100 million iterations is a lot, and it is more than I've ever reached.
The iteration record for a zoom movie is 750 million, here: <a href="http://www.youtube.com/v/ModQ59muXmU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/ModQ59muXmU&rel=1&fs=1&hd=1</a>

However, I am not sure of the record for a single image.

[quaz0r]

well the highest escape time is of course infinity, so 

just keep zooming in on the edge of a bulb and you will reach prohibitively high escape times after only a few zooms.

[apeirographer]

That's encouraging, PieMan597. Thanks!

Quaz0r,  what are prohibitively high escape times? A billion? A hundred billion? Orders of magnitudes more than that?

I don't use third party fractal programs, so I can't readily try your suggestion to see for myself.

[apeirographer]

The 750 million iterations deep video claimed to zoom in to 10^99 magnification. Is there a 1:1 relation between how high an iteration count is and how deep you can zoom into the surrounding area?

Would my 100 million iteration  find be zoomable to only about a 7th as deep?

[apeirographer]

100 million iterations is a lot, and it is more than I've ever reached.
The iteration record for a zoom movie is 750 million, here: <a href="http://www.youtube.com/v/ModQ59muXmU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/ModQ59muXmU&rel=1&fs=1&hd=1</a>

However, I am not sure of the record for a single image.

Isn't this video a lot deeper of a zoom?

<a href="https://www.youtube.com/v/WgzW_jr0xSw&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/WgzW_jr0xSw&rel=1&fs=1&hd=1</a>

But then the location parameter file (unless I am really misunderstanding it) suggests that the focus coordinate is only 807,345 iterations.

How can the slower and shallower zoom of the video you posted have a higher iteration count than the faster and deeper video I found?

Sorry if I am asking odd questions, but the "standard" approach and terminology to Mandelbrot rendering is unfamiliar to me.

[lkmitch]

Other than the iteration count and the zoom level both generally going to infinity, there isn't one specific relationship between the two.  At the tip of the spike (-2,0), you can zoom in quite deeply without racking up a lot of iterations.  On the other side at the cusp (0.25,0), you can easily get beyond the iteration count of most programs before running out of zoom.  Any point on the boundary of the set essentially has an infinite iteration count, so you should be able to reach arbitrarily large iterations relatively easily.

[apeirographer]

That makes a very obvious sort of sense, now that you pointed it out.

Thanks, lkmitch!

Are high iteration count spots interesting then, from the perspective of wanting to do deep zooms?  Or are these two issues orthogonal to each other as well?

[quaz0r]

this is one of my images zooming in several times on the edge of a bud:

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=18151

the zoom level is very shallow, i think around 1e10, but i could not zoom much beyond this point before the escape time gets too high.  the brighter parts (most of the image) is the high-iteration boundary area, the narrow dark-colored lines are the lower-iteration more in-between sections.  basically the more you zoom in to the edge, the iterations get prohibitively high very soon and the border becomes just a dense featureless mass.  what mandelbrot explorers tend to find more interesting is julia morphing in less dense areas, where the escape time increases more gradually.

[apeirographer]

Thanks, quaz0r.

Would you agree then that particularly deep points are not particularly noteworthy within the context of Mandelbrot escapetime visualization?

Or is there something else that they are useful/interesting for, just not interesting deep zooms?

[lkmitch]

I have an image highlighting structure similar to that in quaz0r's:

http://www.kerrymitchellart.com/gallery14/adrift.html

To me, both high-iteration and deep-zoom images are technically and artistically challenging, which makes them both interesting classes of images.  Deep zooms are typically unremarkable artistically, but they can reveal some interesting mathematics.  High iteration images present the challenge of not looking like white noise, discerning structure in some compelling way.  And you can often get them without needing arbitrary-precision arithmetic, which makes exploring them more practical.  So I guess it all depends on what you're after.

[apeirographer]

Thanks, lkmitch!  I've been noticing the artistically mundane part...

[Adam Majewski]

http://www.kerrymitchellart.com/gallery14/adrift.html
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=18151

it seems that these are very dense images

http://mathoverflow.net/questions/187842/is-there-an-almost-dense-set-of-quadratic-polynomials-which-is-not-in-the-inte

Can you post the parameters ?