Butterfly

[Pauldelbrot]

A zoom into Infinity, going not for the core of the infinity symbol but for a dendrite sticking out from it.

The magnification of this image is about 2x10⁵⁹; the width of the image in pixels being about 2x10³ and the width of the M-set being about 1.5, the size of a pixel of this image in relation to the size of the whole M-set is smaller by a factor of about 6x10⁶².

For reference, the Planck length is about 10^-35 meter and the observable universe's diameter is about 10²⁷ meters, making the observable universe's width in Planck units 10⁶².

If the whole Mandelbrot set was rendered to this resolution, and the image made as small as is physically possible (a pixel being one Planck length wide), the thing would be about six times the size of the universe.

Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0.

Detailed statistics:

Name: Butterfly
Date: February 10, 2010
Fractal: Mandelbrot
Location: Near the big spike minibrot.
Depth: Very Deep (70 decimals)
Min Iterations: 2246
Max Iterations: 4575
Layers: 1
Anti-aliasing: 3x3, threshold 0.10, depth 1
Preparation time: 30 minutes
Calculation time: 5 hours (2.5GHz dual-core E5200)

[kram1032]

a lot of nice eights and infinities in this one

[Pauldelbrot]

Thanks. An even deeper zoom in this region is forthcoming ... eventually.

[Pauldelbrot]

By the way, I occasionally post lower-resolution fractals at Facebook. (The site's limit on image dimensions seems to be 600x450; anything larger gets downsampled and doesn't seem to be accessible at its original resolution.)  These are sometimes previews of coming attractions here, and sometimes other things (including many deep zooms that are much quicker to render at 600x450 than they are at 2048x1536, though the best of these will get a bigger rendering posted here eventually).

Unfortunately, it doesn't seem to be possible to browse to the fractals from that link without a Facebook login, though I'm pretty sure I made the things as public as possible. Individual links to images can be found that seem to work, but no "master link" to browse them.

[Timeroot]

There should be a URL facebook gives you so that you can share them publicly... I tried the link and, even though I was logged in to Facebook and everything, I just went to your profile. I guess this was Facebook hinting I should become your friend to view them. There wasn't even a link to your photos. If you go into your photos, then open one album, there should be a "public viewing" URL at the top. Post that, and anyone can see the photos, without even logging in. And it will still only be that one album.

[Pauldelbrot]

If you go into your photos, then open one album, there should be a "public viewing" URL at the top. Post that, and anyone can see the photos, without even logging in.

Yes, I know; that's the problem, it's only one album at a time.

[Timeroot]

Ohhh, and you have a whole host of albums with the fractal pictures is it? 

[Pauldelbrot]

Ohhh, and you have a whole host of albums with the fractal pictures is it?  

Indeed.

Try viewing my profile again. Logged-in users should be able to see "Info", "Photos", and some other tab without friending me. See what's visible under "Photos".