04.06.07
Nebulabrot
While reading Wikipedia’s Mandelbrot set article, I stumbled upon the exceedingly cool Buddhabrot, and the even cooler Nebulabrot:
I’ll write more about the math later, but what I find most interesting about it is how it naturally fills in the “boring space” inside the Mandelbrot set:
The interior of the Nebulabrot is also a fractal, as a zoom shows:
Those little buds are all Mandelbrots.
Being a CS-type, once I saw the definition, I immediately set out to render the most detailed Nebulabrot ever seen. It’s 10240×7680 and gorgeous. Here are some zooms (click for full-res versions):
The most “nebular” part
“Island universes” along the negative x-axis
Here’s a link to the full JPEG (4.3MB) and the full PNG (44 MB).
If you zoom all the way in, you’ll see some graininess, even in the PNG. This isn’t a compression artifact. It’s a hint of further structure. If I’d cranked up the dwell limit in my rendering, the noise would have been even more miniature Mandelbrot sets!
Update: MarkCC over at Good Math, Bad Math has a post about MapReduce that discusses the way I generated this at length.
Lepht said,
July 11, 2007 at 1:05 pm
holy fucking shit. that’s some eyebleedingly awesome mathematics right there. i’m gonna show these to the next person that tells me maths is for nerdy assholes. cheers
Lepht
cleek » danvk.org ยป Nebulabrot said,
August 5, 2007 at 6:39 pm
[...] Nebulabrot Filed under: Uncategorized — cleek @ 2:28 pm [...]
vm ganata said,
January 23, 2008 at 10:51 pm
OMG. It looks almost like a coronal section of an MRI of the brain.
lb said,
January 26, 2008 at 5:20 am
impressive work! and good looking stuff.
Tim Wintle said,
February 3, 2008 at 7:47 am
That is amazing - a really great image. Out of interest, how many machines were you running it across, how long did the job take, and what implementation of map-reduce were you using (Hadoop / Google / A custom version)?
Steve said,
March 3, 2008 at 6:26 am
This is very cool. I am currently learning about MapReduce in a class I’m taking on parallel processing. I would be interested in seeing the code you used to generate the image to see how you split the algorithm/data. All of the MapReduce examples I’ve seen are all about counting words in documents and distributed searches/grep. They are overly simplistic and don’t really provide a clear idea of how to apply it more complex problems.
Is your code posted somewhere?
tom said,
March 25, 2008 at 11:10 pm
how long did it take to render?
Cody-7 said,
May 8, 2008 at 10:25 am
Or better yet, what program did you use to render the nebularot?
I’m trying to make my own renders but I’m not having much luck finding a good program. It seems it’s the big thing for everyone to render a mandlebrot sent and not tell what program was used.
Tim Wintle said,
May 23, 2008 at 12:53 am
Cody-7:
The point is that he wrote the software himself using the map-reduce programming model - it’s not that tough if you happen to have a map-reduce cluster lying around (or even if you don’t - the map-reduce model works with unix pipes; which are in OSX, and were on Windows NT too, but I think they removed pipes in XP)