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I've been idle for a while, but here's something new.

http://www.youtube.com/watch?v=IJrzX4d-_0U

I'm not sure who first discovered/invented this, but the only reference I can find to it is on theory.org.

This fractal is absolutely amazing. This just scratches the surface, one particular zoom into an area that kind of resembles the Burning Ship. It seems to be a dust-like region, with no mini-Buffalos found despite careful searching. But it's not as boring as most Julia sets are for ultra-deep zooms. Quite a treat.

This is a deep zoom from 10 to 1e-227. It is 15 minutes long, 27000 video frames of 1600x900 HD. I uploaded a 10Mbps MP4 file to YouTube, but who knows what they will do to it. The adulterated, high-quality version is available at  www.hpdz.net/Animations/BuffaloDeep1.htm   (http://www.hpdz.net/Animations/BuffaloDeep1.htm), along with nice video frame images and a ZIP file with a representative sampling of the huge primary images that fed the interpolation to make the video frames.

I made a 20 Mbps version and burned it to a Blu-Ray disc, then played it on my Blu-Ray player on a 55-inch TV. Very cool. Unfortunately, it's 2.3 GB, and not practical for download, or upload either. Maybe I can offer it on BD with some other videos?

This took about 6 days (151 hours) to render on my Core i7 980X system. 870 very large primary images were interpolated to generate the 27000 video frames.

Music by Technetium.

Enjoy. More to come soon.

I'm trying to work out the Buffalo formula as code.

so if a Mandelbrot is.
r2=r*r
i2=i*2
i=r*i*2+y
r=r2-i2+x

Buffalo is ?

r=abs(r)
i=abs(i)
r2=r*r
i2=i*i
i=2*r*i-i+y
r=r2-i2-r+x

Yes, that looks right to me.

If Z = a + bi

then for each iteration let Z = |a| + |b| i

and proceed as with the Mandelbrot function Z = Z*Z + C and it looks like what you wrote is right.