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A slightly early Christmas present to y'all: a (slightly) deep M-set zoom I ran into on the way to deeper things. Because it only barely requires bignum arithmetic and the iterations are so low, the image could be rendered in only half an hour or so on my equipment. Consider it a bonus of sorts.

Without further ado...



A straightforward one-layer image colored by smoothed iterations, of a microbrot on the spike in the big minibrot's Elephant Valley. Zoom into a "cumulus" mini-julia on the spike, then at the spike between the left pair of big spirals, then into another mini-julia to find a microbrot similar to this one.

This one was right on the border between long double and bignum arithmetic, to the point that the 640x480 preview didn't use bignums but the final 2048x1536 render did.

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

Detailed statistics:

Name: All Roads Lead To Rome
Date: December 23, 2009
Fractal: Mandelbrot
Location: Elephant Valley of big spike minibrot
Depth: Moderately Deep (21 decimals)
Min Iterations: 269
Max Iterations: 17,257
Layers: 1
Anti-aliasing: 3x3, threshold 0.10, depth 1
Preparation time: 10 minutes
Calculation time: 35 minutes (2.5GHz dual-core E5200)

So it takes 1/2 hour to render this as a 3x super-sampled 2048x1536 image? (6144  4608 samples) That is using "bignum" arithmetic? How many bits of precision are in "bignum"? Is it arbitrary?

Where did you get the math library to do your bignum calculations? My app uses long doubles to calculate pixel coordinates, and doubles for iterating. I haven't resorted to long doubles, even, because I want it to be fast. I've debated recompiling with long doubles, or even finding a higher precision than that. I think I would add a preference to switch between types so I could still offer fast calculations.

For comparison, I rendered a plot that looks a whole lot like yours, at lower zoom. I don't support super-sampling, so I rendered it at 6144x4608 pixels, and it took about 4 minutes. That's on a 2.4 ghz Core 2 Duo (2 core) Mac. It's definitely worth only using higher precision when you have to, since the native double precision on current hardware is VERY fast.

I used fractional iteration counts to get smooth coloring. If I had turned that off it would have been a lot faster because I would have been able to use boundary following That would enable me to not even calculate quite a few of the pixels.



Duncan C

Yeah, sure, though in a real life scenario you don't have an infinite iteration count, lowering the lenght....

Actually, in this case many of the tendrils are basically just straight lines. (Some curve slightly, and some a lot more.) Most other areas of the M-set though and they would indeed wind and wiggle at every scale.

I think they call that "sepia".    
 

Ha!  You're right!  I guess it turns out that I'm just a fan of old photographs.