SuperFractalThing: Arbitrary precision mandelbrot set rendering in Java.

[quaz0r]

so did anyone end up having any thoughts on if this could be applied to 3D fractals?

[cKleinhuis]

when i asked a mexican pysics prof, he was wondering why we were not using the method all the time, because they are
so, it is obviously perfectly appliable to other stuff as well, and might work as well in the 3d world, but it is a time consuming
act to crteate such a derivative, and for 3d, we have just scratched the surface, in the mandelbrot we are now so deep, but
in 3d we are just happy playing in the floating point range of single precision and being happy when using double precision
haha, just my 5 cents for now!

[claude]

I wrote up the maths for applying perturbation technique to the derivatives (including interior distance estimation):

http://mathr.co.uk/mandelbrot/perturbation.pdf



7 layers rendered
1920x1080
10000 maxiters
256bits mpfr reference
long double deltas
view height 1e-28
view center -1.98550202011904056068063519696893288601496598579e+00 + 2.885647596682972207197242785497600947886440918943e-05 i
reference period 242
reference point -1.9855020201190405606806351970070281728451e+00 + 2.8856475966829722071972434856944234406073e-05 i

calculations took 3m45s (13m45s CPU), considerably longer spent taking 5 of those layers and colouring/combining in Gimp (ended up with 57 layers/groups, mostly non-destructive)

[Roquen]

The blue lines are period boundaries?

[claude]

Yes - edge detection filter on the period layer (iteration count when |z| reached its minimum).  The other layers are binary "did it escape", integer iteration count, fractional iteration count, final angle, distance estimate (interior and exterior), error estimate.

Currently thinking about modular data interchange between different programs http://www.fractalforums.com/programming/separation-between-calcuation-and-colouring/

[simon.snake]

The black ring two thirds to the right are like ants defending their queen.

Interesting shades.

[Kalles Fraktaler]

Thanks claude, I have used a variant of your method http://www.fractalforums.com/movies-showcase-(rate-my-movie)/many-colors/msg67653
I wish there were a way to find any internal structure in thos one-iteration blobs arising from passing the elephant valley of a minibrot.
Can you create an image of such blob with structure?

[hapf]

Thanks claude, I have used a variant of your method http://www.fractalforums.com/movies-showcase-(rate-my-movie)/many-colors/msg67653
I wish there were a way to find any internal structure in thos one-iteration blobs arising from passing the elephant valley of a minibrot.
Can you create an image of such blob with structure?

Coordinates?

[Kalles Fraktaler]

Coordinates?

The final Minibrot in the movie is at

Code:

Re: -1.985548413352953418245678803517026040561987431985854276276406746845711126058992474579439478412845298466360323561521794573490777860670882406445312
Im: 0.000000000000274306712672969455617528764603215423726345502418759902114885912945984840541117978004928867607475994687127795505515616117151017291663
Zoom: 6.99920231869E100
Iterations: 142811

The images in the explanation is the left detail on Zoom 7e71

[hapf]

The final Minibrot in the movie is at

Code:

Re: -1.985548413352953418245678803517026040561987431985854276276406746845711126058992474579439478412845298466360323561521794573490777860670882406445312
Im: 0.000000000000274306712672969455617528764603215423726345502418759902114885912945984840541117978004928867607475994687127795505515616117151017291663
Zoom: 6.99920231869E100
Iterations: 142811

The images in the explanation is the left detail on Zoom 7e71

Like this?

http://img19.imageshack.us/img19/7751/qv96.jpg


Can be done with one good reference point. (Excuse the horrible colours. They show detail at least.)

[blob]

Like this? (Excuse the horrible colours. They show detail at least.)

Nothing wrong with those colors at all, I really like that kind of coloring. 

[hapf]

Nothing wrong with those colors at all, I really like that kind of coloring. 

 

[Kalles Fraktaler]

Like this?
Can be done with one good reference point. (Excuse the horrible colours. They show detail at least.)

I also like your colors , but what I wanted to see was if claude's error function, with all the square roots and use of the complex datatype instead of treating the imaginary and real parts separately, would give any structure in the big one-iteration-count blob at right...

Anyway, where did you put that one reference, is it inside one of the dense round formations just right of the center of the image?
I can also get a decent image if I put one reference there, but the image will still not be correctly rendered. The reindeer-horn shaped glitches do get some structure inside, and I selected colors on the images below to make it more visible, but the structure is simpler than the real structure. It might not be significantly visible on this image but it will be more obvious if you zoom in on one of the reindeer horns.
But I am not sure, you may be able to get a correct image with one reference only since I believe you use long double also for this zoom level?

Here is how it looks when I render the location with one reference only:

And here with additional references in the reindeer horns:

Close-up on the horn with one refrence

And with additional references

[Nahee_Enterprises]

            ..............
    But I am not sure, you may be able to get a correct image with one reference only since I believe
    you use long double also for this zoom level?
    Here is how it looks when I render the location with one reference only:
            http://biphome.spray.se/karl.runmo/glitch1.jpg
    And here with additional references in the reindeer horns:
            http://biphome.spray.se/karl.runmo/glitch2.jpg
    Close-up on the horn with one refrence
            http://biphome.spray.se/karl.runmo/glitch3.jpg
    And with additional references
            http://biphome.spray.se/karl.runmo/glitch4.jpg

Until you showed the close-up, it was difficult to discern any real difference between the two images.   
 

[hapf]

Anyway, where did you put that one reference, is it inside one of the dense round formations just right of the center of the image?

That is the multi million dollar question.  
You have to put the reference where the image has the highest iterations.