*Continued* SuperFractalThing: Arbitrary precision mandelbrot set rendering in Java.

[Kalles Fraktaler]

Where is the "button"?

[claude]

In KF2 after you've implemented it

There should be enough hints in recent forum postings for you to be able to code it up

(I'd try myself but you haven't ported KF2 (or at least its build system) to Linux yet )

[hapf]

... which could be offset to some degree if you also increase the number of terms in the series approximation as you go, but the return on that seems to be negligible without using a prohibitively large number of terms.

In the typical deep zoom scenario with a central dominant minibrot each doubling of coefficients gives you another reference period of iterations to skip till the iteration range of the image is reached. Whether it pays off depends on the period, image size and iteration range of the image.

[Kalles Fraktaler]

In KF2 after you've implemented it

There should be enough hints in recent forum postings for you to be able to code it up

(I'd try myself but you haven't ported KF2 (or at least its build system) to Linux yet )

claude, I read your hints but I got stuck on the very first step, to determine the period of the minibrot.
What is "I" in the function m_d_box_period_new?

Code:

box->z[0] = box->c[0] = center + ((-radius) + I * (-radius));

[claude]

The imaginary unit (square root of -1).  It's how to construct complex numbers in C99.

[Kalles Fraktaler]

The imaginary unit (square root of -1).  It's how to construct complex numbers in C99.

Code:

box->z[0] = box->c[0] = center + complex<double>(-radius, -radius);

?

[claude]

yep, and similarly for the other corners of the box

[Kalles Fraktaler]

Cool, works like a charm!
The period grows brutally, an also the required time, especially when close passing minibrots
Sometimes it fails to get the period but then I just need to do one or two further zooms and it works again. The cause is probably miss-centered guessing point or too close to a minibrot.
I haven't encountered the Newton function to fail yet, as long as I get the period

[claude]

yay! 

[hapf]

Cool, works like a charm!

What exactly does the "button" do now? 

[Kalles Fraktaler]

What exactly does the "button" do now? 

I'm just familiarizing a little with this function currently.
What should the "button" do?
Jump directly to the minibrot? Or jump to 3/4 depth of the minibrot, where the pattern in view is doubled?
Perhaps let the user choose?

[stardust4ever]

Cool, works like a charm!
The period grows brutally, an also the required time, especially when close passing minibrots
Sometimes it fails to get the period but then I just need to do one or two further zooms and it works again. The cause is probably miss-centered guessing point or too close to a minibrot.
I haven't encountered the Newton function to fail yet, as long as I get the period

I'm just familiarizing a little with this function currently.
What should the "button" do?
Jump directly to the minibrot? Or jump to 3/4 depth of the minibrot, where the pattern in view is doubled?
Perhaps let the user choose?

Kalles, I have a set of coordinates for you to play with. I have just earlier today generated a row of "X" chromosomes consisting of 1024 copies.

Please view my 1024X long formation here in the image gallery for coordinates and download of the Mandel Machine parameter file.
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/1024x-long/

See also my deviantart page for full view of the formation. I'll admit he image (25600x640) is a bit lengthy with it's 40:1 aspect ratio.
http://stardust4ever.deviantart.com/art/1024X-Long-595637805

I haven't played with Kalles Fraktaller or updated recently but generally I find the "Find Centroid" button in Mandel Machine to be unreliable with the results being little better than human guessing. Zooming into the various points that lie between the little X chromosomes generate a form of binary gray code (if you find a short row of X chromosomes after zooming in a few levels, you have guessed wrong), the patterns therein which allow me to make an educated guess as to how many units sideways I need to move over. After a few tries I usually get it, but the process of trial and error is not quite intuitive. Perhaps you can zoom out of the 1024X formation a bit and test the minibrot finding algorithm.

Take care...

[hapf]

Kalles, I have a set of coordinates for you to play with. I have just earlier today generated a row of "X" chromosomes consisting of 1024 copies.

Please view my 1024X long formation here in the image gallery for coordinates and download of the Mandel Machine parameter file.
http://www.fractalforums.com/images-showcase-%28rate-my-fractal%29/1024x-long/

That's a cool looking place, and pretty easy on the CPUs too. 
Can you see how much Mandelmachine skips here? It's a very skippable place.
I have to look into this automatic fork points and other interesting places finding stuff some more, definitely. 

[stardust4ever]

That's a cool looking place, and pretty easy on the CPUs too.  
Can you see how much Mandelmachine skips here? It's a very skippable place.
I have to look into this automatic fork points and other interesting places finding stuff some more, definitely.  

Define "skippable" for me. Not sure what you mean. I purposely chose a seed location near the seahorse valley area of the large west minibrot with basic dendrites and low zoom depth, so I could take the XX formations to extreme proportions without excessive zoom depth or iterations.

Each "chromosome" has a pair of Xs embedded in it, although the true centroid is located between the two centermost chromosomes. Generally I find that the majority of the image renders successfully following the first orbit (I zoomed into the centroid about 60 zooms or so beyond the target formation so it is flawlessly centered for the purpose of rendering the image), and the little pairs of Xs within the centers of the larger X formations generally require a second pass to render. These orbits of these areas likely point to a different minibrot somewhere within the set with different periodicity. At normal aspect ratios and preview resolutions, you cannot resolve the individual X components while the entire formation is in view. Once zoomed in, it is impossible to determine visually which shape is the true centroid.

Reason why I posted this formation is because the "find centroid" button typically fails in formations like this where a single object is multi-replicated a gazillion times in a straight line. You may need to zoom out slightly here since the true centroid is located on the central pixel in this image. By knocking the image off center, one can select the "find centroid" tool to let the software attempt to relocate it. If when zooming a few dozens of zoom levels deep between two of the chromosomes, you find a formation consisting of a shorter row of little X formations, you are on the wrong path and guessed wrong, or the "find centroid" function has failed to select the correct path to the minibrot. The true centroid leads only to "X of Xs" formations with 4 or higher symmetry from here on to the Minibrot which should be located close to ~4000 zoom levels. A minibrot finding algorithm that fails on fringe formations such as this one would likely fail again and again because with every wrong turn it will eventually encounter the same tricky formations over and over, and possibly never locate the true minibrot.

[hapf]

Define "skippable" for me. Not sure what you mean.

One can skip here over 99% of iterations. Very skippable. 

Each "chromosome" has a pair of Xs embedded in it, although the true centroid is located between the two centermost chromosomes. Generally I find that the majority of the image renders successfully following the first orbit (I zoomed into the centroid about 15 zooms or so so it is fairly centered), and the little pairs of Xs within the centers of the larger X formations generally require a second pass to render. These orbits of these areas likely point to a different minibrot somewhere within the set with different periodicity.

The whole region is dominated by the central minibrot of period 82432 so it's trivial to go further in that direction and using this as reference the image can be rendered cleanly without further references according to my program (for the resolution I chose which was < 4K ). Minibrot has size ~5E-1197. There is no problem in such a case if you want to go towards the central minibrot. There is only a problem when the dominant minibrot is further up. Here something based on image features might be useful if you need to go down in the center of the current circular structures. Maybe the period of the upcoming minibrot can be computed from the current position before it's dominant. There must be some rules...