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Author Topic: Fractal eXtreme  (Read 8021 times)
Description: very fast and very deep
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Dinkydau
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« Reply #30 on: February 14, 2012, 08:52:01 AM »

Bruce Dawson of Cygnus has kindly built the plugin under MSVC2010 and the crash problem has gone away.
New link for the plugin http://www.mediafire.com/?sllaetoodr3txg7

and now we have a 64bit version too! http://www.mediafire.com/?4w4jc5scv3z2ixw

Thanks for this. I'll try it out.
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panzerboy
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« Reply #31 on: February 19, 2012, 12:13:45 AM »

New plugin for Fractal Extreme.
It includes the Burning Ship with a slight improvement for the Julia's if you zooming in on the Origin (reflecting the real and imaginary axises (axisii?)).
Now includes Celtic and Buffalo fractals plus their julia variants.
To install remove the Burning ship plugin as you can't have two plugins generating fractals with the same name.

http://www.mediafire.com/?c84ep2e281a6bve 32 bit
http://www.mediafire.com/?52ih8j80p2h9oev 64 bit
http://www.mediafire.com/?nimv9h31mp6nwtr Source code

I've removed the Burning ship plugins as this superceeds it.
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panzerboy
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Posts: 200


« Reply #32 on: February 19, 2012, 02:38:00 AM »

Decided to create a SourceForge project. Saves having to change mediafire URLS each time I upgrade.

For Burning Ship, Celtic and Buffalo fractals (and Julia versions) download one or more of the files here.

http://sourceforge.net/projects/fxabsmandvar/files/
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PhotoComix
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« Reply #33 on: February 19, 2012, 03:13:49 AM »

Hem sorry this was a old post and i had no the patience to see if get a reply along this long tread

James,

Fractal eXtreme and UltraFractal both work *mostly* well under WINE.  I say mostly because of FeX's export of anims not, well, exporting.  At least in the test runs I've done, it doesn't do anything and throws an error about pathing.  I'm wondering if it's the CODEC interpretation, permissions, or some other bugger.  Haven't figured it out.  Of course, haven't looked very hard, either...I like both FeX and UF, but even now as I type this, Mandelbulber, Mandelbulb3D and MDZ are the ones running, soooooo....you know... smiley

In case not i believe the path error come simply by the Linux and Windows path using different syntax :
"/" instead of "\" so should be simple to fix (but since is not a Open Source program fix may be more complex)
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stardust4ever
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Posts: 97


« Reply #34 on: February 19, 2012, 11:54:49 PM »

Thank you Panzer for generating these fractal formulas. I watched a video of your Buffalo fractal a few days ago and thought it looked fascinating. I also have a small request if it isn't too much to ask; I would like to see the perpendicular Mandelbrot (order 2 Mandlelbulb vertical slice) and the three-armed Mandelbar variation, which includes minibrots as well as minibars within it. It seems while I have a decent grasp of the mathematics involved, I don't know a thing about computer coding (though I did once write a simple TI-Basic program using floating point complex math to draw a mandelbrot on a Texas Instruments Voyage-200 calculator screen, but never published it because it took over 24 hours realtime to draw the set with a 25-iteration bailout - I emulated the results on a PC in a couple of hours time, but on an actual calculator with fresh batteries, the batteries would likely die before the program finished).

I downloaded the zip files, but can't play with these new formulas yet because I'm in the process of rendering a zoom movie. If I attempt to replace the files while FX is running, the results would likely not be pretty.

Is there any chance that Bruce Dawson will upload these fractals to his website or include them in a future FX release? The only third-party plugins I was aware of beforehand were the Serpenski triangles and some packed circles fractal, which looked exactly the same no matter how deep you zoomed.
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stardust4ever
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Posts: 97


« Reply #35 on: February 20, 2012, 12:28:55 AM »

Sorry for the double post. I installed the 32-bit plugin so it won't interrupt the zoom movie I'm doing in the 64 version.

Here's something you won't find in a million years within the Mandelbrot set: A deep zoom with two minis. Just select the buffalo fractal and zoom into the rightmost tip of the needle. You have to pick a dendrite on the top edge of the needle. There you will find the twin mini-buffalos! This render was done at a modest 179 zoom levels... afro


* Twin Buffalo 179 zooms.jpg (231.34 KB, 856x480 - viewed 76 times.)
« Last Edit: February 20, 2012, 12:37:10 AM by stardust4ever » Logged
panzerboy
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Posts: 200


« Reply #36 on: February 20, 2012, 05:50:42 AM »

If this is the mandlebar
http://en.wikipedia.org/wiki/Tricorn_(mathematics)
Then you wont get any advantage from Fractal Extreme's fast arbitrary precision maths.
Fractal Extreme's plugins work in two modes, the first is floating point and the second is Bruce Dawson's 'High Precision' type which can be up to 7200 bits long.
But there are only enough high precision arithmetic functions to do a mandelbrot - multiplication, addition and subtraction.
There are a few other like left and right shift and most importantly for my plugin a negate and negative test so I was able to do the abs() function.
The tricorn does a power of -2, which is like (1/x)/x. Trouble with division is that its a computationally intensive operation.
Check out the clock cycles for any microprocessor and you'll see division takes the most cycles (if provided at all, early ARMs had no division).
With multiplication you can speed up the process by working in parallel, each bit of the multiplier is ORred with the entire multiplicand and then shifted to the relevant position.
The results of the ORs are then summed. The ORring can happen all at once as nothing is dependant, the summing can be sped doing half the additions in parallel and so on.
Division requires the input to be the output of the previous step, to do division its essentially repeated subtraction of the divisor then shifting the divisor down and repeating.
http://en.wikipedia.org/wiki/Division_(digital)
No parallelism is possible. (Okay a GPU could work on many divisions at one time but Fractal Extreme calls the calculation plugin one complex coordinate at a time).
So you'd be limited to the floating point 42 zoom limit, and  for that UltraFractal is just as fast and has much easier customised equations.

I had a look for the mandlbulb and the formula I found has square roots and atan functions.

Bruce has offered to add a link to my plugin on the Cygnus Software web page.
« Last Edit: February 20, 2012, 09:21:41 AM by panzerboy » Logged
stardust4ever
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Posts: 97


« Reply #37 on: February 20, 2012, 06:37:16 AM »

I recall there were two different formulas for the 3D Mandelbulbs. One formula version used trig functions, and the other version used polynomials. The poly functions were much faster for the lower orders than the trig functions (especially 2nd order), but due to the complexity of the higher order polynomial, the trig functions became much faster for bulbs higher than order 8. I'm trying to find some old posts about it here in fractalforums which I remembered reading a long time ago, but the search function is practically broken. I know the polynomial functions did not use trig, but they may have still incorporated a variable "r" where r = sqrt(x^2+y^2+z^2) which would still be problematic. I can't find it, but there is a post somewhere on fractalforums which lists the polynomial equivalents of mandelbulbs for orders 2 through 8. If I can find that post, I can just reduce the set x,y,z by setting y=0 and then reducing the equation to x and z using basic algebra, but I know for a fact there is a polynomial version of the equation which does not use trig functions.
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simon.snake
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Posts: 447


Experienced Fractal eXtreme plugin creator!


simon.fez SimonSideBurns
« Reply #38 on: February 24, 2012, 12:16:22 AM »

Hi guys

Panzerboy, thanks for the information on what operations are available in Fractal eXtreme.  I have written the following formula in Fractint:


smf-test-03 {
  z = p = (0,0) - pixel
  i = imag(p)
  r = real(p):
  z = z * z + i - r
  |z| < 4
  }

I don't expect for one minute that I have come up with something new (I thought I had the other day and it turned out to be the buffalo previously mentioned above) so if anyone has seen this one before and knows the name of it, that would be useful to know.

Now, I believe this code wouldn't be too hard to turn into a plugin but I simply have no clue about it.  The resulting output in Fractint looks like the following images (successively zoomed in):











Please could someone take the time to create a plugin if possible (64-bit version) as I'd love to explore this one much quicker.

Thanks in advance.

Simon
« Last Edit: February 24, 2012, 07:45:20 PM by simon.snake, Reason: Wanted to clarify a few things... » Logged

MOTEL BRAND = Anagram of MANDELBROT

Can anyone do any better?
simon.snake
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Posts: 447


Experienced Fractal eXtreme plugin creator!


simon.fez SimonSideBurns
« Reply #39 on: February 24, 2012, 07:42:44 PM »

I've asked for a new board to be set up for Fractal eXtreme and this has been done.  It has two child boards, one for plugins and one for gallery.

I don't know if it is at all possible but I wonder if this long post can be split (as it has become a bit muddled) and relevant parts placed in individual posts?

Maybe someone could see if it can be done, or is it something one of the users will have to do (copy and paste into several new posts).

Simon
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MOTEL BRAND = Anagram of MANDELBROT

Can anyone do any better?
panzerboy
Fractal Lover
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Posts: 200


« Reply #40 on: February 25, 2012, 12:39:18 PM »

Hi guys

Panzerboy, thanks for the information on what operations are available in Fractal eXtreme.  I have written the following formula in Fractint:


smf-test-03 {
  z = p = (0,0) - pixel
  i = imag(p)
  r = real(p):
  z = z * z + i - r
  |z| < 4
  }


I'm having problems trying to implement this. I've never used Fractint but I found a page giving a tutorial.
http://www.nahee.com/spanky/www/fractint/frm-tut/frm-tutor.html#learn_more_complex_anchor

My code looks like
Code:
double zrsqr = zr * zr;
double zisqr = zi * zi;
double origzi = 0 - zi;
double origzr = 0 - zr;
zi = origzi;
zr = origzr;

int count = 0;
for (/**/; count < MaxIters && zrsqr + zisqr < OverFlowPoint; count++)
{
zi = zr * zi * 2.0 + origzi - origzr;
zr = zrsqr - zisqr + origzi - origzr;
zisqr = zi * zi;
zrsqr = zr * zr;
}


This results in an interesting shape but nothing like your examples.



* SnakeBrot.jpg (3.65 KB, 260x221 - viewed 302 times.)
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simon.snake
Fractal Phenom
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Posts: 447


Experienced Fractal eXtreme plugin creator!


simon.fez SimonSideBurns
« Reply #41 on: February 25, 2012, 05:43:31 PM »

Panzerboy.

It's getting closer, but not quite there.

I just can't seem to get my head around converting z = z * z + c into the required arithmetic operations that work on the real and imaginary parts of the pixel coordinates at all!  For example, where does the 2.0 in the middle of the calculation come from?  Just doesn't seem to sit right in my brain.

I've got even less chance of working out how to change the sample plugin code into something resembling my formula.

Ah well, keep up the good work.

Simon
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MOTEL BRAND = Anagram of MANDELBROT

Can anyone do any better?
stardust4ever
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Posts: 97


« Reply #42 on: February 25, 2012, 10:20:48 PM »

One thing that I found fascinating, was there are a lot of minis in the Burning Ship fractal that look like Celtics, as well, there are a lot of minis in the Celtic that look like burning ships. Because the Celtic Mandelbrot uses the abs(r), and the Burning Ship fractal uses the abs(i), while the Buffalo uses it on both (I think). Because the minis have all sorts of orientations, a mini in one fractal set can have a variety of different shapes, which is fascinating.

Because the positives and negatives behave differently on the real axis, I wonder if -abs(r) would produce something different from the abs(r) formula of the Celtic Mandelbrot, or would it just flip it? I noticed both the burning ship and Buffalo appear flipped on the real axis (needle points right instead of left) compared to implementations in other software. Not really an issue, just an observation.

Panzerboy, you mentioned earlier that the Fractal Extreme software cannot handle arbitrary precision on long division or irrational functions, but it has built-in plugins for fractional and complex powers, which can be calculated to arbitrary precision, albeit much more slowly than the others. Non-integral powers are definitely irrational, as well the sqrt function which is equivalent to a power of one-half, eg sqrt(Z) = Z^0.5
« Last Edit: February 25, 2012, 10:27:28 PM by stardust4ever » Logged
panzerboy
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Posts: 200


« Reply #43 on: February 26, 2012, 01:27:40 AM »

My First attempt was upside down which clued me in that I needed to subtract the imaginary (y-axis) component.
Most examples I found had the bowsprit pointing left so I subtracted the real constant (flips x-axis) as well.

I'll bet that the fractional and complex powers code exists in the MandN plugin.
There's no way for another plugin to access that code.
Bruce Dawson would need to expose the code in a library, as he has done for High Precision Math.
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stardust4ever
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Posts: 97


« Reply #44 on: February 26, 2012, 09:25:23 AM »

I know I'm asking the wrong person here, but does anyone have any idea what kind of formula the Hidden Mandelbrot uses? It's like it has all the normal features of the Mandelbrot set, but it's full of parasitic cobweb-like structures which really become vividly detailed at higher bailout values (I used 1024). There's also an ugly triangle shape with distorted minis embedded in the cobweb material. It's totally unique fractal I've not seen elsewhere, which is mostly-connected, quite unlike Panzarboy's fxabsmandvar fractals. I'm not at all familiar with x86-64 assembly code, so I have no idea if it's possible to reverse-assemble a .DLL file to look at it's guts. Probably not an ethical thing to do anyway, even if it is possible. cop

On an unrelated note, does anybody else use free Avast Antivirus? I noticed that my anit-virus updated the other day, and it flagged the FX main executable and the zoom movie player (both 32-bit as well as 64-bit versions) as potentially unwanted/malicious program and prompted me to open it in a sandbox environment. I selected the "Open normally" option and checked the box to "always perform this action." Kind of a nuisance, but I'm sure it's all on Avast's end. Maybe the new update has an over-zealous heuristics engine? For the record it also flagged a couple of other open-source non-fractal-related software I downloaded as well.
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