Welcome to Fractal Forums

How many of you have ever heard of, or seen, the "Burning Ship" fractal?

Within FractInt (http://www.Nahee.com/spanky/www/fractint/fractint.html), the basic formula is just this simple:

        z = abs(z)
        z = z*z + #pixel

It is a favorite of many a fractal enthusiast.   And a brief explanation may be found on Wikipedia (http://en.wikipedia.org/wiki/Burning_Ship_fractal).   Several good links can be found at the bottom of that web page in the "External links" section (including a URL to a video).

Here are a few more that hold images and/or information:
    http://local.wasp.uwa.edu.au/~pbourke/fractals/burnship/ (http://local.wasp.uwa.edu.au/~pbourke/fractals/burnship/)
    http://sbchukill.blogspot.com/2008/09/burning-ship-fractal.html (http://sbchukill.blogspot.com/2008/09/burning-ship-fractal.html)
    http://www.flickr.com/search/?w=all&q=burningship&m=text (http://www.flickr.com/search/?w=all&q=burningship&m=text)
 

Ah...yes, I know the burning ship formula and I know it is one of GFWorld's (Margit) favorite formulas.  one example: http://www.fractalforums.com/gallery/?sa=view;id=154

i also like the burning ship formula :D especially because of its simplicity ...

Thank´s for Info Paul  :)

As Titia wrote >Ah...yes, I know the burning ship formula and I know it is one of GFWorld's (Margit) favorite formulas...

Yes  - I like this Formula :-)))

I like it for both, Fractal - and Photoplays.
And, a lot of images at my site have beside PP their
* roots * here :-)))
***
Trifox wrote > simplicity  ... I think too, would
mention here  * abs & symmetry * components too :-)))
Margit

another reason why i absolutely like the formula is its decent 3d effect ...

After Lloyd Garrick ("Jack Of TraDeZ") followed the link Titia gave to your graphic, he had this to say about the image:


I am sure he would love turning that into one of his famous videos at Fractal-Animation.net (http://www.fractal-animation.net/).     ;)     :D
 

Paul wrote >After Lloyd Garrick ("Jack Of TraDeZ") followed the link Titia gave to your graphic, he had this to say about the image:
Quote
   Awesome!  Looks gothic, almost H.R.Gigerish -- like something from the "Alien" movies.
   Give me a FractInt .PAR for it .........

Hi :-)))

I took time for a look now ...

The file is created with a version from DigiGraph
developped by Dr. Joseph Trotsky & Rico Wack,
but the program is not available anymore.

We all liked to do a lot in the past here, actual I am happy to
have a still working version, with Win Vista too :-)

***
The Image / Fractal is a * Mini Version * very far
away & a photoplay here.

***
I think it makes no sense to send the file,
but I keep the 3200 x 2400 Image - if you like it, tell me :-)))

The photo for itself is not really a great one, but it works & I could send it too :-)))

Margit

ehrm, i lost something, about what speciall image are you talking ??!?

This:

Burning Ship {; correct?
z = abs(z)
z = z*z + pixel }

or this:

Burning Ship {; correct?
z = abs(z)
z = z*z + #pixel }

do not work, just get a blank screen.
I put in an ascii file named SHIP.FRM and navigated to it in fractint from the T key.


hey hey hey hey .... it's just a sunny day ....

can't get it out of my head
love that tune wish I knew who is singing

missing semicolons after each statement =?

I only had a few seconds to give it a try, but here is something that might get you started in the right direction.

Hmmm i'd not heard of this so had to look. Interesting!

(http://www.wackerart.de/FractalGraphicsII/burning-ship.jpg)

http://www.wackerart.de/burning-ship.html (http://www.wackerart.de/burning-ship.html)

I have some Burning Ship fractals on my homepage. With a Java-Plugin in your browser it is possible to explor the details.
This algorithm produces fascinating structures:

(http://www.wackerart.de/FractalGraphicsII/burning-ship-2.jpg)

Hermann, I love that dark red fractal-they really do look like tall ships!

Yeah, I'm familar with the burning ship fractal. I always thought it looked a bit like a mistake. I wonder if this formula can be 'made 3D'?

The combination of a _folding2 and a integer power 2 alternated leads also to a burning ship variant, with some crap around.
But there should be more than one ways to get a 3d version.

The following is a detail of a burning ship fractal.

(http://www.fractalforums.com/gallery/2/1307_18_07_10_11_05_20.jpeg)

This one is a detail of a Burning Ship Julia.
(http://www.fractalforums.com/gallery/3/1307_02_08_10_9_54_48.jpeg)

It will be interesting to see a 3 D Version.

there are some REALLY good images here:

http://www.wackerart.de/burning-ship.html

sure wish I could do them in FRACTINT, maybe animate ...

Here is a burning ship julia fractal!

(http://www.fractalforums.com/gallery/3/1307_11_09_10_9_51_14.jpeg)

Anyone know what fractal type I'd need to use to get a Burning Ship in Incendia? Nice Julia by the way!

As suggested by hermann, I post here the 3D version of the burning ship, done with Mandelbulb3D:

(http://nocache-nocookies.digitalgott.com/gallery/4/492_01_12_10_10_57_48.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4057

That 3D image is AWESOME!  Looks like a Gothic Alien city on some planet - would be cool in a movie or viddie game! I still can not get any of these to work in FractInt; maybe I should try to learn another software and join the 21st century ...........

Thanks :) Credits go to Jesse for the program and the formula scripting, and M Benesi for the formula itself.

I have never used Fractint, so I can't tell how complex it would be to learn the new 3D programs. But I was quite used to Ultrafractal, and switching to Mandelbulb3D was quite easy. For Mandelbulber I would say it would probably be a little bit more complex, but really worth the investment.

what i love most about the burning ship is that also in 3d it looks like an old ship or big space galleon

 :happy:

Wow.

That 3D version of the burning ship is the _most_ amazing 3D-version-of-a-2D-fractal I've ever seen. What I mean is, it actually looks like I would expect a 3D version of the burning ship to look like.

Well done.

...I'm still getting my head around Mandelbulb3D.

Can anyone tell me how i get this fractal in incendia?

That 3D image still looks wonderfull! Perhaps one of the more timeless jewels found here on the forums.

But anyway, not only to bump this topic. Could we do a comparison between the Mandelbrot set and the Burning ship Fractal? Just add and explain, we'll organize into a nice table later on.

Similarities
- Both have a west antenna
- Formulas are very similar
- Miniships are found in the BS, same as Minibrots are found in the MS
- When zooming into a mini, period doubling takes place

Differences
- BS is not symmetrical on the horizontal axis
- BS is not connected
- BS has sharp corners
- BS does not have infinite spirals (the ones without a mini) .... ?? Not sure about this one

My math is not very strong, but it would be nice to apply the comparison on this area aswell. And add visual examples.

Hi guys.

I know this post has only just been resurrected but is anyone still stuck on getting the burning ship working in FractInt?

Only reason I ask is that I've just spent two minutes writing this and I'm happy to share the code if anyone's stuck.  I've also created a slight variant of the fractal too, which I've named KungFuPanda.  You'll see why if you give it a try.

Anyhow, here's the code:


What seemed to be missing in the early replies to this thread was the bailout condition at the bottom (the last line essentially).  Unlike the colon : which simply separates the initialisation from the per iteration code, there's nothing separating the bailout from the rest of the code.  It takes some getting used to, but can give undesired effects if you forget about it.

In case you were wondering about the if (ismand) section, this allows the user to display julias too.  Essentially, you press space bar.  This brings up a crosshair, which you move around on the screen (hold down control if you want it to move faster).  When you are happy with your coordinates, press space again and you will get the julia of the location under the crosshair.  To return to the non julia variant press space once again.  The status of the ismand flag and the location of the julia are saved in the parameters (and embedded within any saved .gif file), but if you want to set one manually or see what it is set to, press z while displaying the fractal to go to the parameters screen.

Here's the KungFuPanda variant I've found:
(http://www.needanother.co.uk/uploads/frac1150.gif)

Any problems, let me know as I've been using FractInt for some time.

There is at least one kind of infinite spiral.

(https://farm3.staticflickr.com/2932/14273592222_b9cf4aa64d_n.jpg) (https://flic.kr/p/nKiTFC)may24_02 (https://flic.kr/p/nKiTFC) by ellarien (https://www.flickr.com/people//), on Flickr

They can be found to the south of the western antenna, on the 'whiskers' that come out where the bulbous part at the eastern end of a miniship dips down below the axis. As far as I can tell there are no minisets down there at all.


Another difference is the tendency in some areas for minisets to appear in close symmetrical pairs, and relatedly the existence of areas where quite elaborate symmetrical patterns form around an empty centre rather than a miniset.

Also in common with the Mandelbrot set:

(http://i.imgur.com/Km6oN2e.jpg)

Looks pretty symmetric around the most vertical axis.

When searching the web, not so many burning ship fractal galleries are found. The few pictures that do exists seem to be focused on the (mini)ship(s). In order to share the beauty of the variety of shapes in this set, it feels good to post some more zoom pictures here in the general discussion:

  1. (http://i.imgur.com/RO9QRnX.jpg)


  2. (http://i.imgur.com/wE1qzkF.jpg)


  3. (http://i.imgur.com/0kKetDf.jpg)


  4. (http://i.imgur.com/j086g8J.jpg)


  5. (http://i.imgur.com/XGcLgsZ.jpg)


  6. (http://i.imgur.com/dNHybms.jpg)


  7. (http://i.imgur.com/GgQmLXP.jpg)


  8. (http://i.imgur.com/VZgOzt1.jpg)


  9. (http://i.imgur.com/h5cvTPI.jpg)


  10. (http://i.imgur.com/y0oZkPm.jpg)


  11. (http://i.imgur.com/bntl5vq.jpg)


  12. (http://i.imgur.com/adYckQz.jpg)


  13. (http://i.imgur.com/XneMerZ.jpg)


  14. (http://i.imgur.com/GaLNz3C.jpg)


  15. (http://i.imgur.com/v4fFUlP.jpg)


  16. (http://i.imgur.com/SeyPBsm.jpg)


  17. (http://i.imgur.com/1XXswSi.jpg)


  18. (http://i.imgur.com/iWZKRbz.jpg)


  19. (http://i.imgur.com/rkemDVS.jpg)


  20. (http://i.imgur.com/SCOyrHB.jpg)


  21. (http://i.imgur.com/iKBpzW0.jpg)


  22. (http://i.imgur.com/rk8GFZI.jpg)


  23. (http://i.imgur.com/UystmZJ.jpg)


  24. (http://i.imgur.com/K46j8PW.jpg)


  25. (http://i.imgur.com/paQ4XFf.jpg)


  26. (http://i.imgur.com/rlAZFGr.jpg)


  27. (http://i.imgur.com/30YCtLD.jpg)


  28. (http://i.imgur.com/o3ZrOJU.jpg)


If anyone is interested, I can attach all location in a zip file. Please let me know if you want the Kalles Fraktaler location files.

Link to gallery on Imgur: http://imgur.com/a/gkCBz/

Wow, nice pictures, youhn!

I've heard a couple people mention that they couldn't find miniships south of the western antenna. Well, I don't know if this counts, but if you look near the lower-rightmost roundish bulb on the bottom of a miniship on the antenna, then look at the whiskers underneath of the antenna tucked right in the cusp above this roundish bulb, you will find miniships.

Interestingly, as you move away from the bulb on the miniship, the miniships will disappear, first by becoming distorted, then collapsing into dust, then turning into an empty void. This could have something to do with the iteration function being locally very non-conformal near those points, whereas above the antenna, the function is locally almost completely conformal, except at the folding lines. That's just my speculation.

Wow, that's really diverse patterns in your set of images!
Very beautiful!
I really like the ones with thick lines in them, image 10, 17 and 25, but all are awesome and while I was scrolling down it got better and better  :o

Btw yes I would like to have the locations in a zip :)

Some are missing, but most locations of the 28 images are zipped and attached to this post. Anyone without Kalles Fraktaler could download it at http://www.chillheimer.de/kallesfraktaler/ or just open the kfr file, since these are regular text files.

Too bad imgur randomized the image file names, but the location should be more or less in the same order as the images.

  Funny, while I worked with the formula that did the 3d burning ship, this other formula I worked with (original mag vs. xyz) seems to follow the pattern of the above image (whoops, page before... ehhh  Youhn's post with the symmetry).  Wondering about the more basic formula now...  Gotta look at that.


  (https://lh6.googleusercontent.com/-TJNNfYmPoc8/TXwtXXUwxXI/AAAAAAAABJY/SZTAdw-NVwU/s480/southern%2520quadrant.jpg)

I think it would be possible.

The current implementation of the 2D Mandelbulb has the Perpendicular Mandelbrot on the XZ plane with the Mandelbrot on the XY plane. Although an original triplex trig system was created to generate the fractal, a polynomial version was subsequently created. I've forgotten the polynomial Mandelbulb formula, but setting all the Ys to zero gives the Perpendicular Mandelbrot set on the XZ plane.

The formula for the Perpendicular Mandelbrot set is:

Zr1 = Zr^2 + Zi^2 + Cr
Zi1 = |Zr| * Zi * -2 + Ci

The formula for the Mandelbrot set is:
Zr1 = Zr^2 - Zi^2 +Cr
Zi1 = Zr * Zi * 2 + Ci


Because the Burning ship fractal is asymmetric, if doing a mandelbulb burning ship, it may help to make the fractal represent the burning ship along the vertical axis, and use a symmetric fractal along the horizontal axis. The Burning ship fractal is similar to the Mandelbrot with an abs() command applied to the the Zi portion of the equation:

The Burning Ship fractal:
Zr1 = Zr^2 - Zi^2 +Cr
Zi1 = |Zr * Zi| * 2 + Ci

Likewise, applying an abs command to the Zr portion instead will yield the sister fractal "Celtic Mandelbrot":

The Celtic Mandelbrot fractal:
Zr1 = |Zr^2 - Zi^2| +Cr
Zi1 = Zr * Zi * 2 + Ci

The Celtic Mandelbrot, along with Celtic Mandelbar,
Zr1 = |Zr^2 - Zi^2| +Cr
Zi1 = Zr * Zi * -2 + Ci

are sister fractals to the Burning ship, all with similar types of designs withing them. The Burning ship can have minis shaped like Celtics as well as Burning ships and other shapes in between, likewise for the Celtic varieties. (remember, the burning ship is chiral so it along with it's mirror image form half of the group. I have an theory, but not rigid proof, that the orientation of the mini in part determines it's shape)

Anyway, I believe if a triplex system of algebra could be formulated such that the burning ship is on one axis with one of the two Celtic varieties on the other, that beautiful patterns could exist in such a fractal.

(http://i.imgur.com/Km6oN2e.jpg)

EDIT: I've been out of the loop too long on this one, looks like it's already been made. The screenshot definitely looks Celtic to me, if it is in fact a slice of the BS Mandelbulb... :tongue1:

That image was created with Kalles Fraktaler, from the standard 2D burning ship. Params:

Re: 0.642889267562326942967270123357015
Im: -1.22729902944794937886379577301386
Zoom: 1.0E10

I've been hacking the source code of Mandelbulber 1.12-1 a little bit. While understanding just a little about the whole 3D fractal math thing, I came up with this change:



This results in images like:

(http://i.imgur.com/k2ENLWL.jpg)

(http://i.imgur.com/C0jntna.jpg)

Actually I wanted to use the formula for the 3D burning ship in Mandelbulber, but I don't know how ...  :sad1:

I found some combined burning ships in the cubic burning ship:


(http://i.imgur.com/ySrAgxz.png)


Are these common? Are they special? I've never seen any combined mini-set in a fractal this way.

Yeah, with the abs() functions, the sets become mirrored on itself. You can often find Minis in close proximity to each other at moderate zoom levels. When Panzerboy released his absmandvars plugin for Fractal Extreme, one of my first zooms into the needle of the 2nd order Buffalo produced this little formation, at a "moderate" zoom depth of 2^179!
(http://www.fractalforums.com/index.php?action=dlattach;topic=2481.0;attach=6754;image)
http://www.fractalforums.com/fractal-exteme/fractal-extreme/msg42568/

Despite having needles which is very uncharacteristic of odd-order fractals, the 3rd order BS is still very much third order. It contains rotational symmetries of 2 and 6 sided shapes when you zoom in enough, often producing ornate snowflake like patterns, and during deep zoom sequences, minis appear 50% deeper than your last detour rather than twice as deep like with all 2nd order fractals. At shallow zoom levels this causes the minis to appear larger than in the 2nd order abs() fractals, so much so that they often collide with each other. In the cubic Buffalo, as well as Burning Ship, the minis will often get stacked together at shallow depths.

I took some measurements of the set. The three needles of the Cubic Burning ship terminate exactly √2 (square root) distance from the origin, with the diagonal having absolute coordinates of ±1 on both axes. Even Mandelbrots always have needles of legnth (n-1) root of 2. For instance the westward needle of the 2nd order Mandelbrot is the first root of 2, which is located at (duh) -2. 4th order mandelbrot needle terminates at the negative cube root of 2, so the math checks out. Again despite being an odd powered fractal, the presence of abs commands in the formula parameters will create needles due to the even symmetries the reflections create.

The buffalo fractal (2nd or 3rd order) has two abs() functions applied to the entire formula. This confines the resultant exponent to the upper right quadrant always, so reflections occur across both axes. If one of these reflection planes happens to pass in close proximity of a mini, the mini will be reflected as well. The Burning Ship and Celtic fractals have one plane of symmetry in the 2nd order sets (For clarity, the reflections I'm referring to occur in the orbitals, not the shape of the resultant fractal itself. During Zoom sequences, the Burning Ship reflects objects across the X axis while Celtic reflects objects across the Y axis, ultimately deleting the other half of the pattern. This property can be used constructively to customize the levels of complexity during a zoom sequence, much like repeating patterns can be generated in the base 2 Mandelbrot by selective zooming), but I'm still figuring out the symmetries of the Cubic Burning Ship.

Specifically with the Burning Ship fractal, the abs() command is applied to both the real and imaginary components prior to the exponent. The dual abs() commands confine the initial complex value to the upper right quadrant. In the 2nd order Burning Ship, this results in complex coordinates within the upper half of the complex plane after squaring. As a result, you won't find minis in this area (remember the BS fractal is normally rendered flipped vertically). In the 3rd order Burning Ship, the coordinates can exist in one of three quadrants, lower right being the exception. As a result, minis can exist anywhere in the fractal except the upper left quadrant of the fractal behind the twin masts (assuming the fractal is not rendered flipped or rotated).

The reflections in the The Cubic Burning ship appears to have some sort of quasi 3/4 reflective symmetries which ultimately get divided by symmetry lines into forths and twelths due to 3rd order periodicity. Somehow this 270 degree symmetry also generates a third needle equidistant and diagonally offest by 135 degrees to the other two. Being 3rd order, this ultimately creates rotation symmetry of modulo 2, 6, 18, and so on during a zoom sequence. The masts in the 3rd order Burning ship show similarities to the 2nd order BS being assymetrical along the orthagonal needles, and also shares similar properties to the 2nd order Celtic, being perfectly symmetric along the diagonal needle. As an added bonus, the third order Burning Ship also has less "rats nest" material outside of the mast areas compared to the 2nd order version, with even more options ripe for exploration.

Sadly (and this is only my humble opinion) the 2nd and 3rd order Burning Ship fractals are where the amazing symmetry ends. Starting with 4th order and up, the Burning Ship fractals begin to get chaotic and disorganized, with niether the beautifully ornate masts of the 2nd order nor the amazing symmetries contained within the 3rd order. Also like with any progressively higher Mandelbrot powers, fractals eventually tend to get "blobby". That's why I'm not insisting on arbitrary powers. The attempt to expand into a generic arbitrary powers formulation with Kalles Fraktaler might have been why the previous attempt failed. If you can just get the 3rd order BS working alongside the 2nd order, I'll be a very happy camper! :D

EDIT: Man, I'm becoming like a spokesperson for this formula, or something...  :tongue1:

Hi!

I made some burning ship images and I guess this is a good place to post. I haven't seen too many renders with interior, but I think the interior is interesting.

Here's a part of the bottom showing all kinds of interesting patterns: http://tam3n.deviantart.com/art/DIST-BS-150-halfsize-489019896
I cut the noisy part away to save on the file size.

Here are some glory renders of the mini ship, though you might already be bored with it...
Ver1: http://tam3n.deviantart.com/art/BurningShip-TEST-halfsize-489014844
Ver2: http://tam3n.deviantart.com/art/BurningShip-TEST-ver2-big-489016121

I don't know too much about internal rendering methods. I guess anything is possible, but typically, the glorious fractal detail is within the iteration bands, not the main fractal or minis. I'm not saying that an interior couldn't be made into deep zoom material, but typically the entirety of the video is spent starting with the main fractal and ending with the mini. Don't get me wrong, I think internal render methods are great for stills, but I don't feel they are much use for deep zoom videos because in most deep zoom movies, the vast majority of the video contains only iteration bands.

I think the those interior shots look great! They really show the strong connection this fractal has with Kalisets (both use cabs() for their folding operation, but use different stretch operations). I also like how the burning ship has actual minisets in its interior. Interior zoom videos present a challenge, but maybe if you keyframed the iterations to increase with the zoom, you could get something nice.

Nice pictures, youhn, although your 3D fractal has a Buffalo cross-section along the xy plane (and no BS cross-section), so you've found the 3D Buffalo fractal, not the burning ship. This is because you take the absolute values after the power operation- if you take instead take the abs values at the start of each iteration, you'll get a nice Burning Ship cross-section along the xy-plane.

Here's the formula I'm using, in glsl. It's equivalent to yours except with the abs() in a different spot and without the negated z-component (which doesn't seem to affect the shape in any way...).

Here are some pictures. The first is a head-on view of the front. The second one is rotating over the top to see part of the the backside. The third one is a different view of the back.

This next one is a view of the main miniship. You can't see it well from here, but it has a long "tail" sticking out behind it one the z-axis. The last one is a closeup view of the tail, with some interesting lattice patterns.

(http://www.fractalforums.com/index.php?action=dlattach;topic=1689.0;attach=10509;image)
So cool. Even looks like a real 3D pirate ship! ;)

That picture is so nice, it's like watching color tv for the first time.

I can just imagine the cannon balls blasting out from the side, that's how real it looks...

super cool, indeed! it is realy looking like... erh yay like a pirate ship :)

are you planning/calculating a high-res version of it ?!

Do it! I'm not actively rendering 3D mandelbulbs but I love looking at others pics of them. Go big, like as in 25600x19200 big... :evil1: O0

Here's a much bigger one. 6600x4050 res. Click to follow link.

 (http://2imgs.com/2i/t/5fb1a78d5e.jpg)  (http://2imgs.com/5fb1a78d5e)

It certainly is cool to see the namesake ship in 3D. But the Julia sets are where the really interesting stuff is, IMO. For those who haven't seen them in the gallery, here are a few interesting Julias I've discovered (these are all raw burning ship Julias with simple orbit trap coloring). I was totally surprised to see such organic-looking shapes in a fractal known or it's angular towers. Of course, there are also Julia sets with the classic tower look, which will be my next gallery post.

(http://nocache-nocookies.digitalgott.com/gallery/16/8614_19_10_14_7_33_06.jpeg) (http://nocache-nocookies.digitalgott.com/gallery/16/8614_19_10_14_7_33_06.jpeg)

(http://nocache-nocookies.digitalgott.com/gallery/16/8614_18_10_14_11_01_50.jpeg) (http://nocache-nocookies.digitalgott.com/gallery/16/8614_18_10_14_11_01_50.jpeg)

(http://nocache-nocookies.digitalgott.com/gallery/16/8614_13_10_14_9_38_29.jpeg) (http://nocache-nocookies.digitalgott.com/gallery/16/8614_13_10_14_9_38_29.jpeg)

Neat. Those sprouts in the middle image almost look like real vegetation.

If anyone wants to play around with the formula, here's the Fragmentarium script: http://www.fractalforums.com/fragmentarium/3d-burning-ship-formula-and-frag-file/ (http://www.fractalforums.com/fragmentarium/3d-burning-ship-formula-and-frag-file/)

The above Julia sets are included as presets. Also, arbitrary powers are supported.