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Author Topic: Quadray Sets  (Read 16669 times)
Description: Quadray representations of the mandelbrot set
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knighty
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« Reply #45 on: April 30, 2011, 06:31:05 PM »

Hey Darkbeam!
I've attached the fragmentarium shaders. You have to rename them to .frag instead of .txt.
Anyway, here is an image:


* img0.JPG (45.19 KB, 666x719 - viewed 295 times.)
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Kali
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« Reply #46 on: April 30, 2011, 06:39:46 PM »

Aexion, me contaron que eres de España... por lo tanto te doy la bienvenida en nuestro idioma también! smiley

Cuando tenga un poco de tiempo voy a probar Incendia, he visto muy buenas imagenes realizadas con tu programa, te felicito por él.
(espero no incendiar nada smiley)
Estoy actualmente trabajando en un programa de combinacion de fractales 2D, algo mucho mas modesto porque no soy un gran programador  embarrass

Espero que disfrutes tu estadía aquí, a mí personalmente me ha parecido un muy buen foro, e incluso me hice de algunos amigos aquí.

Saludos desde Argentina!

Edit: Just for the case, I was only saying hello to our new friend in spanish, I know I must speak english in public messages, it will not happen again  wink
« Last Edit: April 30, 2011, 06:44:37 PM by Kali » Logged

DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #47 on: April 30, 2011, 07:58:58 PM »

Hey Darkbeam!
I've attached the fragmentarium shaders. You have to rename them to .frag instead of .txt.
Anyway, here is an image:

smiley smiley smiley smiley

This is freaking awesome, congrats the wave

Exactly, which is the shader you rendered?
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knighty
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« Reply #48 on: April 30, 2011, 09:22:34 PM »

Thanks grin
That image is from the second script. parameters are offset=0 and sign=-1.
This one is with the first script. offset=-1 and sign=1.


* img2.JPG (58.5 KB, 495x561 - viewed 298 times.)
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Aexion
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« Reply #49 on: April 30, 2011, 10:14:56 PM »

Aexion, me contaron que eres de España... por lo tanto te doy la bienvenida en nuestro idioma también! smiley
Cuando tenga un poco de tiempo voy a probar Incendia, he visto muy buenas imagenes realizadas con tu programa, te felicito por él.
(espero no incendiar nada smiley)
Estoy actualmente trabajando en un programa de combinacion de fractales 2D, algo mucho mas modesto porque no soy un gran programador  embarrass
Espero que disfrutes tu estadía aquí, a mí personalmente me ha parecido un muy buen foro, e incluso me hice de algunos amigos aquí.
Saludos desde Argentina!

Edit: Just for the case, I was only saying hello to our new friend in spanish, I know I must speak english in public messages, it will not happen again  wink

Muchas gracias Kali!! Este es un muy buen foro.
Por cierto, aunque no soy español, llevo ya viviendo mas de una decada en España!
Espero que te guste Incendia (no quemes nada! smiley )
Saludos desde Cordoba
ps. I will speak in english, I promise, I was just answering in spanish to Kali smiley
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Aexion
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« Reply #50 on: April 30, 2011, 10:39:54 PM »

My first tries of a general quadray transform before some 4d formulas were a bit disappointing, not that good as Aexion's suggested formula.
But it seems that the rotated 4d box likes it...  smiley
(You need the _QuadrayTransform2 formula from the 'NewFormulasSince1697_3.zip' update:
http://www.fractalforums.com/index.php?topic=6061.msg28944#msg28944)
Very good render Jesse! I think that you will find many others.. smiley


Back to the quadray sets:
It seems to me that its mainly a 3D slice of a highier dimensional fractal. So why not use other directions for the slices? One way to do it would be by applying a rotation to the 4D (or 8D) variables before the loop.
And it is! as far as I suspected
I have trying to go toward higher dimensions, but saddly my results are well..not as good as the 4D version..
I have used the MandeBox formula first since it works with any number of dimensions and its symmentrical appareance serves me to test the formulas. Then I tried to implement the mandelbrot formula..But with no luck.. sad
For the Quadray, I have tested other formulas, such as the mandelbrot powers and the burning ship formula. The Burning Ship formula appears to look like a fish,a nd the mandelbrot powers, well, they look like mandelbrot powers smiley

Anyways, for the Mandelbox, the 12D is interesting to see (I call it "The Humongous Formula", for being overly big and impractical!)
Here is an example how it looks:

another render is at my DA gallery:
http://aexion.deviantart.com/art/Near-the-Core-207032701
(BTW: anyone interested on this multidimensional headache?)
« Last Edit: April 30, 2011, 10:52:59 PM by Aexion » Logged

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msltoe
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« Reply #51 on: April 30, 2011, 11:10:12 PM »

The posted picture is very nice. Who would've thought pentagonal faces could emerge from 12-dimensional square boxes?
It's frustrating working with 4+ dimensional functions because it's hard to predict what's going to happen...
 
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knighty
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« Reply #52 on: May 01, 2011, 09:35:53 PM »

(BTW: anyone interested on this multidimensional headache?)
Me!  grin
Have you tried negative scales or a bigger max-radius?
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Syntopia
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« Reply #53 on: May 01, 2011, 11:25:59 PM »

Thanks Knighty, for your answer on the Jacobian method.

I'm already familiar with the 'Hypercomplex Iterations' book - most of it is beyond me, but it seems to me they end using a formal derivative (defined iterativately - see e.g. p 56), which is a 4-component quantity for the quaternion systems, and I'd expect it to be same for other 4-component numbers.

Like you, I also tried to generalize something of the form "r*ln(r)/dr". I ended up with a scalar 'dr', because I was not sure how to multiply quadray numbers, but your Jacobian method works better anyway :-)
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Aexion
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« Reply #54 on: May 02, 2011, 01:10:14 AM »

(BTW: anyone interested on this multidimensional headache?)
Me!  grin
Have you tried negative scales or a bigger max-radius?
Still no, but I begin to have a collection of those multidimensional boxes, so I will make another post specially for these formulas.. smiley
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Jesse
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« Reply #55 on: May 02, 2011, 01:19:38 AM »

before that, a tweak with Lucas _PolyFolding and _UpdateC as pre-pretransforms... i like the 2 bulbs on the z axis this way:


* Aexion 10bulbs.jpg (163.61 KB, 800x766 - viewed 319 times.)
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KRAFTWERK
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« Reply #56 on: May 02, 2011, 10:02:32 AM »

These Quadrays are so beautiful, got to try them out!
Nice render Jesse!!  A Beer Cup
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Aexion
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« Reply #57 on: May 02, 2011, 11:09:17 AM »

before that, a tweak with Lucas _PolyFolding and _UpdateC as pre-pretransforms... i like the 2 bulbs on the z axis this way:


Beautiful render is that one!! I like it!!



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Fractals all the way..
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #58 on: May 02, 2011, 06:44:56 PM »

before that, a tweak with Lucas _PolyFolding and _UpdateC as pre-pretransforms... i like the 2 bulbs on the z axis this way:


Include it in the examples of next release the wave
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #59 on: May 03, 2011, 01:31:47 PM »


 Azn

Bicomplex Julia (some interfering sets) - isn't it cool? cheesy Quadray mode enhances a lot the bicomplex formula

Mandelbulb3Dv16{
O....Es....V1...Y..........2rXaBRoe0.Paa6W47ro1EHyT5CtWpUy9XhxEcNLGkzqQ.FKZ2A9uj
................................yC2UA3yxpz1......Usk./..................y.2.....
................/M.00....6.T3...60....E2.....wwcfrzyAlpD/..........c./...w1....U
z.EnAnQD1E../2EVf53iSIswzcNaNaNaNavDY0LD8QxcUz9..................y1...sD...../..
.w1...IE4yOZIRl95unO6UcJLwmVywW6gYzyAlpDHaIyouKDOx99CT.f7EHFzKu9VOfDiscDnoQpoa.B
3xHnT0ghipXKzieMUdJATabD......oX0.....................sD.2kz0...................
..............................MRS4.4qtN.kObb/UoRS4.srtN.sVbb/.FSS4..............
................E.....Ak.1.U.M6......c0...EB....70...6/...Uyzzzz6....EXz...oXl22
...mHwdel0A9le3kTeOg.ToMK81.3c..zzzz.Q6Fbf24LNvD5Got8VlJaz1...........k.8.klLS4.
Mo0FIhT67.A4hE2Jv5G0.1..........22.3vHSwl1EmZOxSfJ7zzUMqleHQhszDDOoz6DuFoy1/Gc.z
zzzz.UyriyqJ3nzDqwlf0WigyzHRUbsUnBIgzIW24dzzzzD.7aDex53nqzHVKH7bON3..N0RYP/mgmzj
/6U0.wzzz1....................................Ak.1EHVM/.iF.U.06.B3W3.gA0.1Ak.UqH
b..yEs6Ul/kF.V1.fH/U.06.B3W3.wl6/5wz.oI6K.UIr.Ak.1EHVM/.VLJrRzD.B3W3.2uKtXzr.oI6
K.Eyz/6U.0EHVM/....crI0.zzFoTu2.yzngi84.xzZX.45..ooFT3XAt2X98/pF................
E....6....E.....I....2....kLFJLMY7LMtFZQVtqQaxaQh71...................k/........
...................wz0........yD................................................
................................................................................
.....................A.....3..../....oIMiFKNgF1F0ZqE............................
........06U..........cNaNaNaNaxj.....................AnAnAnAnAxDnAnAnAnAHz1.....
................................................................................
................................}

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