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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: Jesse on February 24, 2010, 05:45:03 PM

Title: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 24, 2010, 05:45:03 PM

NOTE: This Post was a reply in the http://www.fractalforums.com/images-showcase-(rate-my-fractal)/interior-shots-of-the-mandelbox/ Thread! O0

Impressing images, twinbee! I love the excellent shadows.
Lowering the Bailout could be like "ruins after some thousand years", maybe. There are lots of options, astonishing.

Tglad, are the last two ones still the default formula? Nice locations.

Just took a timeout from programming and did some experiments, i present a kind of "bulbox" :)

Only change is to use the bulb formula when square of R is below 4...
all cut at Z=0

scale=2
(http://www.fractalforums.com/gallery/1/1127_24_02_10_5_29_53_0.jpeg)

scale=3 (this may be also a 2D option with default and perpendicular Mset + some other 2D sets?)
(http://www.fractalforums.com/gallery/1/1127_24_02_10_5_29_53_1.jpeg)

scale=3 and multiplying the values for the bulb by 10
(http://www.fractalforums.com/gallery/1/1127_24_02_10_5_29_53_2.jpeg)

zoom into and using the bulb formula when R is below 0.04
(http://www.fractalforums.com/gallery/1/1127_24_02_10_5_29_53_3.jpeg)

same, but using minR of 0.25 for the box
(http://www.fractalforums.com/gallery/1/1127_24_02_10_5_29_54_4.jpeg)

Title: BulbBox - An Amazing Fractal extension
Post by: bib on February 24, 2010, 05:51:22 PM

WHAOOOOOO ! This is really incredible. The potential of 3D fractals never ceases to amaze me. What a fantastic find! These pictures are totally CRAZY O0 O0 O0

Title: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 24, 2010, 05:54:30 PM

Wondering, if there are more "flying chickens" somewhere in the last one ;)

Title: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on February 24, 2010, 07:21:02 PM

as you might have noticed, i took the time and split this topic in a completely new

again amazing, i think this method can be used in a more general manner, i am a fan of combination methods of formulas, like alternating a formula, but this method offers new possibilities:
define some radius treshold, and use completeley different formulas for each of these thresholds, here we would have 2 formulas, the box, and the bulb!
finally a method i can implement using UF5 reb.uld Quat formula, with object codes, will send impressions this evening !

Jipiii!

Title: Re: BulbBox - An Amazing Fractal extension
Post by: David Makin on February 24, 2010, 09:37:47 PM

Excelent - I was contemplating the same idea to put a Mandelbulb in the middle of every Sierpinski Tetrahedral space :)
I did essentially the same thing in 2D a while ago but just using 2 IFS fractals, including wrapping the image around the standard Mandelbrot:

http://www.renderosity.com/mod/gallery/index.php?image_id=1191072&member (http://www.renderosity.com/mod/gallery/index.php?image_id=1191072&member)
http://www.renderosity.com/mod/gallery/index.php?image_id=1083644&member (http://www.renderosity.com/mod/gallery/index.php?image_id=1083644&member)
http://www.renderosity.com/mod/gallery/index.php?image_id=1075961&member (http://www.renderosity.com/mod/gallery/index.php?image_id=1075961&member)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: bib on February 24, 2010, 09:43:02 PM

OK David, now I want to be able to do the flying chicken in the amazing cube with 3D ferns and Menger sponges all around. Is that possible in a single layer? :D :D

Title: Re: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on February 24, 2010, 11:27:14 PM

here are 2d slices of:

first: a mandelbox and a mandelbrot formula in 2d plane

second: a zoom somewhere

third: a mandelbrot^8 and a mandelbrot^2 at an separator distance of 1.0

the brot8 and8 combination yields interesting results when played around with the parameters ( i am with gpu here ;) )
O0

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 24, 2010, 11:50:46 PM

Quote from: David Makin on February 24, 2010, 09:37:47 PM

Very nice, i want a slightly different bulb in each round hole in the Box, where now is a little cube instead :D
So we had just one formula with all possible bulbs which parameters are varied by the specific location...

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 26, 2010, 01:26:34 PM

Quote from: Trifox on February 24, 2010, 07:21:02 PM

again amazing, i think this method can be used in a more general manner, i am a fan of combination methods of formulas, like alternating a formula

Good idea, here are the alternating results...

first iteration bulb:
(http://www.fractalforums.com/gallery/1/1127_26_02_10_1_16_25_0.jpeg)

middle detail:
(http://www.fractalforums.com/gallery/1/1127_26_02_10_1_16_25_1.jpeg)

first iteration box:
(http://www.fractalforums.com/gallery/1/1127_26_02_10_1_16_25_2.jpeg)

zoom:
(http://www.fractalforums.com/gallery/1/1127_26_02_10_1_16_26_3.jpeg)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: KRAFTWERK on February 26, 2010, 01:50:29 PM

WOW, that "middle detail" looks like a mandelbulb at a distance, but is a mandelbulb of mandelbulbs, this is toooo much!!!
O0 O0 O0 O0
O0 O0 O0 O0
O0 O0 O0 O0
O0 O0 O0 O0

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 27, 2010, 12:00:00 AM

Testing the reverse mode:
doing the bulb iteration on R > 2 and scaling the bulb by 10...
refections inside the bulb from the outside because of the spheric folding???

(http://www.fractalforums.com/gallery/1/1127_26_02_10_11_57_34.jpeg)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Timeroot on February 27, 2010, 01:05:20 AM

Quote from: Jesse on February 27, 2010, 12:00:00 AM

refections inside the bulb from the outside because of the spheric folding???

What's the radius of that little "Mandelhole"? If it's equal to 1/2, then I'd be willing to be it is... is there any way to check easily with the software you're using to render these? Personally, I would love to see the Julia Set of the fractal... I'd expect it to have an infinite number of these little holes... A real Swiss cheese Mandelbulb. ;D

Title: Re: BulbBox - An Amazing Fractal extension
Post by: M Benesi on February 27, 2010, 03:13:33 AM

A tip for the higher order ones (z^4 on up): set your scale value lower. Lowering the folds and other values can help renders too, but you lose more details that way. Learned about the scale thing 5 days ago (at around 4am... go figure, there's that time again) when I was making the first full-hybrid rotational/amazing fractal types over in this thread. (http://www.fractalforums.com/3d-fractal-generation/amazing-fractal-hybrid-types/msg13290/#msg13290) I even mentioned trying the bulbs in the very first sentence of the thread.. so you know. Anyways, I prefer hybrid type D because it reminds me of old video games I used to play, but this one is nice as well.

Here is a series of z^3's with scale = .5 (Trifox, made them with low quality jpeg so they take up less HD space)

Bulb type 1, bulb type 2, Type D.1, type D.2:
(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_08_0.jpeg)(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_08_1.jpeg)(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_08_2.jpeg)(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_08_3.jpeg)
Then some z^5's, same order
Bulb type 1, bulb type 2, Type D.1, Type D.2:

(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_32_0.jpeg)(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_33_1.jpeg)(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_33_2.jpeg)(http://www.fractalforums.com/gallery/1/1170_27_02_10_3_02_33_3.jpeg)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on February 27, 2010, 06:56:30 PM

OMG, great new variations O.o

Those bulbox mixes are amazing!

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 27, 2010, 09:16:38 PM

Quote from: M Benesi on February 27, 2010, 03:13:33 AM

Ah, now i found the code, i think type-D is the second code in the thread you mentioned...
So you already did the alternating hybrid, very nice!

I guess i have to program this in a general way, choose 2 (or more) forumlas in a row. I like these hybrids.

And yes, too high scale values would thin out the structures too much, as can be seen in my versions.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 27, 2010, 09:53:01 PM

Quote from: Timeroot on February 27, 2010, 01:05:20 AM

It must be something like 3 1/3 or Sqrt(10). The bulb was scaled by 10, iirc.

Hmm, julia type is another thing for the todo list, could be interesting, yes.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on February 27, 2010, 11:27:47 PM

Here are alternated types with a lower boxscale of 0.5 plus power 2 bulb...

first box then bulb, think i have seen it before:
(http://www.fractalforums.com/gallery/1/1127_27_02_10_11_23_34_0.jpeg)

first pow2 bulb:
(http://www.fractalforums.com/gallery/1/1127_27_02_10_11_23_35_1.jpeg)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on February 27, 2010, 11:37:08 PM

this marks a new animation parameter :)
it should be perfectly possible to fully transform a bulb into a box that way and viceversa :D (Maybe, bulb to box with bulb first and box to bulb with bulb first?)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: M Benesi on February 28, 2010, 02:56:11 AM

Quote from: Jesse on February 27, 2010, 09:16:38 PM

Ah, now i found the code, i think type-D is the second code in the thread you mentioned...

Type b was pretty boring.... although it does have some very interesting structures if you search for them. I suppose the type-D was a bit more 'Mandely' than the B, at least in terms of details, which is why I focused upon it.

Quote

I guess i have to program this in a general way, choose 2 (or more) forumlas in a row. I like these hybrids.

Make that the lot of us. I even threw together a couple Serpinski hybrids, after trying out these ones. My favorite being the Cantor Dust set (Sierpinskiesque) hybridized to 3 rotations- looks like a 3d bifurcation diagram, especially as you increase the iterations, but I digress.

I've tried a few other hybrids (D2, R2D2 and Mandala found in other threads) although they just aren't as regular as these, except for the Mandala, which really isn't fractal, but instead makes pretty.. umm.. mandalas.

One more thing (in case I missed you saying you tried it), try lowering your magnitude (for a 3 rotation, only square your magnitude) or varying your rotations. Interesting things occur in type D, and may occur in the Mandelbulb variants as well.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on February 28, 2010, 10:56:00 AM

I have just updated my formula collection in the uf database, the should be downloadable in the next few hours

i created formulas for working with complex numbers

- radi alternate - radius based formula selection
- section alternate - based on x/y or real/imag values determination of used formula

Code:

Fractal1 {
fractal:
  title="Fractal1" width=1024 height=768 layers=1
  credits="c.Kleinhuis;2/28/2010"
layer:
  caption="Background" opacity=100 method=multipass precision=20
mapping:
  center=-0.029478395/-0.310017716 magn=0.19398004
formula:
  maxiter=1525 percheck=off adjust=yes filename="Standard.ufm"
  entry="GenericFormula"
  p_formulaClass="ck.ulb:RadiusFormulaAlternate"
  p_formulaClass.v_generic=100 p_formulaClass.v_formula=100
  p_formulaClass.p_power=2/0
  p_formulaClass.formulaClass1="ck.ulb:Mandelbox"
  p_formulaClass.formulaClass1.v_generic=100
  p_formulaClass.formulaClass1.v_formula=100
  p_formulaClass.formulaClass1.p_power=2/0
  p_formulaClass.formulaClass1.v_divergentformula=100
  p_formulaClass.formulaClass1.p_bailout=1e20
  p_formulaClass.formulaClass1.seed=0/0
  p_formulaClass.formulaClass1.scaleval=2
  p_formulaClass.formulaClass2="Standard.ulb:Standard_Mandelbrot"
  p_formulaClass.formulaClass2.v_generic=100
  p_formulaClass.formulaClass2.v_formula=100
  p_formulaClass.formulaClass2.v_divergentformula=100
  p_formulaClass.formulaClass2.start=0/0
  p_formulaClass.formulaClass2.p_power=2/0
  p_formulaClass.formulaClass2.p_bailout=1e20 p_formulaClass.radi=3
inside:
  transfer=none
outside:
  transfer=linear filename="Standard.ucl" entry="Basic"
  p_type=Iteration
gradient:
  smooth=yes index=0 color=8716288 index=100 color=16121855 index=200
  color=46591 index=300 color=156
opacity:
  smooth=no index=0 opacity=255
}

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Tglad on March 04, 2010, 04:28:05 AM

Jesse-

Quote

Tglad, are the last two ones still the default formula? Nice locations.

Yes, the first is if you fly into the top bay window thing, the second is if you go through the middle cathedral arch and down a hole.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: aluminumstudios on March 04, 2010, 07:04:35 AM

I need to learn about mandelboxes and mandelbulbs. I don't have anything technical to contribute, but I just had to say that the images, particularly the last two of the original post are absolutely stunning! Great work.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on March 04, 2010, 09:11:42 PM

Wow Trifox! That is a great mix of Mset and Mbox :D

Title: Re: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on March 05, 2010, 02:31:35 AM

ok, here is another example of formula combination, only 2d, i am sorry,
this image has been created with the mandelbox formula after iteration 5 O0

Code:


Fractal1 {
fractal:
  title="Fractal1" width=640 height=480 layers=1 frame=60
  credits="c.Kleinhuis;3/5/2010"
layer:
  caption="Background" opacity=100
mapping:
  center=-0.75605792705/0.0173250805 magn=1.2214028
formula:
  maxiter=250 filename="Standard.ufm" entry="GenericFormula"
  p_formulaClass="ck.ulb:ChangeFormula_AfterNIterations"
  p_formulaClass.v_generic=100 p_formulaClass.v_formula=100
  p_formulaClass.p_power=2/0
  p_formulaClass.formulaClass1="Standard.ulb:Standard_Mandelbrot"
  p_formulaClass.formulaClass1.v_generic=100
  p_formulaClass.formulaClass1.v_formula=100
  p_formulaClass.formulaClass1.v_divergentformula=100
  p_formulaClass.formulaClass1.start=0/0
  p_formulaClass.formulaClass1.p_power=2/0
  p_formulaClass.formulaClass1.p_bailout=4
  p_formulaClass.formulaClass2="ck.ulb:Mandelbox"
  p_formulaClass.formulaClass2.v_generic=100
  p_formulaClass.formulaClass2.v_formula=100
  p_formulaClass.formulaClass2.p_power=2/0
  p_formulaClass.formulaClass2.v_divergentformula=100
  p_formulaClass.formulaClass2.p_bailout=1E20
  p_formulaClass.formulaClass2.seed=0/0
  p_formulaClass.formulaClass2.scaleval=2
  p_formulaClass.atIteration=10
inside:
  transfer=none
outside:
  transfer=linear filename="Standard.ucl" entry="Smooth" p_power=2/0
  p_bailout=128.0
gradient:
  smooth=yes rotation=1 index=0 color=6555392 index=64 color=13331232
  index=168 color=16777197 index=257 color=43775 index=343 color=512
opacity:
  smooth=no index=0 opacity=255
}

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on March 06, 2010, 12:11:54 AM

hey, nice :)
Now, what's about alternating iterations?

mandelbrot at even, mandelbox at odd.
And viceversa :)

Title: Re: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on March 06, 2010, 03:05:28 AM

the alternation mandelbrot-mandelbox yields a smaller mandelbrot with rings

Code:

Fractal1 {
fractal:
  title="Fractal1" width=640 height=480 layers=1 frame=60
  credits="c.Kleinhuis;3/6/2010"
layer:
  caption="Background" opacity=100
mapping:
  center=0/0 magn=1
formula:
  maxiter=250 filename="Standard.ufm" entry="GenericFormula"
  p_formulaClass="ck.ulb:AlternatingFormulaObject"
  p_formulaClass.v_generic=100 p_formulaClass.v_formula=100
  p_formulaClass.p_power=2/0
  p_formulaClass.formulaClass1="Standard.ulb:Standard_Mandelbrot"
  p_formulaClass.formulaClass1.v_generic=100
  p_formulaClass.formulaClass1.v_formula=100
  p_formulaClass.formulaClass1.v_divergentformula=100
  p_formulaClass.formulaClass1.start=0/0
  p_formulaClass.formulaClass1.p_power=2/0
  p_formulaClass.formulaClass1.p_bailout=4
  p_formulaClass.formulaClass2="ck.ulb:Mandelbox"
  p_formulaClass.formulaClass2.v_generic=100
  p_formulaClass.formulaClass2.v_formula=100
  p_formulaClass.formulaClass2.p_power=2/0
  p_formulaClass.formulaClass2.v_divergentformula=100
  p_formulaClass.formulaClass2.p_bailout=1E20
  p_formulaClass.formulaClass2.seed=0/0
  p_formulaClass.formulaClass2.scaleval=2
inside:
  transfer=none
outside:
  transfer=linear filename="Standard.ucl" entry="Smooth" p_power=2/0
  p_bailout=128.0
gradient:
  smooth=yes rotation=1 index=0 color=6555392 index=64 color=13331232
  index=168 color=16777197 index=257 color=43775 index=343 color=512
opacity:
  smooth=no index=0 opacity=255
}

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on March 06, 2010, 09:43:24 AM

also nice :D
If you rotate it upward, it would serve perfectly for kind of a magic symbol or something :)

Do zooms in either of them reveal interesting structures, different to those in the default box or Mset?

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on March 06, 2010, 07:38:49 PM

Quote from: Trifox on March 05, 2010, 02:31:35 AM

ok, here is another example of formula combination, only 2d, i am sorry,
this image has been created with the mandelbox formula after iteration 5 O0

Nice, i just got it: iterating 5 times pure mandelbulb formula, and afterwards the mandelbox.

Must have a try on this, if i will ever find time for it...

Title: Re: BulbBox - An Amazing Fractal extension
Post by: quaternion on March 06, 2010, 10:07:42 PM

fantastic fractals.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: Jesse on March 06, 2010, 11:07:22 PM

Glad that i had give it a try..

first 5 bulb then alternate:
(http://www.fractalforums.com/gallery/1/1127_06_03_10_10_59_57_0.jpeg)

first 6 bulb then alternate:
(http://www.fractalforums.com/gallery/1/1127_06_03_10_10_59_57_1.jpeg)

first 5 bulb then box
(http://www.fractalforums.com/gallery/1/1127_06_03_10_10_59_57_2.jpeg)

Especially with the last pic it looks like that you can make a special form from the first formula, and fill it with these box structures.
It is every time really astonishing...

Should also say, that these are cuts at z=0

Title: Re: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on March 07, 2010, 12:05:38 AM

awesome!
the process is clear, first iterations get the shape of the base fractal, areas that are not bailouted are then passed to another formula, which gives nice starting values

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on March 07, 2010, 08:32:44 PM

O.o 6 then alternate looks AMAZING!
One of the best things I've seen so far!

This reminds me of the random sign Mset... what about different intervals of alternation or even random alternation? :D

EDIT: Oh, and if I remember all I read about it sofar corretly, then the Mbox has more parameters than the Mset/Mbulb... So... What about alternating parameters through iteration? (Not just increasing but alternating in different ways)
A lot of awesomeness to be discovered, I guess.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: M Benesi on March 07, 2010, 08:34:41 PM

Someone sent me my fractal xmas tree early. Reminds me of spring too (the top and bottom one: daisies coming up). Those are nice happy fractal images.

Title: Re: BulbBox - An Amazing Fractal extension
Post by: cKleinhuis on March 07, 2010, 11:33:40 PM

Quote from: kram1032 on March 07, 2010, 08:32:44 PM

you can try this out with the uf5 formulas i posted, you even can make (binary) trees of alternation rules, it is real fun, i
also make good results with linear interpolating values ( the blend formulas )

Title: Re: BulbBox - An Amazing Fractal extension
Post by: kram1032 on March 08, 2010, 08:24:07 AM

I really don't know what I do wrong but I can't get the code to work :S

As what should I save it to use it?
I currently tried .upr...