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Author Topic: BulbBox - An Amazing Fractal extension  (Read 10334 times)
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Jesse
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« Reply #15 on: February 27, 2010, 09:53:01 PM »

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.  grin

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.
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Jesse
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« Reply #16 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:


first pow2 bulb:
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kram1032
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Posts: 1863


« Reply #17 on: February 27, 2010, 11:37:08 PM »

this marks a new animation parameter smiley
it should be perfectly possible to fully transform a bulb into a box that way and viceversa cheesy (Maybe, bulb to box with bulb first and box to bulb with bulb first?)
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M Benesi
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« Reply #18 on: February 28, 2010, 02:56:11 AM »

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. 
 
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cKleinhuis
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« Reply #19 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
}



* mandelbox.jpg (83.02 KB, 1024x768 - viewed 377 times.)
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divide and conquer - iterate and rule - chaos is No random!
Tglad
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« Reply #20 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.
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aluminumstudios
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Posts: 135


« Reply #21 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.
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kram1032
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Posts: 1863


« Reply #22 on: March 04, 2010, 09:11:42 PM »

Wow Trifox! That is a great mix of Mset and Mbox cheesy
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cKleinhuis
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formerly known as 'Trifox'


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« Reply #23 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  afro

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
}



* mandelbrot_atiteration_mandelbox.jpg (21.57 KB, 640x480 - viewed 355 times.)
« Last Edit: March 05, 2010, 02:33:37 AM by Trifox » Logged

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divide and conquer - iterate and rule - chaos is No random!
kram1032
Fractal Senior
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Posts: 1863


« Reply #24 on: March 06, 2010, 12:11:54 AM »

hey, nice smiley
Now, what's about alternating iterations?

mandelbrot at even, mandelbox at odd.
And viceversa smiley
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cKleinhuis
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formerly known as 'Trifox'


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« Reply #25 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
}


* mandelbrot_box_alternate.jpg (12.72 KB, 640x480 - viewed 373 times.)
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divide and conquer - iterate and rule - chaos is No random!
kram1032
Fractal Senior
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Posts: 1863


« Reply #26 on: March 06, 2010, 09:43:24 AM »

also nice cheesy
If you rotate it upward, it would serve perfectly for kind of a magic symbol or something smiley

Do zooms in either of them reveal interesting structures, different to those in the default box or Mset?
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Jesse
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Posts: 1013


« Reply #27 on: March 06, 2010, 07:38:49 PM »

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  afro

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...
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quaternion
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« Reply #28 on: March 06, 2010, 10:07:42 PM »

fantastic fractals.
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Jesse
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Posts: 1013


« Reply #29 on: March 06, 2010, 11:07:22 PM »

Glad that i had give it a try..

first 5 bulb then alternate:


first 6 bulb then alternate:


first 5 bulb then box



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
« Last Edit: March 06, 2010, 11:10:31 PM by Jesse » Logged
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