Welcome to Fractal Forums

Dear Jason (owner and administrator of this Fractal Forum),

I want to wish you a lot of success with this initiative for a Fractal Forum.

The most inspiring fractal is the Mandelbrot set, described bij Benoit B. Mandelbrot is his book 'The Fractal geometry of Nature' (1977).

An example of a 3D Mandelbrot set (for z'=z^2 + c) you can find on: www.fractal.org/Beelden/Mandel.jpg

Image tag for our readers:
(http://www.fractal.org/Beelden/Mandel.jpg)

Thanks for the 3D Mandelbrot Set.

It looks like a break-dancing Buddha  ;D

LOL @ "break-dancing Buddha" - or perhaps the Enlightened One is rolling on the floor laughing at the foibles of frail fractalists. It  makes me wonder what it would look like much "closer up" ... very very closer up :)

btw, there are meany posible ways of doing a 3d mandlebrot set.
That one looks a bit like a 2d shape put though a lathe http://i2.sitepoint.com/graphics/lathe.gif
Im not saying thats a bad thing though.

Alan that's quite obviously cheating!

lol, I know
Iv'e never seen a really good 3d mandlebrot set that dosn't just look like a lathe thing, I would like to though.

(http://www.superliminal.com/fractals/bgram/anim/anim.gif)

Interesting site, the image above is from http://www.superliminal.com (http://www.superliminal.com).  I have invited the site's owner to this forum.

The 'Buddhabrot' is one of the more beautiful variations / drawing-methods on the Mandelbrot-set imho. Maybe it should even get it's own forum in the future  :).

btw, is it allowed to post software announcements, and if so, which forum is most suitable?

Friendly regards,
Stijn Wolters.

In one of the "Fractal Generation Software" boards off the main site.  Either that or Commercial Corner if you are selling software yourself.

The original 1977 edition of the book doesn't have anything on the Mandelbrot Set, which was discovered in 1980.

One must get the 1982 or later editions, where he mentions the set but only once, and mentions rather off-handedly that other people named it the Mandelbrot Set. One gets the impression that he was backing into fame.

I think we badly need a central forum like this one for all fractallographers to come to. Thanks to Jason for making it a reality!

thx for the link to the "Buddhabrot" site

Here again is a 3D image of the Mandelbrot set, made by the Fractal Imaginator (Fi).

see: www.fractal.org/Beelden/Mandel-3d.jpg

Julesruis that's quite obviously cheating
all of the other ways look better than that, it's just a 2D shape spun around one axis, like a lathe
look on Ultrafractal, there are several formuli for doing it in diffrent ways.

What do you mean by 'cheating'? I do not understand your remark. Please explain a little bit more.

Attached I give you the link to the .obj file, so you can turn around the Mandel 3D in all wanted directions.

www.fractal.org/Beelden/Mandel-3D.obj

Jules

Th users of Fi can click on the .fim file and download it.

www.fractal.org/Beelden/Mandel-3D.fim

Its just spun around like a lathe program would
Like this http://i2.sitepoint.com/graphics/lathe.gif
Not even trying to make a good 3d representation, there is no infomation in that image that is not displayed by the 2d one. especally considering there are sevral much better ways of viewing the mbot set in 3d.

I am really doing my best to understand you, but I do not have any idea what you mean.

I succeeded in printing in wax this 3D Mandelbrot, so in reality.

Please show me a better 3D Mandelbrot.

Regards,
Jules Ruis.

Jules Ruis wrote:
>
>    Th users of Fi can click on the .fim file and download it.
>    www.fractal.org/Beelden/Mandel-3D.fim

Basically, this file format is still the same one that Terry uses for all of his programs, which is based on the one from the ZPLOT program.  I can change the file extension from .FIM to something like .QSZ, and then open it within QuaSZ.  Or I could change it to one of the other file extensions that Terry uses on his programs so I can open this parameter file in those other programs as well.

It shows the formula used was:   z=c#/(1*cos(1*z)^(2) - 1*sin(1*z)^(2))^(2)
And it incorporated the "cloudy background".
Some of the settings used were:   F(600)t(5)GFX[?(.5)~(30)-(30)t(5)G][?(.5)~(10)+(30)t(5)G]
And:   X[^(45)F(400)][&(45)F(400)]FX

If you open the .FIM file using Notepad or Wordpad, you can then see what I am talking about.

Alan Tennant (alan2here) wrote:
>
>    Its just spun around like a lathe program would
>    Not even trying to make a good 3d representation,
>    there is no infomation in that image that is not
>    displayed by the 2d one.

Yes, when the parameters are set to create a spatial 3-D image a specific way, it does come out looking as if it was turned on a lathe.  But that is only the way the User has chosen the view and settings.

When other values are used with the basic M-Set formula, then something else altogether will show up, as in the follwing:
    http://www.Nahee.com/Fractals/QuaSZ/Images/3DMSetVariation.png (http://www.Nahee.com/Fractals/QuaSZ/Images/3DMSetVariation.png)

(http://www.Nahee.com/Fractals/QuaSZ/Images/3DMSetVariation.png)

As you can see, this uses the QuaSZ (http://www.mysticfractal.com/QuaSZ.html) program, which can be downloaded as a FREE Trial (http://www.Nahee.com/Software/) program.

Jules wrote >The users of Fi can click on the .fim file and download it ... www.fractal.org/Beelden/Mandel-3D.fim ...

Thanks for the file Jules - thats my first try with FI now ...
I dont have any mathematical background for discussion, but I am always curious with Fractal programs :)
(http://i14.tinypic.com/43c4sco.jpg)

I rendered the .fim file here with 2560 x 1920 Pixel.

The 1920 x 1920 part is online here ...
http://www.graphicandfractalworld.com/Fr4/Mandel-3D.htm

Margit

For more information of 3d iamges see:

http://local.wasp.uwa.edu.au/~pbourke/other/quaternions/

Here's something I did in a terrain editor.  I also made these same things for DeltaForce2-4 but people didn't seem interested in traveling through a fractal in a FPS....  at least not with the crappy graphics engines those have anyway... :)  I've wanted to find a way to get this sort of thing going in a better graphics engine....

http://www.infraxes.com/kizzume/artwork.html

I thought this was an interesting way of representing the mandlebrot (and similar).

That's GREAT! :)  I particularly liked the animation of movement in 4d space.

Brandon  (Kizzume) wrote:
>
>    Here's something I did in a terrain editor.  .......
>    http://www.infraxes.com/kizzume/artwork.html
>    I thought this was an interesting way of representing
>    the mandlebrot (and similar).

Greetings, Brandon, and welcome to this Forum!!    :)

May I ask about some of the fractal generators you have been using to explore and create fractals??

I've been primarily using Sterling to create the fractals, and I'm using whatever programs I can find to work with 3d terrains to import the heightmap version of the fractal (a lower-res monochrome fractal) and the bitmap overlay (the highres version of the full color fractal).  The terrain program I was using in those pictures was from before a hard drive crash--I'll have to figure out which program I was using.  I've also imported them into Delta Force 2, Land Warrior, and Task Force Dagger. 

Hi all,

Just thought I'd point out that there are various ways of viewing the "Mandelbrot" in 3D.

First of all you can take the standard complex Mandelbrot but use the real and/or imaginary values of the start value of z as one or two extra axes giving you a 3D or 4D object - this is in fact the classic 3D/4D "Julibrot" and does not appear like it's simply rotated on a lathe.

Secondly one can use quaternionic numbers instead of complex numbers i.e. using q^2+c instead of z^2+c where q is quaternionic and z is complex. Quaternions are naturally 4D so you can view part of a quaternionic Mandelbrot as a 3D figure i.e. this is a "true" Mandelbrot. Unfortunately the default figure just looks like the complex Mandelbrot rotated to give a 3D result.

Thirdly one can use other 4D number forms - generally referred to as hypercomplex numbers or Cayley algebra. The classic hypercomplex 3D Mandelbrot is actually a squarish figure.

You can also use algebras with higher numeric dimensions such as octonions.

You can create 3D(/4D) Mandelbrots in Ultrafractal using the "Solid3D" formulas from my own mmf.ufm or using some formulas from Stig Petersons sp.ufm or 3D fractal raytrace from Ron Barnett's reb.ufm (all available in the Ultrafractal formula database http://formulas.ultrafractal.com/
Currently Ron's formula is the fastest but only allows colouring by lighting/shadows.

With my own "Solid3D" formulas you can opt to choose colouring by lighting (including optional self-shadowing) or to colour the object using any Ultrafractal colouring formula - this gives a huge range of choices especially when using multiple layers to combine say "Orbit Trap" colouring with lighting layer/s.

All three choices (mine,Stigs and Rons) allow Julias in 3D as well as Mandelbrots and a range of formula options.

If I've missed anyone else's 3D escape-time formulas for Ultrafractal then I apologise for the omission :-)

Of course to generate 3D escape-time fractals faster you need dedicated 3D software such as that produced by Terry Gintz.

Of course there's also the possibility of viewing a complex Mandelbrot in 3D by using the usual 2D colouring values as a heightfield.

Just thought I'd show some more images of the 3D Mandelbrot and give the Ultrafractal parameters.

First here's a different view of the "lathed" quaternionic Mandelbrot:

(http://tn3-2.deviantart.com/fs12/300W/f/2006/320/a/7/Quaternionic_Mandelbrot_by_MakinMagic.jpg)

Here are the parameters:

MMF-MandyQuat {
::EvuGNhn2tf1SvxtNQ47Gw/HE2Tto128h4rWwDpNIABI5QR75GwdXpdVjeVJu2ezv+OUicEd6
  hmeOBIAZnhz7v5hc9k7g31+T3eTRhvx3WZ39+3/mi7Kevr/41f7izvr4pmj+zWZJp4cVzpz+
  lf26uWNNbZBFPMVdsxPb39a3jNHBV/YT/PTpPQlPwIE5ubvZR6Fn0V5PPc02dp13M6mnLO4G
  9ND92dvLITBdXxwo7Qj/qlSIF+JX/8obqq3bvWNvahpTVdDHriGp96t305GHb6Pt4hDgsVTW
  yDkiO3peL9ext3UPMBS7WDB3zNBJolFjVTHOXd4j2h66i6m2qeXHUC66qv/Sd3ug0g1muuUV
  8397DtNH5vOUWqm6hoeeXx4HqXrh2d/9fy+hDBOjPNZ5PQCqvQQXimxPAhQdz0s32PEoClYb
  oQX1ufawDs27aaHu4tl3HV2/8V7dk7liF99fySuP8jp0/Ttslf8YT1TBtChjlyQ1hQDADoGE
  e5wFf70qvbrq9Ap9u1XmC4agGF0vHEc1I79dZi6HGfhg17XtY90QfuJ3DeOK4qZAi5DOoDDV
  NgUTVxaDSTj5W3wjVBDkCDoCtSuKMQmkclitRNPeuCM8ioTvIIWf5FOOnVuvRjguP3sHah23
  22QTJQdsyDInltYvO3kPyvfYfTvD6fwaZDg2jw4EVGMyZX/poBjDGvF6schBiV0b8RX7S3Di
  njZJeUAWMTivyye1fdsCaxO134vcsa1IXmrA3GG1fVbbxyPX6jB++zTVznHaPuGTbkkwQUQ5
  umewjANNkqh5B7fkkC4sYNopkdvIRxgyyquLk8Y0BTcg/iEPfAmlSEXzJ+UkY1CPl/0hBYWZ
  y+uQvLM8Dca6nbg9C7+un/xrffIlcd7bCrOgwNG/HbqrhENkQiFwH6xadh5Jekcu5TVWxqHa
  ddjp9OwQzy2vfFWRM5iNJrsWHpC/kalrB3CFzyJpOvFGcrc71y4kw8Z3xhnCR0ab2CaW/h6e
  qFyme/t3smXrLpDLErhtXtN9VupPfp1h2dZbsc3B794vG2jBLV+3mofovqYFDhg80k7YoYtI
  zc3wA0lG6iDdsPbJFhy9kVwiMYSdklhRkSpJynbMLbhXeiKVKFLU7jL1zNOU1S2OtynJEfZH
  L+FY7ypphL9Hfx9ivdJ4bXC+2lgvWvE82l1kv8OAEQ+vGPFw/8bB87eTTV7x3ByOvbNOeE+C
  +w20X1GWiB9aPGKejDPB2cdZyfdptxtmTzfsZcZZZMJqbeOwapf+/66SJzUakKmR8lemRSoU
  NPdTpMytkxIamOyVvdnhVy1EjK+AlFZrJCFhzTsNJ2KimLopDZkM7QLFlw1g4LikflEhgLTX
  4SBZQYOnvcvL+0mGUGnlMUJqBhKUa0BlisTllGuhoFxnEoKMlE+DuSJtQghqWbIiNfLzCLGR
  lSPZSBKlTBDlufreRaTlSayFqkGKOlzxISnsvSI1lGSidWOYg79bomB/mBCgDlpkGgpk55GG
  NLDC/BfpkWbEGiEfQgf+BH+GhEbaWOQZCFkfYPAFVhzVlCsJgh+gzlcdm3R4WyICJWxpb4NI
  PvUjugnl6Ab4fpiLFR8SF3AACyH9RI5ZsM3jIuiB9gG09IizLFUSJyXmDgSOdz5IkrLBV4oG
  qkHMGGnwz8NC5g0gYbORTyaPlEOFfIL3VBwihlFE3ZsS5WjC1k5ENsQIL5ZIyLgMnRNIfsdH
  +5WTNLH5FQ2jdXME3VwgMaHWalQJsDhyQ7wUZphgq4KUFE21atA+qWkPChSF0nSyyit58439
  iPgpeZJlZMbbYy7ghdGw6N0RIwXGagxQGnzhNSMqMz9bj6Q7gmRQvgAP0MZECKaLVeHMVUKx
  mbWGyLJSQP8hsZRYiLb7Hzs5HjGgRO+AGZwiAcRDnkl9hNNqsdsIwrhJeSySc624L0EkN+yR
  gXShtya0S4APssRu5AWWqLhyrygPlNwTpGFC9cE61Mo9VkNBx3g+Q3IRhGDhe4Gogi7h45Iv
  hz0Ylnj4OlA31MoGZL4Ja40jKz9I0LECtA7h4IyD7l5McPEPH4BYDO3igiebtNFGW24LyAXj
  Sk14zRgnzMaoLC5vN+WCAR5/r/Ow/BgD3gWE
}

Here's one showing that the "lathed" effect applies to other fractals too - this is the standard quaternionic Newton for the roots of z^3-1:

(http://tn3-1.deviantart.com/fs12/300W/f/2006/320/5/9/Quaternionic_Newton_by_MakinMagic.jpg)

Here are the parameters:

MMF-QuatNewton {
::fnLgJjn2tj1SPutNQ47Lw+fQwnSB66lP0zWwDpdbASR2UU0euB0SU2sRvqE9617v+O8lE1GE
  0kgW0DxnMHSOfzwhz8NiuekXq4Nf31XFFpkqGBbz93/qobi+1jc1bFnU9dbiOJrUHYpxooDC
  5+DKWcOKqhfWMOxi1aWOKqkqJ2m74PIriun/eZ33jx3iTvlgQpbu+KzuNWpVoO0XxaP2okD8
  ppoS+gS23x28G9eiobi6H4lS1ZGGhgtPuX02XJYNaTL6u+qW+wgsbvBtSRnSMyQ3C7kvvjh3
  iu+q6+RAeu1c8Hl6dgRRDixyDiy3z6rrjqlNiOeLcebbr3esudje3AajnNhA1N/WfjsienOQ
  IG7APcaT0w7qtBM2Gbw5F/B9b0TPcakRvFpxwIgNu0w7A/oWOOpYd9aJeX1Z2PfsRyBpdcZT
  /RIauVvT1jn16YRQ9EDZmd0/LmRMDeQKO50omhtzpAfCi42DvW9yjqmRrJbE1KQkdD2ijOIq
  ltiwI1O7G3pa97z5D9Dr2Ytbj1j9dhQuDM+qNOVyh8oQnRfLNKchkZZs7s12/gQDgB9xeld8
  sywM+dalILSTDHEAwWNdOhVR7KrMc4Uh2eGErmgFChtsBSTbaYnFTgUlQB3aMiBvW+oyNfX/
  OZHHyd8oAiViBoshQ1gcg3t3BorA41QWFXn4bvAHeg3gDSAgZCO4uNQcnE3qkgVVnHEs7hSA
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  4lIMqz7NiUn3BVbg9cCPWC1Rw1EM8sdod+ncCW9PFuUZPUlMyejOzFK7hZkdTSgQYzLe8bPb
  q+4t7kw1q2ZdeflsuGOmM79Oke1w1lS5JO5J5TCDnAc/ybHc3iGKG2PC0CjcXUAyPszarm0D
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  FuZwpYCOPBCyOO6Pi+eGcierf6c/4PG3vVjmzXI/vQ+fh8/C5/nI5/Cfvl/Pk8PZ7K2frmhN
  A+MY/DU+DbA8/N7/XOZfMBjJ55/HR2TWI7LoBc9QMfEQ5CV/Fq+LU9f9R1/aDT4X9E90nz0T
  3dzLb0MUAN1r+h7f9r34KA0VhGqvwMtFWaoQGyYbeKcct8xgKIzW1hx7kPoZh7U6g9RgXo/k
  wRvYHScEBW+McqHCt5tJRIn0J7fUUiLC2v36hVPD8y56In4KLgZ4f6mkQvu0FnBvts+Y1+lq
  ZjkfZ+upSXVN4WHBSqbRLuZJDF64WXt8Z+a5sz+0O+EQ6+LQzEQwS6BpgOzyhUUcqjjRnuCB
  xocT6KEM5gH+WoLFvRHoFiKgKnGnk6supn2bs3+2WO+UnJ3gKZpwdoqO22emZN04wh5Tu4xB
  3OaEQW8EjYSE7PB9Pnc36N89IHDm2KIA9MUm7MMOh8xt2h5hd7Ru7Tt24AtxOtNqiXSkAtxL
  aPzZoVnEoOJUdyK1JLqDDxbJe9pB6TD1nuSf6i+UGluNzrfcg+xh6HvS/4F9j13q5zAkEAQS
  IAJrAIZBgE4Lp2SnBINAg0QASXBQ6CApMS+W8cIILAgsQAyWBQ2CAZA1X6s+5B6nHqfuuobW
  /cXiHofODXsNdJGUEgQRICFrQoYBhCGNdbyiPgDTCxoV5RoVgYW0hCMOfb8SoEvKZcd2IW/N
  TLooXk4hByIT2SXio4wsS8q0SQaFOkQcgUTYxgTVY2JeV6JIlHijeR8MQUdPligDWYaKO+ZF
  p4YPRjGJ9qOfQDVME9yDOaJLt6MgtKnFkokZk0LhoLeVCLmsFDX7f2vpQ782HFQy8vhIpggy
  JupxIsfeSGKNBn63P2EksrRzzLIwTCcvHhQWwKPGll+v+7R+B4Lb3P2fsra1//0lXgc5FIXe
  BylXg8VwLQm+rR1/07Pu5VSRTl+rVncP9A+A3JNBq/dJwzHmfqg28/pm+xl2O9e5ghe0dCgP
  mXPlJL+LuNTWur1QWSWRKpwNdhv7TMCXgKw+uP44lmMJks4s05GTEPSQLKo3DO2vANZeBKFh
  SK0Q4Xz/PllnkQp5+/BNccsb+UaROO27W4E6i9LiJgRz8LlS9zTyoJxzucax8JEnmSTCseuv
  vYaWBGTm94CfP248iMSiHKCKw6g/mGjL+s6k+3AwgxlP
}

Somewhat more interesting than the standard quaternionic Mandelbrot is the hypercomplex one:

(http://tn1-3.deviantart.com/fs12/150/f/2006/320/9/9/Hypercomplex_Mandelbrot_by_MakinMagic.jpg)

Aplogies for the small size of this one - the link to the larger one fails.
You can see the larger one in my "scraps" folder here:

http://makinmagic.deviantart.com/ (http://makinmagic.deviantart.com/)

Here are the parameters:

MMF-HyperMandy {
::nso8bhn2tr1SvNuNQ47BI/HE8pW0aFRSR9oF8wuNdRDwmWgu9cXQLRZLsUPgkcid+13hPkIl
  L2DBL6eYrzFzhDnvZ4whznZSqG4FTc5Pd7NBBT1TSBbzjP+ugtB/25exwj82yzbCeuuc6ALJ
  KK4goe/hJWGMUyPLGGZxKLLGEl1TjsN3zfquM4R+nqb/ZE6OUyd4ookN3eje1av0ImO0VyaO
  Knq75jjBF8+p6uW2m3rWTAZTQXPvoe6MDjDmG4tj98BR7E7sY0AwweRTXpgdgPUKVB0t30w7
  7rb3r9QBsYxAbbUYUeEJNikkeXUIKmkggfCa47bZow4UMJHnEwb3D768obvpqbAiKuJK5nqV
  ggwBQeo4go4Tsuqqgqapol3AppmmqwjVNbUrGc4wZdm742P0JrLJ3rzfFdN9SxpNB9fsykoZ
  bO834foQbV/HbU5XmKLLk7G6mgp+EjcXE8pkFp/cHvW2dciFDjnOdWtroaFTvwgNoBHYziUf
  gY4QlunqFPzi1DrYU1iBvDnJM1qKOOJHYtdGTliqJYGAA9yHUpTlsREGNtDWrKQma8W3UXvd
  VGYAhK7CrG6a9hcH46VIOWwhMuvpqTsBhdHvIjUbQVWq7JhCAN6QWyMexYYm5VakwOpx+DCA
  YjlrCYjmVO2fKffvAiNZ3tC2CJUGLlqqTQqUMBHYMkx6xG+wkVTb3u6WOUmMjDIWK6hLWYiC
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  Lg19bWAgwSCX0FD+Fr87BeZ3z2sLcUqPYr+YVLiB7m2Jl9KRMbsu92bMbSTfcVPzKo5lsuVw
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  GM73FiFK91QJhdUSIg5zRApPwEtXpfuS/cl+5K9zV6n/DpfAqiMMKKG6Z+Z4h8aF+NLVE6zR
  FZsQe+KX0VuorcRX5i+y5iCp0V0R+kR0lK2ZCpXPbkHDkiQ6VzGNzAZJk+axG9/vHB9Wor1+
  hujtlrIfuy0clp5KTzVmGPmmH09d/C5ZCJfDy0Qukqhsb7bkQtWLfS8u3+4DPYzS67p6ug+V
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  CJMd2+412H7bfsz+Yn9xqz1sFAorBg6DA1BA1BAF+uWhkFASWDQiPAJOAScAkAfruQ0SKIdN
  Ap+Ak6AI1BQK0NMZx+s12n5bfm9mHYfmtXGYfGDlHm4yB5rRI3HhcHC5OEyZkkQqLGQXUEiW
  VFCSLgo1YRBGnFG7SloLLGXXNisfrKFKKN4ZYgKSaIxlRRXUViWVWCSOcw+4AlmgGvd1FVno
  VlngU2COKNoFgga0owcYjZtVhVslzSD0q6UU8crGFSKVqYYhrGmBHm5t7o+ItqgFkI45mgKw
  UajIuAjyixhoMVg917lNRUSecaida688JECOKhYnOD79ymMCJLzqAhILPsJDRjpzzHnannAP
  RaGdUWiDHC4Ca6yjnwLeGhzpLOATxzrngyTR6/TGsqyRzqiJkE8cwSizmnPPKOGenyyjwceP
  BRQ6nH9KeG2/AkGLATK=
}

Finally here's one way of viewing complex fractals in 3D - the classic 3D Julibrot where the 3rd axis is taken as the real part of zstart:

(http://tn3-1.deviantart.com/fs12/300W/f/2006/320/e/d/Classic_3D_Julibrot_by_MakinMagic.jpg)

Here are the parameters:

MMF-Julibrot {
::IKscGin2tX1SvNuNQ47BI/HE0pWsx2kUvsbBP0msFYXs5S390eoB0SU2shiUgi2xO/67wHyx
  OFtoLQRR3F6k4Ma43Mce8NtGWtlJ/hrvKJxKsSON9+7/lkZJvfnUs2otpJPJasbpl5oktcxm
  tWa+SUikdkbGo5u7Vb4NC7AN9O2eRTy9sHFqfEjXgLXQQoy0rvybt3Hdc7WdDtbn0K6ZDDJ1
  serQropfwZTCJNR3zqF2j0sVJWDTN0zMcllekPEAwsh3pb40tMTj0FQXfVHrvXo249QNYM3Q
  RLQJdsNKKeO66ra1GwlsQIwOIcWgxJ9cT9We9jUdbbSrQyVsOID011OfXbXqzaANzRfSxM7j
  apoJ7ub1d9S+h0k+HaDpPa6z/m6N1ONPSJLQuL2/QtWt3Ft07E+vKLocNTI17gk4cEIZPckO
  DPnUswL9MF5VbcfDgYwUiX3eB/p4tap4gOI/UDJb3b05vdWphq0wRJv1CiOsHxxlpcqOZrdd
  w212uRTdQq7vwqWnVBIaNal9MTXDO/CbHqZQD0JRXlwwdViY+YUFO+M7075OA8hB0rd6McAE
  xvkFCKIx75cV/WOgd4mvEEB1v2xnr9cffBI6LwsWCtnS5YXX/DNcLU5oEvX6YGfDJcWpXLUM
  oFJkLFqGePMugLdgslp2wPl/i9+vDa+Yue+QBsfP0/gWELn9QcEjQnk9YPneP0GLs7a4BY2N
  wBYdTq/kUm4POkG0b3a4Db1ymQ08iIaeRMGEKv/mjdvDX/M9TjWBaYH4wc8tmbuVcznN38Zh
  DYvLw0sY20LSAxxzZxAGGigQYsGph2cD9Du2OY0McVhaQATupf3hbO+9eo7WLcD3Q8U4Syi2
  W4ZQDlSo3QycjCLLGrj86Bxzc6SfFi11HLCeaA6tv5XfzH3ya0PNESHNcwf2jnKAyGu0yo43
  ODn7E7fyEHucdDBQODQc4N6PTozKjvfvcGtc+pfmTJuoz7aIcrKC9T+qa7DtKMFe1Kr76ORS
  Q0fOjOIUXfVIxEYhdcetA/kUo4MzrplqlpnxJxmBMbZ3BMVAnyfGClWxTCVZI43YYNust3mh
  OtG6TdPXXP7BIn7KZAtYGuYZJKqFvqKqvYFBnVNqPb1KPZb4KlVVVEMUlic3n7BoTc0BjM7k
  iivkdC4X2JgRoz2A4T+c1E//E//E//E//E//fD/fOZJweXhLJf9uII7vaRQ4GyjTbCm2EMtJ
  4bqNBA5/FLDe1mgigLm2F8PaXwXjU//Mwtsxo3paug9fiqfiqfiq//nU9vzzg9fERPM8aYfT
  yx3097XwxDyz+kR4T/+MZv+J4ekYFqVy2rdUBmOmEUE/bcqNQAhfLB9vx+h88qsC04ig8x9D
  rwISWxyo6qyXWPskkhxryG3ogWdCpMyyKUZ8Hk88xVNLryXlX5QIutBdy7lk8l4iRwyyHBjU
  RQFfhrg+DoEm1sB=
}

Dear Davis,

Some of our members are expecting bulbs on each ax i.s.o. the so clalled 'lathed' one.

What do you think about it?

Jules.

It's just the way that quaternions work - I'm not personally familiar enough with them mathematically speaking (yet) to give further explanation  :(

David Makin wrote >Just thought I'd show some more images of the 3D Mandelbrot and give the Ultrafractal parameters.

David - I think its a great demonstration here !  - thanks for sharing files :)

Margit

I should mention what I said in the "meet+greet" forum - I don't think there's a numeric form whereby the standard Mandelbrot (a^2+b) will produce bulbs on all the axes.
In the same message I suggested a couple of ideas for modifications that may produce bulbs in all 3 (or 4) directions and I'm now trying them out - along with a couple of other ideas.
The idea of swapping the (quaternionic) axes of "q" in "q^2+c" on each iteration before calculating q^2+c is not producing the desired result but it is producing some very interesting 3D objects :-)

Hell, yeah, i recognize some of the objectts, i achieved by programming in Processing.

Never thought that Ultrafractal is able to display that. Looks like it has a built in  programming
language.  But the code looks very crypric. Is this compiled ? Is raw UF code available ?


Greetings,

Marco Vernaglione

Hi Marco,

The cryptic stuff is not code it's just compressed parameter files, UF can compress them to save space/memory. The formulas themselves are freely available as the "Solid-3D" formulas in the "mmf.ufm" file from the Ultrafractal formula database http://formulas.ultrafractal.com/ (http://formulas.ultrafractal.com/)
I'm part way through writing improved 3D formulas - the existing ones don't use distance estimation for optimisation in finding the solid boundary, my new ones do and are considerably more optimum in terms of speed/accuracy but they're not even really ready for beta-test yet :-)

David Makin wrote:
>
>    .....Here are the parameters:
>    ...
>    MMF-MandyQuat {
>    ...
>    MMF-QuatNewton {
>    ...
>    MMF-HyperMandy {

You know... you can add the parameters to this site and make them a "clickable" link for downloading.  It would make the scrolling through a bunch of lines of data unnecessary for everyone.  That way those that care not to use UF will not have to view and read more than they have to.      ;)

Just checked out what you mean in the parameter forum - will do so in future :-)
Are attachments automatically clickable (e.g. upr files ?) or after attaching the file do I need to do something else to make them clickable ?

The current list of supported extensions is as follows:

ttf,fim,txt,doc,pdf,jpg,gif,mpg,png,avi,psd,frs,dz,xep,loo,ufr

I can add more extensions as required.

Ultrafractal parameter files are .upr
They are actually just plain text files.
Unless you've got a really clever way of displaying the embedded images from .ufr files then you shouldn't really allow that format - it includes embedded copies of the actual image as well as the parameters (the image presumably in some custom Ultrafractal format).

Hi David,

I think i should stop to try to program stuff in Processing,  instead to move to do something with Ultra Fractal!

It could be also be much faster than that Processing Java code.

Is it also possible to bring UF to save frames of any (modification) layer ?

To explain it further... my code reveals the body of the 3dfractal as slices of "onion rings", every slice is saved
to HD, for later composition.

It goes from the very outerior ( Infinity ), through the chaos wrinkles ( The frontier between chaos and order )  to the core ( The (M)-Set ).

e.g can this be done within UF ?


Greetings,

Marco Vernaglione

hmm, that's an interesting question... on the one hand, i wouldn't really expect uf to be that much faster than java since most java implementations have just-in-time compilation, which has been tuned for a number of years and i suspect uf's scripting is interpreted*; on the other hand i'll bet uf has built in functions for dealing with complex numbers and quaternions (which will be a real boon for you given what i said in your cubic/quintic mandelbrot set thread), which will use fast c/c++ routines internally. depending on the mix of native vs scripted operations the results can go very much either way...

unfortunately there are too many complicating factors for a direct comparison, for example support code around the basic execution, like java's display classes or uf's gui rendering code.


* if it's actually compiled to machine code then it boils down to the efficiency of said compiler versus java's ridiculously conservative/safe execution (eg array bounds checking etc).

I think UF compiles rather than interprets (a really long formula takes a while to load when selected) - maybe Kerry or Frederik himself will confirm this. I think it's multi-level compilation in that any parameter changes are allowed for in the way the code is compiled.
Also the main speed up is for investigation of new ideas rather than final generation time - most of the background work is already done when writing formulas for UF (or ChaosPro).
The only real bugbear for me is that UF was originally designed with 2D escape-time fractals in mind so writing efficient 3D or IFS code is not straightforward - I'm hoping a future release will allow a mode giving user formulas direct access to the screen.

If you're asking what I think you are then yes you could do that.
Any formula/rendering method can now be written using UF so you could write your own UF formula for this.
Or (if you mean what I think you mean) you can use my "Solid-3D" formulas from mmf.ufm - these allow you to cut a 3D fractal to up to 6 rectangular planes and/or to a sphere plus you can colour the fractal using lighting or using any "inside" colouring method.
If you mean rendering successive images closer to the "inside" then you can of course do that too.
If you want to know how to code a more optimum 3D algorithm for UF than my "Solid-3D" ones let me know as that's what I'm working on when I get chance - it's already massively faster but lacks the bells and whistles such as full phong shading, shadows and the option to use any UF colourings.

forgive my nitpicking-aside, but the phong model is easily the worst brdf ever invented and is entirely responsible for the bulk of all povray renders looking as 1980's as they do ;)

I'm not well up on recent lighting algorithms - I got the models I use from "Computer Graphics - Principles and Practice" by Foley/Van Dam/Feiner/Hughes - if there's a better model that's as fast as doing phong as described in there then please just point me at it :)

Of course in Ultrafractal the default colouring method is tied to the use of a user adjustable palette, so you can usually make up for any shortcomings in the phong model by adjusting the palette accordingly, personally I think the combination works quite well:

(http://tn3-1.deviantart.com/fs9/300W/i/2006/058/e/b/Apprentice_Piece_by_MakinMagic.jpg)

Full-size: http://www.deviantart.com/deviation/29678693/ (http://www.deviantart.com/deviation/29678693/)

Obviously  UF would be handle the Zoom, Perspective, coloring of the formula. I think i would swap to UF.

Hey, all three options are of high intrerest!

But actually i had no occasion to try the present methods. I am into the progress of oving to UF...

Thank you David Makin for you'r first two post's, They where verry usefull.

You're welcome  :)

Actually the image is a quaternion version of the Mandelbrot formula Z=Z*Z+Z the rotated appearance is natural to the set. Give it a try on your favorite Quaternion software.

I've run a sample animation of a slight modification to the formula Z=Z*Z+Zo where Zo is the original starting point being evaluated not the result of the last iteration.

It's not a great animation, but good enough to see the potential:
https://fractrace.dev.java.net/files/documents/6137/46632/Quaternion.avi

what happens when you introduce a complex term to the exponent in z=z^2+c so that it's z=z^(2+ix)+c using the principal value expansion?  Nothing pretty but some interesting log scaling