Print Page - Kalis Inversion Circle Fold

Title: Kalis Inversion Circle Fold
Post by: thomas314 on April 18, 2012, 01:41:50 PM

Hi,
it seems i can't stop creating those magical dense symmetric patterns ;D
In this thread: http://www.fractalforums.com/new-theories-and-research/ducky-fractals-with-conjugate-only/msg45688/#msg45688 (http://www.fractalforums.com/new-theories-and-research/ducky-fractals-with-conjugate-only/msg45688/#msg45688)
Kali posted there an interesting code snippet and i couldn't resist to implement it in Ultra Fractal but with some
small enhancements.
At this point i want ask you kali for permission to publish it in the UF-database (with giving credits to you of course)

Kalis original

Code:

if (|z|<1)
  z=z/|z|
endif
z=z*m+c

Code:

class THMKalisInvCircleFold(common.ulb:UserTransform){
public:
import "common.ulb"

  func THMKalisInvCircleFold(Generic pparent)
	UserTransform.UserTransform(pparent)
  endfunc
	
  func Init(complex pz)
	UserTransform.Init(pz)
  endfunc

  complex func Iterate(complex pz)
    fpz=|pz|
    if fpz<@radius
      pz=pz/fpz*@radius
    endif
    pz=pz*@m+@o
    return pz
  endfunc
default:
  title="KalisInvCircleFold"
  param m
    caption = "faktor"
    default = (1,0)
  endparam
  param o
    caption = "offset"
    default = (0,0)
  endparam
  float param radius
    caption = "radius"
    default = 1
  endparam
}

After this pre-transformation i simply use a Mandelbrot.

Code:

pz=pz^p+c

Some pictures:

Mandelbrot with p= -2.0, 0.0i ,all other parameter have default values

(http://i1255.photobucket.com/albums/hh621/thomasmichels/fractalforum/KalisInversionCircleFold/KalisInvCrclM1.jpg)

and some Julias with different parameter:
(http://i1255.photobucket.com/albums/hh621/thomasmichels/fractalforum/KalisInversionCircleFold/KalisInvCrclJ2big.jpg)
(http://i1255.photobucket.com/albums/hh621/thomasmichels/fractalforum/KalisInversionCircleFold/KalisInvCrclJ3big.jpg)
(http://i1255.photobucket.com/albums/hh621/thomasmichels/fractalforum/KalisInversionCircleFold/KalisInvCrclJ4big.jpg)
(http://i1255.photobucket.com/albums/hh621/thomasmichels/fractalforum/KalisInversionCircleFold/KalisInvCrclJ5big.jpg)

Did you enjoy the show? :)

In the next chapter i'll present the Inversion Elliptic Fold...

Title: Re: Kalis Inversion Circle Fold
Post by: tit_toinou on April 18, 2012, 02:47:03 PM

I didn't understand your small enhancement.. But the images looks great.
I guess there is about less than 50 iterations ?
What is the coloring method ?

Title: Re: Kalis Inversion Circle Fold
Post by: thomas314 on April 18, 2012, 07:20:54 PM

Thanks Tit_toinou,
the way i used the radius parameter avoid sharp circular borders for radius<1 or radius>1 for
the Julia sets.

Code:

pz=pz/fpz*@radius

The radius in this line did the trick :dink:
The next enhancements are the o parameter for the offset of the z-plane and
the separate mandel formula with the parameter p for power. I found that negative
real integer powers gives the best results so far. With a little patient positive powers
of 1 or 2 leads to interesting results too. Coloring those fractals needs patients too.
My prefered inside coloring methods are Exponential smoothing and Lyapunov. And
i used up to 4 layers. Iteration values are about 30 up to 55 :)

Title: Re: Kalis Inversion Circle Fold
Post by: Kali on April 18, 2012, 07:39:34 PM

Quote from: thomas314 on April 18, 2012, 01:41:50 PM

At this point i want ask you kali for permission to publish it in the UF-database (with giving credits to you of course)

No problem. Btw, very nice enhancements.

And the coloring on this particular image is fabulous: (Did you use layering on this?)

(http://i1255.photobucket.com/albums/hh621/thomasmichels/fractalforum/KalisInversionCircleFold/KalisInvCrclJ5big.jpg)

Title: Re: Kalis Inversion Circle Fold
Post by: thomas314 on April 18, 2012, 08:05:58 PM

Hi Kali,

Quote

No problem. Btw, very nice enhancements.

So many thanks ;D :beer:

Quote

And the coloring on this particular image is fabulous: (Did you use layering on this?)

Oh yes,i need 3 layers to do such a rich coloring. Fine tuning the parameters was the most work and i
started 3 times again from beginning...
I'll put these examples in the UF-database too (thm.upr).
But not now because i'm still developing :)

Title: Re: Kalis Inversion Circle Fold
Post by: cKleinhuis on April 19, 2012, 01:18:52 AM

Quote from: Kali on April 18, 2012, 07:39:34 PM

agreed and confirmed!

Title: Re: Kalis Inversion Circle Fold
Post by: Alef on April 21, 2012, 05:54:57 PM

WOW, great pics, but.

Why do you want implement them as UF classes??? :'(

If you 'll look sign up UF mailing list you 'll find, that most of folks have problems using classes, and most of them use simple classless Ultra Fractal 3 style formulas. Probably this is the reason behind unpopularity of kalisets in UF mailinglist.

Probably easyest way to use class based formulas is to load parameters with classes alredy in;) But I would recomend to use simple, easy to load formulas, maybe sometimes with features in simple classes, but not whole formula in .ulb So .ufm;)

Title: Re: Kalis Inversion Circle Fold
Post by: thomas314 on April 23, 2012, 01:23:13 PM

Hi Asdam,

Quote

Why do you want implement them as UF classes???

well, class programming offers great advantages not only for me as a programmer but for the users too.
E.g. they can use one of my formulas in combination with transformations and replace any transformation or
fractal formula with other class plugins without writing any new line of code.
To understand that, some learning is required. If you just only want to have fun, no problem, start clicking
around and play with numerical, functional and class-plugin parameters.
And it is possible to rewrite the class code into procedural code...

If you want to open new doors have a look at Damien M. Jones documentations:
http://formulas.ultrafractal.com/reference/additional/tutorials/Users.html (http://formulas.ultrafractal.com/reference/additional/tutorials/Users.html)
Or at Hidden Dimension:
http://www.hiddendimension.com/challenges/Tutorial1/UF5Tutorials.html (http://www.hiddendimension.com/challenges/Tutorial1/UF5Tutorials.html)

Title: Re: Kalis Inversion Circle Fold
Post by: Alef on April 24, 2012, 06:16:01 PM

Quote

well, class programming offers great advantages not only for me as a programmer but for the users too.
To understand that, some learning is required.

I think, there are some usability issues with the whole class feature.
Actualy, writing own formula is more easy than using classes, and most of folks there don't uses purpoted advantages of using classes. Formula parts don't fit so well together, and classes aren't divided by subclasses and placed accordingly. That is, "transformations" aren't placed under "transformations", but are in many different user files, REB, DMJ, MMF...

I don't want to sound mean;) But maybe you should make some easy to use switch formula with kalisets class alredy in, so that 2 clicks would be required to change one kaliset formula for an other.

Here is last and pretty typical UF mailinglist fractal. They are very conservative in their choices TM1,2,3.ufm and doodads colouring.

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Fractal Math, Chaos Theory & Research => (new) Theories & Research => Topic started by: thomas314 on April 18, 2012, 01:41:50 PM