Varying the power with each iteration

[matsoljare]

Has anyone tried making a Mandelbrot / Julia formula where the power increases with each iteration? That is, first iteration is power of 2, then 3, 4, 5 etc. I know there are formulas where the power alternates between two fixed values, but i'm not sure if this has been tried....

[Sockratease]

I've done it with Mandelboxes and bulbs, but I usually take at least 100 frames to get the power from one value to the next.  So the power per iteration would be something like 2.00, then 2.01, 2.02, etc.

In my opinion, integer leaps would be too abrupt to look good in an animation.

[Rathinagiri]

Hi Sockratease,

I think he mentions a different thing.

Suppose, the iterations of a Mandelbulb be 30.

He wants to render the Mandelbulb, first iteration at power 2, second at power 3, third at power 4 and so on.

It is not about animation. In a single render image, the power increases as iteration increases.

[David Makin]

For standard 2D Mandelbrot/Jullia in Ultra Fractal:

Formulas: mmf.ufm:Transformation Mandelbrot/Julia
Fractal type parameter "z^iter+c"

Code:

Fractal1 {
fractal:
  title="Fractal1" width=640 height=480 layers=1
  credits="David Makin;7/3/2010"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=-.5/0 magn=1.0
formula:
  maxiter=100 percheck=off filename="mmf.ufm" entry="MMFp-TransMandel"
  p_fractal="z^iter + c" p_startpix=no p_start=-0.5/0 p_test=mod
  p_bailout=65536.0 p_smallbail=disabled p_bailout1=1E-5 p_smooth=Off
  p_fixHinrich=no p_cfudge=1.0 p_fudge=10.0 p_fudge1=100.0
  p_fudge2=1.0 p_ang=0.0 p_x=0.0 p_y=0.0 p_a=1.0 p_b=0.0 p_c=0.0
  p_d=1.0 p_sigma=no p_product=no p_selfrot=Disabled p_doscale=Off
  p_scale=2.0/0 p_power=2.0 p_power1=2.0/0 p_ndegree=3 p_nr1=1/0
  p_nr2=-0.5/0.8660254 p_nr3=-0.5/-0.8660254 p_nr4=-1/0
  p_nr5=0.5/0.8660254 p_nr6=0.5/-0.8660254 p_usescale=1.0
  p_usecentre=0/0 p_swscale=1.0 p_swcentre=0/0 f_Fn=acos f_Fn1=cos
  f_Fn2=ident f_Fn3=sin
inside:
  transfer=none
outside:
  transfer=linear filename="mmf3.ucl" entry="MMF3f-ExtCilia"
  p_method="Standard Div." p_bailout=65536 p_dauto=yes p_power=2/0
  p_usedfudge=no p_fudge=1.0 p_fudge1=1.0 p_ciliamode="Just iteration"
  p_split=2.0 p_olditer=No p_iterval=0.0 p_iterweight=50.0
  p_logiter=Ident p_skew=0.0 p_rot=0.0 p_fixrot=no p_rpwr=5.0
  p_fixskew=no p_smallbail=1E-5 p_cauto=yes p_cpower=2/0
  p_usecfudge=no p_fudgec=1.0 p_fudge1c=1.0 p_cfixed=no
  p_cfixedval=1/0 p_cciliamode=Sawtooth p_csplit=2.0 p_fixconv=yes
  p_colditer="1 older" p_citerval=0.0 p_iterweightc=50.0
  p_logiterc=Ident p_cskew=0.0 p_crot=0.0 p_cfixrot=no p_crpwr=5.0
  p_cfixskew=no p_convoffset=0.0 p_zbasin=Off p_zscale=0.1 p_ip=1.0
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
}

[Sockratease]

Hi Sockratease,

I think he mentions a different thing.

Suppose, the iterations of a Mandelbulb be 30.

He wants to render the Mandelbulb, first iteration at power 2, second at power 3, third at power 4 and so on.

It is not about animation. In a single render image, the power increases as iteration increases.

Oh.

Like this?



That's a 6 formula bulb using powers 2 - 7 in order.  Used Mandelbulb 3D.

Interesting shape!

I wonder what happens if the sequence of powers is varied...

Maybe after my animation finishes rendering!

[David Makin]

Just to add that although the 2D ones aren't that interesting I think that both the 3D/4D Julibrot and the 3D Mandelbulb versions probably will be

[David Makin]

Oh.

Like this?

That looks about right (though in my 2D formula the power on the 1st iteration is 1 rather than 2).

[Rathinagiri]

Nice one. In Mandelbulb 3D? How to do that?

[Sockratease]

Nice one. In Mandelbulb 3D? How to do that?

In Mandelbulb 3D there is a "Formulas" window for blending different formulas.  Under Formula 1 I just put an "Amazing Bulb" and set the power to 2.  Then under Formula 2, another Bulb set to power 3, and repeated (increasing the power by 1 for each new bulb) until I ran out of Formula tabs.

I can upload a screen shot or an m3i file if you want.

[Rathinagiri]

Oh. Now I understand. Thanks for taking time to explain.

[msltoe]

I've looked at this before for Mandelbulbs, series such as 2, 4, 8, 16, .... I called it "Fuzzy" because they get quite fuzzy...
http://www.fractalforums.com/theory/'fuzzy'-mandelbub/ It's implemented in Mandelbulb 3D.

[Sockratease]

I've looked at this before for Mandelbulbs, series such as 2, 4, 8, 16, .... I called it "Fuzzy" because they get quite fuzzy...
http://www.fractalforums.com/theory/'fuzzy'-mandelbub/ It's implemented in Mandelbulb 3D.

I love the Fuzzy formula!

This was the first thing I did with my first version of Mandelbulb 3D (and it's a Fuzzy Formula)  (it's a little off center, but I was just playing and learning the program - not making an effort at Fine Art!): 


Bigger : http://www.sockrateaze.com/stuff/1b1.png

Now... those who remember me know that I can't resist image editing my fractals.  Especially when I think I can make something Silly happen!!

So :


Bigger : http://www.sockrateaze.com/stuff/1b.png

Thanks for sharing this formula with us!

[Rathinagiri]

Very creative!