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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: Alef on May 28, 2013, 07:17:51 PM



Title: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: Alef on May 28, 2013, 07:17:51 PM
After writing letter and small conversation with the author of Buddhabrot algorithm I added equalisation to my variation of not so buddhabrot of the thread:
http://www.fractalforums.com/fractal-programs/problems-with-implementing-budhabrot-in-uf/ (http://www.fractalforums.com/fractal-programs/problems-with-implementing-budhabrot-in-uf/)

Equalisation with sigmoid function looks kind of better than plain equalisation. Now it's possible to create less rought images, becouse this allows more hit density. But it allaways tend to be somewhat dark even when the (modified) sigmoid function lightens the result.

Code:
 ;for Equalisation only
; additional loop calculates brightest colour.
IF (@equalisation==true)
  x=0
  y=0

  while x < #width
    y = 0
    while y < #height

    pixR[x, y]=abs(pixR[x, y])
    pixG[x, y]=abs(pixG[x, y])
    pixB[x, y]=abs(pixB[x, y])

    IF ( pixR[x, y] > maxcolour)
    maxcolour=pixR[x, y]
    ENDIF
    IF( pixG[x, y] > maxcolour)
    maxcolour=pixG[x, y]
    ENDIF
    IF( pixB[x, y] > maxcolour)
    maxcolour=pixB[x, y]
    ENDIF

      y = y + 1
    endwhile
    x = x + 1
  endwhile

ENDIF


;goes throught pixels

;for equalisation. Uses sigmoid function.
IF (@equalisation==true)

	resultR=6*(resultR)/(5+maxcolour)
	resultG=6*(resultG)/(5+maxcolour)
	resultB=6*(resultB)/(5+maxcolour)
ENDIF

Normal mandelbrot:
(http://www.ljplus.ru/img4/a/s/asdam/Mandelbrot_se.jpg)

Formula by Kram:
(http://www.ljplus.ru/img4/a/s/asdam/Lens_eye_se.jpg)


Will need long time to wait. But since most of forum members have much younger PCs with number of times more processor frequencies than mine, it woun't be long. Quad Gen formula,  Ultra Fractal parameter:

Code:
Quad_Gen_SE {
fractal:
  title="Quad_Gen_SE" width=800 height=600 layers=1
  credits="Edgar;5/23/2013"
layer:
  caption="Background" opacity=100 transparent=yes
mapping:
  center=0/0 magn=0.85
formula:
  maxiter=100 filename="Standard.ufm" entry="Pixel"
inside:
  transfer=none
outside:
  transfer=linear filename="em.ucl" entry="Brahmabrot"
  p_sampleDensity=20000 p_maxiter=125 p_seedinput=-8
  p_formula="Quadratic General" p_power=2 p_starpower=7 p_stargeom=0.5
  p_unitvector=-0.5 p_talisadd=1 p_quadfactor=2 p_frequency=1 p_spin=1
  p_settype=Mset p_julia=-0.4/0.25 p_srcWidth=5 p_srcHeight=4
  p_switchRGB="Switch Red and Green" p_ambient=0.2 p_postfn="0- None"
  p_palette="Direct Colouring" p_equalisation=yes p_lightR=0.38
  p_scalarR=0.7 p_lightG=0.98 p_scalarG=1.6 p_lightB=0.14
  p_scalarB=0.3
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
}

(http://www.ljplus.ru/img4/a/s/asdam/Quad_Gen_se.jpg)

Faster. Bird of prey -> abs(z^3) +c:

Code:
a_birdofprey {
fractal:
  title="a_birdofprey" width=800 height=600 layers=1
  credits="Edgar;5/28/2013"
layer:
  caption="Background" opacity=100 transparent=yes
mapping:
  center=0.05/0.1125 magn=1.1428571
formula:
  maxiter=100 filename="Standard.ufm" entry="Pixel"
inside:
  transfer=none
outside:
  transfer=linear filename="em.ucl" entry="Brahmabrot"
  p_sampleDensity=26000 p_maxiter=150 p_seedinput=0
  p_formula=BurningSihp p_power=3 p_starpower=7 p_stargeom=0.5
  p_unitvector=-0.5 p_talisadd=1 p_quadfactor=2 p_frequency=1 p_spin=1
  p_settype=Mset p_julia=-0.4/0.25 p_srcWidth=5 p_srcHeight=4
  p_switchRGB="Switch Red and Blue" p_ambient=-0.5 p_postfn="0- None"
  p_palette="Direct Colouring" p_equalisation=yes p_lightR=0.38
  p_scalarR=0.7 p_lightG=0.98 p_scalarG=1.6 p_lightB=0.14
  p_scalarB=0.3
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
}


(http://www.ljplus.ru/img4/a/s/asdam/BirdOfPrey_se.jpg)

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: element90 on May 29, 2013, 12:00:46 AM
My software Saturn and Titan can produce orbit plots of all the fractal types it has defined (except Lyapunov). The technique I use differs from the usual method for producing Buddhabrots and anti-Buddhabrots, instead of plotting random orbits I just calculate the fractal using the Mandelbrot algorithm (good for most fractal formulae except Pickover Popcorn) or the Julia algorithm (good for Pickover Popcorn) and plot the orbits. There are two extra options for orbit plotted fractals: the calculating area can be set to larger than the display area and the density of the plot can be increased (i.e more plots in a given area). All, captive or escaped orbits can be plotted and the a number of values at the start of an orbit can be omitted. The plots are coloured based on the number of times a location as been visited by an, orbit the value is then used to look up a colour from a colour map (gradient). There are also options for taking the square root of the value or logarithm before looking up the colour in the colour map.

I'm satisfied with the results so far. Here's the latest anti-Buddhabrot:

(https://copy.com/l4n2ZrPCDJN2)
https://copy.com/l4n2ZrPCDJN2 (https://copy.com/l4n2ZrPCDJN2)

I'm currently working version 4.0.0 of Saturn and Titan which will feature a new fractal type called "Attractors" which is a based on a strange attractor formula which has been modified to so that it too can be calculated as all other fractals (except Lyapunov) using either the Mandelbrot or Julia algorithms. The Julia algorithm will produce pictures that are close to the true strange attractor but there can be pleasing extras to the image that aren't part of the attractor which are an an accumulation of the initial values in the orbits before the attractor has settled down to its own path.

Here's an augmented strange attractor:

(https://copy.com/zH3J44VT7pKd)
https://copy.com/zH3J44VT7pKd (https://copy.com/zH3J44VT7pKd)

For more information on strange attractors in Saturn and Titan see http://element90.wordpress.com/2013/05/17/strange-attractors-an-alternative-approach/ (http://element90.wordpress.com/2013/05/17/strange-attractors-an-alternative-approach/)

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: hgjf2 on May 29, 2013, 09:31:21 AM
Nice BUDABROT IMAGES
 :peacock: :thumbsup1:
So the images must to go at NIRVANA

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: kram1032 on May 29, 2013, 10:27:29 AM
Alef:
Nice work!
I don't recognize that second one as one of mine. Which one is it?
The third one looks like Creaky Old Attic (the one that's based on "dual numbers" where the "imaginary" part squares to 0 instead of 1)

element90: That Anti-Buddhabrot looks amazing!

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: Alef on May 29, 2013, 02:52:13 PM
Kram:
It was something named eye of summoner or something equaly devilish. I found formula on your deviantart page. That angular were quadratic generalisation formula by Jos Hendrix, as I remember. Not shure what y*y was, probably 1.

element90:

Wow, nice looks, first one looks like coloured with natural colours, like a photo of something natular. You probably used alsou bailout conditions with throwing out |z-oldz|< minbailout, did you ? Becouse I notised that pure orbits produced too much hits at the center and then they owerlighted everything else.

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: Alef on May 29, 2013, 03:51:00 PM
Quad Gen vere something like this:
X = 1*X^2 + 1*Y^2   + C        
Y = 2*X*Y   + C
So then y*y=1
http://www.fractalforums.com/mandelbulb-3d/first-post-something-fundamental-about-fractal-generation-t11008/ (http://www.fractalforums.com/mandelbulb-3d/first-post-something-fundamental-about-fractal-generation-t11008/)

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: KRAFTWERK on May 29, 2013, 04:10:17 PM
Wow, yes, that Kram Formula image lookes very nice Alef (and Kram of course ;)
But that anti Buddah is really beautiful element90!

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: element90 on May 29, 2013, 04:44:49 PM
Regarding my example anti-Buddhabrot.

The bailout was norm(z) > 16, norm being z.r^2 + z.i^2, the orbit length was 3700 omitting the first 700 values for each orbit. The picture is a scaled version of the full sized 12000x8000 original.

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: Ryan D on May 30, 2013, 02:27:18 PM
Quote from: element90 on May 29, 2013, 04:44:49 PM
The picture is a scaled version of the full sized 12000x8000 original.

Note that extreme anti-aliasing can be very helpful in creating nice looking orbit path images.  You can get good smooth images even with something as crude as Fractint with its 256 colour palette and its method of creating orbit paths that does not use any randomness in selecting the initial points (this can create grid-like paths due to the regular spacing between starting points).  Look at these two - the top one does not use any anti-aliasing, the bottom one takes it to the extreme with the anti-aliasing (original image dimensions were 30720 x 17280 pixels).

Ryan

(http://davenportsleds.ca/temp/orbitx.jpg)

(http://davenportsleds.ca/temp/orbit.jpg)

Title: Re: Brahmabrot (halfway toBuddhabrot) equalisated
Post by: Alef on May 30, 2013, 05:12:18 PM
Resizing image can do magic, it can make smooth almoust every generated image, so this could portray used algorithm better than it realy are. So my pictures are 1:1 as they were generated.



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