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To the Honor of Mandelbrot by FractalMonster To the Honor of Mandelbrot by FractalMonster
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This fractal image a gave him as a small frame when he visited Lund (a university town in the south of Sweden) in the autumn 2002. No he is died, see my journal [link] :( The motive is a 2D slice of the four dimensional cubic parameter space using the standard parameterizing z -> z^3 - 3a^2 z + b, critical points z = +a (making the set M+) and z = -a (making the set M-).

*a_real = 0.3
*a_imag = 0
*b_real = #pixel (horizontal)
*b_imag = #pixel (vertical)

M+ and M- are plotted in separate layers. The color map in both layers is one of the standard maps incuded in UF.

No filters or post processing.

Ultra Fractal, formula Cubic Parameterspace3 in the sp3-module written by my dear friend Stig Pettersson, Greenseng here at DeviantART. All his modules,
as well as mine can be downloaded from [link]

More info about Cubics can be found at my Cubic Tutorial [link] and the
"cubic" articles in my Chaotic series [link]

Below the parameter file. Play and have fun :)

ForMandelbrot {
fractal:
title="For Mandelbrot" width=480 height=640 layers=2
credits="Ingvar Kullberg;10/19/2010"
layer:
caption="M-" opacity=46 method=multipass
mapping:
center=-0.410894096536518734/0.641319444444444444 magn=88.6154
formula:
maxiter=10000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="6.(b-real,b-imag)" p_M=M- p_SetBorders=no p_hide=yes
p_areal=0.3 p_aimag=0.0 p_breal=0.0 p_bimag=0.0 p_xrot=0.0
p_yrot=0.0 p_xrott=0.0 p_yrott=0.0 p_zrot=0.0 p_LocalRot=no
p_diff=no p_bailout=100.0 p_dbailout=1E-6
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=0 color=9043968 index=69 color=3158085 index=150
color=14736366 index=302 color=675176
opacity:
smooth=no index=0 opacity=255
layer:
caption="M+" opacity=100 method=multipass
mapping:
center=-0.410894096536518734/0.641319444444444444 magn=88.6154
formula:
maxiter=10000 filename="sp3.ufm" entry="CubicParameterspace3"
p_PlottedPlane="6.(b-real,b-imag)" p_M=M+ p_SetBorders=no p_hide=yes
p_areal=0.3 p_aimag=0.0 p_breal=0.0 p_bimag=0.0 p_xrot=0.0
p_yrot=0.0 p_xrott=0.0 p_yrott=0.0 p_zrot=0.0 p_LocalRot=no
p_diff=no p_bailout=100.0 p_dbailout=1E-6
inside:
transfer=none
outside:
transfer=linear
gradient:
smooth=yes index=0 color=9043968 index=69 color=3158085 index=150
color=14736366 index=302 color=675176
opacity:
smooth=no index=0 opacity=255
}
Add a Comment:
 
:iconmerearthling:
merearthling Featured By Owner Apr 27, 2013
fascinating stuff:-)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Apr 27, 2013
Yeah, 2 related subsets :)
Reply
:iconmerearthling:
merearthling Featured By Owner Apr 27, 2013
ah I see I like the asymmetry
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Apr 27, 2013
Symmetry ^^;
Reply
:iconmerearthling:
merearthling Featured By Owner Apr 28, 2013
:-o in terms of how the image fills the picture plane its asymmetric, surely?
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Apr 28, 2013
Yeah, I maybe misunderstood you ;)
Reply
:iconmerearthling:
merearthling Featured By Owner Apr 28, 2013
:-) no problem
Reply
:iconteamplop:
TeamPLOP Featured By Owner Jun 26, 2012
Wow this one is so in depth. Love it
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Jun 26, 2012
Thank you :) It a twelve years old timer :D
Reply
:iconcrida:
Crida Featured By Owner Apr 21, 2012  Hobbyist General Artist
That's a beautiful colour combination! ;)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Apr 21, 2012
:aww: thank you :blushes: I've used one of the standard color maps, but I like it ;)
Reply
:iconthreepathes:
threepathes Featured By Owner Feb 24, 2012
Awesome ;)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Feb 24, 2012
:aww: thank you :heart:
Reply
:iconphoto-maria:
photo-maria Featured By Owner Sep 11, 2011  Hobbyist Photographer
I love it , baby ! :aww:
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Sep 11, 2011
:aww: thank you dear :hug:
Reply
:iconphoto-maria:
photo-maria Featured By Owner Sep 11, 2011  Hobbyist Photographer
Welcome:aww:
Reply
:iconshizen-nana:
Shizen-Nana Featured By Owner Feb 14, 2011
you know i think it's the best fractal so far :love:
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Feb 14, 2011
Even old fractals may be awesome :blushes: I first drew this one in the year 2000 using the first cubic parameter space formula written by my dear friend :icongreenseng: Now I've converted it into his "cubic parameterspace3 formula" ;) Thank you for your kind words :aww:

..and HAPPY VALENTINE to you :hug:
Reply
:iconshizen-nana:
Shizen-Nana Featured By Owner Feb 16, 2011
i'm not very good in fractal parameters, when i do fractals i let myself go and explore :XD:

and THANK YOU for the valentine whishes ! :love:
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Feb 16, 2011
That's what we all do ;) The term "parameter" has two senses:

1) A mathematical one, the Mandelbrot set and is relatives are situated in a parameter plane (or spaces).. So "parameterspace" in "Cubic parameterspace" is merely a part of the formula name..

2) A technical one (the most common). Here a "parameter" is a heap of text, often in a file which is intended to be loaded back into a fractal software in order to redraw a fractal image. A parameter file takes only 2 or 3 kb. Speak about data compression :wow: I myself nearly always share the parameters to my fractals under "Artist's Comments", see my journal [link] ;)

..and don't become hypnotized by obscure words :dizzy:
Reply
:iconminetherzog:
MinetHerzog Featured By Owner Feb 13, 2011
like it!!!
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Feb 13, 2011
:aww: thank you :)
Reply
:iconwarningcadillac:
warningcadillac Featured By Owner Feb 8, 2011
wow, this is great .
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Feb 8, 2011
You like some of my raw fractals :wow: BTW, have you heard about fractals before?
Reply
:iconwarningcadillac:
warningcadillac Featured By Owner Feb 8, 2011
noo ,
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Feb 8, 2011
:D Then below some recycled info about fractals:

First: Check out the zoom sequences (only images) from page 4 in the pdf's [link] and [link] . The end motives are my deviations [link] and [link] :D

Second: In my journal [link] you have some links to short cool fractal animations I stumbled over at YouTube

Third: If you wanna try some free simple fractal software, go to my journal [link]

Fourth: Wikipedia has a nice site [link]

Fifth: Maybe you would appreciate my "Chaotic series of fractal articles" [link] if you have a little theoretical interest ;)
Hope you don't feel spammed :rofl:
Reply
:iconcastleofclouds:
CastleOfClouds Featured By Owner Dec 3, 2010
I like this one (: the colours are beautiful
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Dec 3, 2010
Thanks :) In this one I used one of the default color maps ;)
Reply
:iconcxard:
cxard Featured By Owner Nov 1, 2010  Hobbyist Digital Artist
this is awesome :) may i worship it?... :worship:
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Nov 1, 2010
Thanks :) Of cause :D
Reply
:iconbuddhakat9:
buddhakat9 Featured By Owner Oct 23, 2010
man, this is profound!!!!
:)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 24, 2010
..and yet the this motive is completely raw :blushes: Thank you :aww: :heart:
Reply
:iconbuddhakat9:
buddhakat9 Featured By Owner Oct 25, 2010
I know it's raw...
probably what, 1 layer!!!
bu t that's what makes it so cool!!!
:)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 26, 2010
No, this image has two layers, one for each of the two subsets of the cubic parameter space. So the two layers are mathematically related to each other and have not been put there according to any artistic improvement ;) But it COULD have been drawn in one layer using the technique of SetBorders. Yo ucan test that if you,

1) delete one of the layers.
2) under Formula tab M: switch M+ or M- (depending of wich layer you deleted) to CCL.
3 activate "SetBorders" just under M:

But all of these you can read in my articles 19a and 19b in my Chaotic series. Yeah, also read the preciding 16 - 18 :D
Reply
:iconbuddhakat9:
buddhakat9 Featured By Owner Oct 27, 2010
I shall enjoy exploring!!!
:)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 27, 2010
:thumbsup: :hug:
Reply
:iconteddybearcholla:
teddybearcholla Featured By Owner Oct 23, 2010  Hobbyist General Artist
Very beautiful Ingvar and it is so kool that you met him!! :heart: :hug:
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 23, 2010
Thank you Barbara :aww: Yeah, I were lucky :) :hug:
Reply
:iconteddybearcholla:
teddybearcholla Featured By Owner Oct 23, 2010  Hobbyist General Artist
Welcome Ingvar! :huggle:
Reply
:icontheabodip:
TheAbodiP Featured By Owner Oct 21, 2010
Man this design is pretty cool i like it so much

look forward ^_^ peace
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 21, 2010
..and yet one of the standard gradients in UF ;) Thank you :D
Reply
:iconasclaire:
asclaire Featured By Owner Oct 20, 2010
Extraordinaire! :)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 20, 2010
An old one, but yet ;) Thank you :aww:
Reply
:iconmonikatherese:
MonikaTherese Featured By Owner Oct 20, 2010  Hobbyist Photographer
this one was simply awsome:):+favlove:
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 20, 2010
:aww: Thank you :blushes:
Reply
:iconsushka:
sushka Featured By Owner Oct 20, 2010
nice, reminds me of the sky @ night
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 20, 2010
..in fact the original title was "Sunset around Midsummer" ;) It's a fractal image. BTW, have you heard about fractals before?
Reply
:iconsushka:
sushka Featured By Owner Oct 20, 2010
yeah, I have, in Maths :D and I tried it :)
Reply
:iconfractalmonster:
FractalMonster Featured By Owner Oct 20, 2010
:w00t: Then maybe you would appreciate my "Chaotic series of fractal articles" [link] if you have a little theoretical interest ;)

Regarding deep zooms in the Mandelbrot set, if you check out my deviation "Cauliflowerfort" [link] and click the link under "Artist's Comments", from page 4 you can follow the entire zoom sequence in 28 steps :wow:
Reply
:iconsushka:
sushka Featured By Owner Oct 20, 2010
I'll probably read it, if I have enough time, right now I have to eat :) xD
Reply
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