Old 27th February 2008, 21:58   #1
hexcollie
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Need serious help with fractal equations

Ok, so I got this book (The Beauty of Fractals, by H.-O. Peitgen & P.H. Richter, if you're interested). It has amazing prints of fractals, along with their accompanying equations. So I have all of these equations to create some truly incredible fractals, however, I have no idea where the hell to put them to get them to display as what i am seeing on the page (which i have also seen dripping off of my arm, back on the the page )
Anyway, i'm gonna try to put some of these equations on here, which may be pretty difficult since half of the variables are greek and latin characters, and if anybody could tell me what to do with them, or even use them to create something cool and just show me, Cool stuff would be made!

Here's a few samples_______________________________________
(I'm trying to copy this character for character, but some greek characters and sub/superscripts will have to be anounced)
::Key::
^=anything after will be a superscript
*=anything after will be a subscript
Ï€=pi
λ=Lambida
Є=Epsilon
___________________________________________________________
-Julia set for x->(1+Є)λx+x², λ=e^2πi/20, Є=0.001;x*0=0 is a repelling fixed point.

-Binary decomposition of A(0) for u->u^2/(1+cu^2), c=-0.12+0.74i
____________________________________________________________
There are a bunch more that I wanted to put up here, but after trying this much, I feel that I am missing fundamental parts of these equations, and thus also in way over my head, but all of the information is right in front of me and it's driving me mad trying to figure this shit out enough to use it within my presets. If somebody could please help me, even if you don't feel like replying to this drag-ass post, please feel free to im me, My AIM handle is hexcollie, Please god help me! I would gladly scan these pages for anyone interested!!

^_^ Don't Panic!! ^_^
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Old 28th February 2008, 23:13   #2
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on emule there is a video called something like fractals-the colours of infinity - it's highly recommended
it's also on the torrent search engines
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Old 29th February 2008, 05:02   #3
hexcollie
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just started the torrent, btjunkie pulled it right up. Thank's a ton brother, i'll tell you what i think

^_^ Don't Panic!! ^_^
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Old 29th February 2008, 21:57   #4
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HOLY HELL!!!!! That was the most amazing video I have seen in a long time. I swear I had to wipe a tear from my eye several times throughout this film. I have a brand new respect for mathematics. When they called the fractal the fingerprint of god it seriously got to me. I'm checking out sacred geometry, I seriously want to integrate math much more greatly into my life after having seen this video! bdrv, I thank you so much for having shown this to me. But beyond the spiritual experience i just got out of that, I also have a much better understanding of what goes in to a fractal than this book even touches on conveying. I don't know what to say man, that was seriously touching. To anyone who has not seen this video, please god go check it out, if you have a torrent client the direct link to the torrent tracker is http://dl.btjunkie.org/torrent/Fract...wnload.torrent to start the download. There are plenty of seeds, and I'm certainly keeping mine up, so check it out!

^_^ Don't Panic!! ^_^
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Old 8th March 2008, 03:40   #5
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Finally here's the fractal to your settings - Beautiful! Did you expect something like this? I'm totally bewitched.

cheers
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File Type: milk flexi - a julia fractal for hexcollie.milk (12.1 KB, 430 views)

Last edited by Flexi; 8th March 2008 at 04:06.
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Old 8th March 2008, 22:41   #6
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flexi that is beautiful

I know the film is monumental, mathematics is so humungous that looking at the rules of infinite patterns of chaos for a while really is beyond any type of rationalisation that goes into regular making a cup of tea and stuff!
it's hard to figure out where the order of maths and and the chaos of life starts.
makes you wonder about every tree, and whether every day from sunrise to sunset and every different person's life is also self similar like a fractal.
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Old 10th March 2008, 18:51   #7
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and here's a decent preset made of it.
biiig thanks for that equation!
(come up with more of them - the interesting part is the decomposition)
check out this vid too :
http://www.youtube.com/watch?v=UXAaDqPl7oY
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File Type: milk flexi - stangely dynamic world.milk (14.1 KB, 390 views)
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Old 10th March 2008, 19:12   #8
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Wow, that is the shit! I have lots more of these equations if you want me to put them up here, still don't know if I posted them correctly. Only wish i would have had internet access out in Borden, Indiana this weekend, these would have been the shit!! Thanks so much for making my dreams a reality, you rock flexi!
--BTW, I fucking LOVE OZRIC, no way you could have known that, but thanks for that vid too (check Live at The Pongmasters Ball if you havent seen it yet)

^_^ Don't Panic!! ^_^
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Old 10th March 2008, 20:13   #9
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More Julias

again, the key
::Key::
^=anything after (or in between) will be a superscript
*=anything after (or in between) will be a subscript; ex. Z*(n)*(X)--is Z subscript (n) times (X)
Ï€=pi
λ=Lambida
Є=Epsilon
∞=Infinity
!=Just inserted for space
/=division, or fraction indication
------------------------------------------------
-(had trouble finding julia set for this one, but it appeared to be:: P*c(X)=X^2+C
-Binary decomposition of A(0) for u->u^2/(1+cu^2), c=-0.12+0.74i
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-Binary decompositions of A(∞) for x->x^2+c; insert: c=0; c=0.32+0.0043i; or c=i
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
##Newton's Method for x^3-1##
-In the attempt to extrapolate from our experience with Newton's method for p(x)=x^2-1 one might expect that the Julia set for: N(x)=x-(x^3-1/3x^2)=(2x^3+1/3x^2)
is the set for...blahblahblah
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-Julia-like set; f(s)=s-s^2, ų=3.2: h=0.3; or h=1.0; or h=1.4; or h=1.7 (coolest)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-Z*(n)*(X)=Z*(n-1)*(X^1)φ*(n)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-Map for Mandelbrot set: z->(z^2+1)^2/z(z^2-1)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-Julia set: Z*n+1*=z^2*n+c
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Ok, I don't know what you can actually use out of those, but the pictures i took them from were definitely awesome, and judging from what you created last time, i'm sure you can pull something from all this. I'll personally be spending the rest of my time dissecting the presets you made of the original equations i posted. Have fun!!!

^_^ Don't Panic!! ^_^
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Old 10th March 2008, 20:54   #10
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most impressive, here's is an experimental remix, not sure exactly what is going on, and that video is awesome!
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File Type: milk flexi - stangely dynamic world shifter fx.milk (14.7 KB, 354 views)
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Old 10th March 2008, 23:29   #11
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wow! fat remix

this one is a correspondet to what you called the "map for the mandelbrot set"... it doesn't look like the M set, but it's cool either...
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File Type: milk flexi - strangely dynamic world 2.milk (14.5 KB, 332 views)
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Old 11th March 2008, 06:23   #12
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been playing with the toys you gave me, mixed this up. thank you again flexi
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File Type: milk flexi - a julia fractal for hexcollie embossed.milk (13.6 KB, 379 views)

^_^ Don't Panic!! ^_^
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Old 11th March 2008, 16:22   #13
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heres sum remixes
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File Type: milk flexi + various mashup - julian affairs [csmic edit].milk (11.2 KB, 384 views)
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Old 11th March 2008, 16:23   #14
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...
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File Type: milk flexi - julian affairs [6 edit].milk (6.2 KB, 337 views)
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Old 12th March 2008, 00:09   #15
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it's time for knotting fractals together!

take a closer look at the last two lines in the warp shader: the fractal in the green color channel is interpolated from the two other fractals, you already know

have fun.
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Old 12th March 2008, 00:35   #16
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Not been able to check any new presets for a bit. looking forward to these....

"Rules are for the guidance of wisemen and the obedience of fools"

Visuals - Morphyre www.Morphyre.com
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Old 13th March 2008, 00:10   #17
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Quote:
Originally posted by Flexi
it's time for knotting fractals together!
Awesome stuff.
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Old 13th March 2008, 18:28   #18
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here's some shit
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Old 13th March 2008, 18:29   #19
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...
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Old 13th March 2008, 18:35   #20
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3
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Old 13th March 2008, 23:05   #21
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hey cool, i also did some emboss experiments.
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File Type: milk flexi - copper stamp fractal.milk (13.2 KB, 379 views)
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Old 13th March 2008, 23:11   #22
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...and another sick remix...
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File Type: milk flexi - julia cell tissue.milk (18.2 KB, 311 views)

Last edited by Flexi; 13th March 2008 at 23:33.
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Old 15th March 2008, 16:02   #23
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total classic!
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Old 18th March 2008, 05:18   #24
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some sweet sites that might aid

I've been playing around with my TI-83+ graphing calculator, trying to make a julia fractal drawing program, and figuring out some really cool motion geometry before I dive back in to making presets. On one of my random wanderings through the internet, I've found some amazing sites for resources and images that will blow your mind. I think there's plenty of information we could integrate in to our milkdrop interface form of art!
(i kinda had to fuck with the urls cause it doesn't want me to post these for some reason, so just add what is indicated to get there)

=The Infinite Fractal Loop (add w ww.)
-sgeier.net/fractals/indexe.php

=The Spanky Fractal Database (add http ://)
-spanky.triumf.ca/www/welcome1.html

^_^ Don't Panic!! ^_^
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Old 18th March 2008, 22:31   #25
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I use a program that can do audio rate graphics, in that it can draw 1 dot @ 44.1khz... it's a good way of making complex oscilloscopes/pics because with fade time you actually have 44.1 pixels the second in memory, it would be nice to use the coloured squares as pixels but it doesn't go fast enough. I wonder what it would be like using the vector to draw a mbrot set with fade time @ 1.00
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Old 12th April 2008, 23:41   #26
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hey you guys, i've just discovered this ingenious movie:

http://*************.net/movies/what_...ep_do_we_know/

have fun
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Old 29th August 2008, 23:39   #27
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okay, the möbius stuff opened my third eye to the crazy universe of fractioned complex polynomes. Does anyone here recognize the original from this derivative? - it is absolutely the same calculation as in the first preset in this thread.

No time to explain what i found this time, but a tutorial will follow.
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Old 3rd September 2008, 00:02   #28
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Long time..

Great stuff you guys!

bdrv, emule rocks! Thanks for the video tip, I'll watch it when I get it.. Flexi too, that youtube video was awsome.

Maybe it's time to learn some more maths.. and Milkdrop(again). About 1.5 years since I messed with it. However I wonder if there has happened a lot of things in Milkdrop since that time. I guess I don't see everything as it should be, I'm using "Milkdrop 1.05 beta6.1". (And winamp 2.95 for the time beeing...).

You watched it. You can't unwatch it!
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Old 3rd September 2008, 00:38   #29
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you can find the other video on google videos

have fun (and upgrade to winamp5.5x with milkdrop2.0!. well i hope your graphics card is supporting pixelshader2.0)

good night
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Old 3rd September 2008, 01:41   #30
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First, sorry for off-topic'ing topic-starters tred a bit..

Flexi, yess!!! I did just now, and WOW! What a difference! I'm (really very, very) embarrased to say, but now your "milkdrop on fire"-mix made much more sense! (Which is kind of on-topic again since its a fractal )

Really nice work btw!

You watched it. You can't unwatch it!
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Old 5th September 2008, 20:46   #31
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I thought this should be here, too. Don't forget your classics...
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