Need serious help with fractal equations

[hexcollie]

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!!

[bdrv]

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

[hexcollie]

just started the torrent, btjunkie pulled it right up. Thank's a ton brother, i'll tell you what i think

[hexcollie]

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!

[Flexi]

Finally here's the fractal to your settings - Beautiful! Did you expect something like this? I'm totally bewitched.

cheers

[bdrv]

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.

[Flexi]

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

[hexcollie]

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)

[hexcollie]

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!!!

[bdrv]

most impressive, here's is an experimental remix, not sure exactly what is going on, and that video is awesome!

[Flexi]

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...

[hexcollie]

been playing with the toys you gave me, mixed this up. thank you again flexi

[bdrv]

heres sum remixes

[bdrv]

...

[Flexi]

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.

[Rovastar]

Not been able to check any new presets for a bit. looking forward to these....

[Stahlregen]

Originally posted by Flexi
it's time for knotting fractals together!

Awesome stuff.

[bdrv]

here's some shit

[bdrv]

...

[bdrv]

3

[Flexi]

hey cool, i also did some emboss experiments.

[Flexi]

...and another sick remix...

[bdrv]

total classic!

[hexcollie]

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

[bdrv]

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

[Flexi]

hey you guys, i've just discovered this ingenious movie:

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

have fun

[Flexi]

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.

[raron]

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...).

[Flexi]

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

[raron]

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!

[Stahlregen]

I thought this should be here, too. Don't forget your classics...