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kram1032 In reply to Sunboom [2008-10-17 12:59:06 +0000 UTC]

[link]
The sum of all Julia-sets, btw, is the Mandelbrot set...
which can be extended to the
[link]
"buddhabrot" and even further to the
[link]
Nebulabrot...

I hope, that wasn't too much info xD

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Sunboom In reply to kram1032 [2008-10-26 19:22:05 +0000 UTC]

Ok thanks for the info! Nope he hadn't told me yet.

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kram1032 In reply to Sunboom [2008-10-26 22:09:49 +0000 UTC]

no problem
Fractals are great
Really many fractals you'll see, will be based on Julia-Sets^^

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Sunboom In reply to kram1032 [2008-11-06 21:13:48 +0000 UTC]

Fractals sure are great. I'm not really into the technical details though; I'm just there for the aesthetics .

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kram1032 In reply to Sunboom [2008-11-06 22:23:46 +0000 UTC]

actually, the technical part also is interesting... It's so simple! just take one formula and map it on itself again and again. What you get, is a fractal (in most cases at least)
Or Lindenmayer systems... - they're used to approximate nature, for example... Trees and plants can be "compressed" to often just a few signs of Lindenmayer-vocabulary, giving infinite details.

Lindenmayer systems also are mappings on themselves again and again but without a formula behind that. Just a simple set of rules.

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Sunboom In reply to kram1032 [2008-11-24 00:10:18 +0000 UTC]

But what exactly does 'mapping it on itself' mean?

Pretty cool about the trees and plants .

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kram1032 In reply to Sunboom [2008-11-24 14:52:30 +0000 UTC]

see this simple formula:
x -> x²+a

this means, that "x" gets replaced by "x²+a" in the next iteration.

so, you'll have x²+a in the next step. Now...
x -> x²+a

that gives you (x²+a)²+a

x-> x²+a => ((x²+a)²+a)²+a

and so on.....

it means, "replace one part of the formula with the whole formula."

MANY fractals (so-called IFSs... Iterated Fractal Systems) are done like that.

Same thing actually happens in Lindenmayer-systems but not with formulas but simple geometric introductions:

a -> a+b

b -> b-b

startvalue: a

a and b both are lines of lenght 1
+ means, rotate by an angle, clockwise
- means, rotate by an angle, counterclockwise

what you get is:

a
a+b
a+b+b-b
a+b+b-b+b-b-b-b
a+b+b-b+b-b-b-b+b-b-b-b-b-b-b-b (<- written that by hand... I hope, I didn't do a mistake...)

the rotation-angle is fixed and chosed before starting the iteration.
What you get, looks like this (for example)

[link]

[link]

those two are rather simple.
The next one has an other two parameters [ and ] which somehow save what was 'till now and plug it into the recursion...
(I understoof WHAT they do but not, HOW they do so, yet... so, don't ask for a more accurate explanation from me xD)

[link]

as you see, it has something like "twigs" - those are made via those parameters [ and ]

[link] <- here's more info about it

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Sunboom In reply to kram1032 [2008-11-27 21:13:03 +0000 UTC]

Thanks! I think I finally understand now. The system IFSs are based on actually is very similar to a subject I'm learning right now on school, it's called 'somrijen', I have no idea how to translate it though. It looks like this:

u[n] = 2*u[n-1]+2

So when you define u[0] as 4, u[1] = 2*4+2 = 10
Then, u[2] would be 2*10+2 = 22 and so on. That is the same concept isn't it?

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kram1032 In reply to Sunboom [2008-11-27 21:38:25 +0000 UTC]

yeah, IFSs are actually recursions, like those sum- and product-recursions but not that direct They can't be solved in an aritmethic way directly, you need to iterate them. (A computer does a great job in doing just that^^)

(Ok, just for correctness, for many IFSs, it's actually unknown, wether there is a simple formula but the guesses are, that there isn't... If you find one, you most probably get famous for that )

L-systems also are recursions, but of pure geometric appearance, while IFSs include (very often surprisingly simple) formulas....

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kram1032 In reply to Sunboom [2008-10-17 12:50:47 +0000 UTC]

[link]
Dunno if Aexion told you already, so, I answer you here^^

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Aexion In reply to Hyric-the-hunter [2007-02-14 12:33:15 +0000 UTC]

Thanks,that fractal is made of little fractals who are made of more little fractals and so on.., but also, it is made from solid blocks... This one was very hard to make, because it is.. well..confusing..

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Aexion In reply to Voracious-Vixen [2007-01-21 01:07:56 +0000 UTC]

Oh, Thanks

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Voracious-Vixen In reply to Aexion [2007-01-21 10:49:14 +0000 UTC]

Very welcome

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Aexion In reply to LaPurr [2007-01-21 01:07:04 +0000 UTC]

Thanks you so much for all of these words, *LaPurr

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LaPurr In reply to Aexion [2007-01-21 02:27:33 +0000 UTC]

You're very welcome. You make wonderful images.

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Aexion In reply to LaPurr [2007-01-21 22:49:31 +0000 UTC]

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Aexion In reply to parrotdolphin [2007-01-21 01:05:03 +0000 UTC]

Thanks a lot *parrotdolphin

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Aexion In reply to o-LJ-o [2007-01-18 23:20:07 +0000 UTC]

Thanks..
A blueberry cake perhaps???
I was originally planning to render an ancient terracota red fractal temple..but at the end, it looks better in blue than in red, so it ends as a blue thing

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o-LJ-o In reply to Aexion [2007-01-18 23:48:58 +0000 UTC]

blue is good, so is this...ive put it in my journal, hope thats okies, if not i can take it out, but it will cost ya

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Aexion In reply to o-LJ-o [2007-01-19 00:38:04 +0000 UTC]

Oh, In your journal , Thanks a lot for that!!

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o-LJ-o In reply to Aexion [2007-01-19 00:53:55 +0000 UTC]

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Aexion In reply to esintu [2007-01-18 19:30:38 +0000 UTC]

Thanks!! *banana-tree

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