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Geek Culture / Eureka moment for me!

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Neuro Fuzzy
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Posted: 12th Jan 2011 17:14 Edited at: 12th Jan 2011 17:20
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Uhh, so I'm studying some fractal geometry in my spare time - fractal dimension and all that rubbish. I've decided I'm going to try to go through mandelbrot's book: "The Fractal Geometry of Nature", and try to re-render all the fractals in there. I tried to generate base-motif fractals today. (described here)

Basically, you start out with a couple line segments. You then replace every line segment with another couple of line segments. As this process repeats towards an infinite number of times, you'll get an infinitely long curve (provided it's not a straight line!) This curve may fill up an area, or it may have 0 area. that's some weird stuff, and I'm still figuring out the math behind it.


Anyways, my first attempt generated this:




Due to a bug where I forgot to include or exclude certain points.

THEN, well... I got it working... but then there are these other types of base-motif fractals called "sweeps" - where you flip every couple of lines, in a particular order... so I spent another couple hours trying to implement that and hunt bugs. ANYWAYS what I finally got is a pretty dang good system for rendering!!! CHEECK OUT SOME IMAGES I MA3D!!!



[edit]
it's coded in DBPro, and I plan on getting an IDE working with it all, at which point I plan on pasting it on the code snippets section. Also, I'm posting this because it's FREAKIN SWEET.

[edit2]
also, there are only 4 different generators used. The top left and bottom right fractals each use their own generator, the bottom right is a sweep. The middle row 3 and bottom left fractals are all just different sweeps of a right angle generator, and the top right three are variations of the koch curve.

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TheComet
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Posted: 12th Jan 2011 17:41 Edited at: 12th Jan 2011 17:42
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Nice job! A little tip : Color the dots/lines proportional to the number of iterations, you will get some beautiful shades Also, does this mean you have good knowledge of imaginary and complex numbers now?

TheComet

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Neuro Fuzzy
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Posted: 12th Jan 2011 18:12
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The construction method is different than that stuff in the complex plane. Some points are obtained with infinite precision after a finite amount of time, however, so I could try to implement a coloring scheme based on that!

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Fatal Berserker
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Posted: 12th Jan 2011 19:05
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awesome, whats the book?

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TheComet
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Posted: 12th Jan 2011 19:59
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Oh I see Nice job! It's good to see someone else interested in fractals

TheComet

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Neuro Fuzzy
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Posted: 12th Jan 2011 20:14 Edited at: 12th Jan 2011 21:09
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My favorites are the bottom right one and the rightmost one above that

The book that I'm following through is "The Fractal Geometry of Nature"

Uhh, he talks... fast in the book... you can't really learn everything from just this book (well, you could try). I'm looking at this book, in combination with this website.

After I polish this up a bit (and make some animations :3) it's on to... I think Iterated Function Systems. Iunno, detailed in the book, there are Base-Motif, IFS, Circle inversion limit sets, brownian motion (and some variants?), complex maps (IE mandelbrot set, and a bunch o' others), curdling, and squig fractals... and probably a bunch more that i haven't read about or have forgotten about xD

ugh, if only I was l33t enough to write my own raytracer, then I'd go on to higher dimensional stuff.

[edit]
also, this is really annoying. I really need to focus on schoolwork ATM but all I can think about is how to go about optimizing and coloring and calculating this stuffz ._.
[edit2]
post-processing in gimp of a fractal sweep


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AndrewT
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Posted: 14th Jan 2011 01:54 Edited at: 14th Jan 2011 01:56
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Very cool stuff, I love fractals!

Since you say that you'll be checking out iterated function systems, you should check out Fractal Flames as well--it's just a variation of IFS that has, IMO, wayyy cooler results. It's what Apophysis uses to generate fractals. It's very easy to generate some very impressive fractals with it.

Fractal Flame Algorithm

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Neuro Fuzzy
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Posted: 14th Jan 2011 09:04 Edited at: 14th Jan 2011 09:08
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Alright. Uhh, I think I'm going to switch to java so that I can embed to da web. Anyways, I'm preparing a code snippets demo post so stay tuned.

(the demo will have pre-made fractals, and simple fractals given parameters)

[edit]
also, that flame IFS looks pretty cool. Is it basically just a pretty standard chaos game IFS that has the probability of a function being chosen proportional to the number of times it has been chosen? The constants a,b,c,d,e, and f (sub i) are just for user input right?

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Neuro Fuzzy
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Posted: 14th Jan 2011 14:15 Edited at: 14th Jan 2011 23:04
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AHAHHHHH i did it again

check out code snippets for the source code to a demonstration of this awesome fractal system.

I've attached the executable, for those of you who... don't.. have a dbpro compiler? How many people on this forum don't have a dbpro compiler??? whatever. for whoever wants it its here.

[edit]
ugh, just realized I left it at my specific desktop resolution. blah 1 sec...

[EDIT2]
DOWNLOAD ROITE HYA!
link to code snippets thread

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AndrewT
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Posted: 14th Jan 2011 21:30
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Quote: "also, that flame IFS looks pretty cool. Is it basically just a pretty standard chaos game IFS that has the probability of a function being chosen proportional to the number of times it has been chosen? The constants a,b,c,d,e, and f (sub i) are just for user input right?"


Kind of. The biggest difference is that it uses non-linear functions, which is why the shapes are so much more interesting. You have a set of "variations" that take a point (after a linear transformation, which is what the a,b,c, etc. constants are for) as input and returns a value, which is multiplied by a weight that's associated with the variation. You create functions by combining variations and giving them different weights. When a point is passed into a function, it's passed into each weighted variation and the results are added together. You create fractals by combining one or more of these functions, and the function used is selected according to its associated probability each iteration.

The algorithm describes twenty or so variations. You can create your own, but it's not easy to develop one that produces aesthetically pleasing results and the variations that are given are more than enough (they're the only ones Apophysis uses).

i like orange
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