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Author Topic: a standard name for buddhabrot-like fractal ?  (Read 2018 times)
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ker2x
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« on: May 07, 2015, 01:18:39 PM »

Friendly greetings \o/

I decided to rewrite buddha++.
Nicer UI, flexible framework for different formula.

The thing is, how to call it ?  :smiley
Is there a name for buddhabrot-like fractal ?

Bonus question : any name idea for the software ?

thx !
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cKleinhuis
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« Reply #1 on: May 07, 2015, 01:27:14 PM »

"butterbrot" cheesy

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kram1032
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« Reply #2 on: May 07, 2015, 01:45:58 PM »

orbit trails?
Bread trails?
Breadcrumbs.
or how about Almond crumbs? cheesy
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lycium
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« Reply #3 on: May 07, 2015, 01:47:50 PM »

Is there a name for buddhabrot-like fractal ?
IFS

(it's just an IFS randomly choosing roots of z^2 + c)
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cKleinhuis
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« Reply #4 on: May 07, 2015, 02:02:42 PM »

i consider it as a special form of ifs as well, although the name ifs for that dot counting is wrong in the first place as well wink not wrong, but i mean ifs is a general name for "iterated function systems"
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kram1032
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« Reply #5 on: May 07, 2015, 02:22:34 PM »

Yeah, an iterated function system is a rather general notion. Buddhabrot style renders concern a certain... well... rendering style of IFS. The MSet and the JSets all are IFS.
Depending on your definition of "Function", it's not hard to argue that L-Systems also are IFS. As such IFS is one of the most general - perhaps also the most fundamental - methods of generating fractals. (And Multifractals. And Nonfractals. And indeed pretty much anything.)

Though perhaps "IFS Flames" is pretty accurate? Those are basically orbit plots like the Buddhabrot, right? - while the standard coloring method is an escape time algorithm.
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3dickulus
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« Reply #6 on: May 07, 2015, 03:02:02 PM »

"2BFrac" or "BBFrac"  as it's a buddhabrot-like fractal rendering program ?
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cKleinhuis
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« Reply #7 on: May 07, 2015, 03:10:42 PM »

if you ask me ... i would indeed go for "ifsOrbitPlotter" or something ...
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Chillheimer
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« Reply #8 on: May 07, 2015, 03:24:27 PM »

Friendly greetings \o/
Bonus question : any name idea for the software ?
thx !

I personally would focus much more on the buddha aspect instead of the mundane bread.. wink
after all the pictures are stunning, what happens there is stunning, the resemblance is stunning.
so it deserves a lees technical name.. BuddhaPlot?
(and nope I'm not buddhist or even close to religios wink
Anyways, looking forward to your update
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lycium
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« Reply #9 on: May 07, 2015, 03:55:42 PM »

Yeah, an iterated function system is a rather general notion.
If you check the linked Wikipedia article, it's actually much more specific than the name might imply.

Buddhabrot style renders concern a certain... well... rendering style of IFS.
Not really, it's pretty standard IFS rendering - build up a histogram and log-display / tonemap it. Literally the only difference is that "Buddhabrot" has two transforms, one for each root of z^2 + c, so it's pure IFS.

The MSet and the JSets all are IFS.
The formulae don't actually prescribe any particular rendering method, and the road forks in two here: escape time methods (the normal Mandelbrot / Julia rendering method) and IFS. The former is a simple evaluation as function of (x, y) on image, whereas the latter is completely different and you have incoherent access all over the image, plus you can't skip computation of what's outside without bias.

So I wouldn't consider them too similar... at least, the distinction becomes extremely clear when actually implementing the algorithms wink

Depending on your definition of "Function", it's not hard to argue that L-Systems also are IFS.
Again, you really should check the defn of IFS, especially since you're a mathematician smiley In IFS you're making a histogram of point orbits under a contractive operator, in L-system you are mostly doing string replacement without any necessary notion of geometry.

Though perhaps "IFS Flames" is pretty accurate?
The very worst terminology in fractals is that of flam3: "variation", "xaos", "symmetry", "sheep", ...
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Sockratease
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« Reply #10 on: May 07, 2015, 04:10:31 PM »

...Bonus question : any name idea for the software ?
thx !

How about Buddybrot?  For the Buddhabrot and his Buddies?

In fact, Bhuddies could be the generic name you are seeking! clown
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ker2x
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« Reply #11 on: May 07, 2015, 04:14:00 PM »

How about Buddybrot?  For the Buddhabrot and his Buddies?

In fact, Bhuddies could be the generic name you are seeking! clown

i like this !  cheesy
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often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
(en) http://www.blog-gpgpu.com/ , (fr) http://www.keru.org/ ,
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ker2x
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« Reply #12 on: May 07, 2015, 05:29:08 PM »

Thx buddy !
http://i.imgur.com/lvVxexA.jpg
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often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
(en) http://www.blog-gpgpu.com/ , (fr) http://www.keru.org/ ,
Sysadmin & DBA @ http://www.over-blog.com/
cKleinhuis
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« Reply #13 on: May 07, 2015, 05:46:15 PM »

very good wink

@ker are you plan to implement those nasty features to use only orbits that have a certain distance to the sets? and hybrids ... and moaaar formulas?!
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kram1032
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« Reply #14 on: May 07, 2015, 06:37:00 PM »

The way it is stated in that Wkipedia article,  an iterated function system is a set of functions that map the space you work in (for instance \mathbb{R}^2) to a smaller region of itself. I feel like that's a bit inaccurate in that, in this definition,  there isn't even a mention of iteration.
As it is written it sounds like an IFS is simply a (finite) set of (contractive) functions.
Such sets provedly have a unique, nonempty,  compact fixed Set.
I.e. there is a specially finite set of points, associated with a given IFS which, if you apply any function of the IFS to that set, the resulting point will again land inside the same set.

For the Buddhabrot, if I understand correctly, the corresponding associated set simply is all the points that are still visible in the anti-Buddhabrot as the number of iterations i \to \infty which,  if I'm not mistaken, simply is the MSet.
However that set isn't the IFS itself. It's just the unique associated set.
The IFS simply is the collection of function.

For the Buddhabrot said set simply is:
f1: x->x^2-y^2+c1
f2: y->2xy+c2

This is actually a Julia Set with fixed constants.
So if we are being super technical, the MSet's generating functions are not an IFS because the corresponding set is not finite nor even countable: they define a family of two functions in one real parameter each. Furthermore one of the two involved functions is nowhere contractive. (Though the article mentions that this condition can and in practice will be relaxed.)

Also,  the family of functions in the MSet do not interact with each other so more accurately one might say that the generating function of the MSet represents an entire family of IFS with two real parameters.

None of this is actually related to how the IFS looks like or is constructed. - the IFS itself,  as stated, does not look one way or another. if you want to construct the associated set, though, one way to do it is in the classic way of iterating (randomly or combinatorially to a finite order) across the set of functions. - that's in fact not how to get a Julia Set either. The two functions are always applied in parallel rather than in arbitrary order (btw how would that look like?)

One way out of this is to take the two functions and interpret them together as a single function in \mathbb{C} but then it's hardly a function system (though granted sets with one element are still sets), just a function, but the associated sets would simply be the given Julia Sets corresponding to c=c1+c2 i.
Those same sets should be constructable in an escape time manner (the set is only the region inside the usually black blobs, not the colorful thing around it) or an orbit map (anti-style) in both cases taking the iteration count to infinity.

So given that,  based on the articles's definition (which, again, somehow doesn't even include iteration), no, neither the MSet nor Buddhabrot are IFS. They are particular renderings of a family of sets that are associated with an IFS with a single function over \mathbb{C} as element.

Finally if you, for instance, take your space to be that of collections of connected line segments and your functions to be ones that map one such collection to another,  you essentially recover L-Systems.
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