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Greetings -

I'm gandreas, the evil brains behind quadrium2 and quadrium | flame, fractal software for OS X.

You can see some of the images I've created with them at my deviantART gallery.

quadrium2 is based on a "data flow model" where you wire simpler nodes together to form complex images, and quadrium | flame is based on IFS and strange attractors (and yes, you can mix the two).  Both use genetic algorithms to help create a wide variety of fractal/procedural art, texture, etc... including the ability to generate QuickTime movies and high resolution prints.

It's nice to finally get to use some of my college/grad school math and color-science background in a creative way.

heya gandreas!

cool to see another experimentalist-coder around; your program looks pretty interesting and seems to contain a few "tricks of the trade" i prized for not being in apophysis ;) particularly interesting is your lucid pairing of graph-based construction of the iteration function and genetic algorithms to explore the resulting large space of possibilities. when i first read about this i imagined that it would be very slow to evaluate (chains of virtual functions are hell for pentium4s in particular, not that it matters for macs ;), but i see your computer science education has served you well... i'm guessing you do an infix to postfix conversion of the evaluation tree and turn the resulting operations into some kind of nicely-executable format (be it actual machine code or a compact binary representation), correct?

anyhow, your work is quite inspiring (in particular what i've seen of the ide) and i look forward to seeing more :) btw, i'd also be very interested to hear your experiences in the business aspect of making fractal applications, since i have absolutely no idea what the market is like!

Greetings, and Welcome to this particular Forum !!!   

I was on your site a couple of weeks ago, after seeing a posting about your software, which came through another fractal group.   Always nice to see the MAC environment getting an additional application for creating fractals.
 

Welcome

it's possible to use quasi monte carlo methods, like for example the radical inverse series, to play the chaos game but:

1. they're subject to aliasing
2. it's not really much different from using a random number generator per thread, and fractals are sufficiently chaotic to nullify the benefit of well-distributed sampling

evaluating all possibilities is an exponential process, and even with only binary decisions quickly becomes intractable - this is the crux of why monte carlo methods are chosen for high-dimensional integration problems (it doesn't suffer from "the curse of dimensionality").

Hi all,

I have been working on a beta IFS formula for Ultrafractal for a while now and thought members here with UF (or ChaosPro) may like to try it out - any feedback gratefully received.

The main formula allows you to generate fractals using either the chaos game or the deterministic method or the inverse (escape-time) method. Because of the way they had to be implimented in UF you won't see the fractal until it's finished being generated when using the chaos game or deterministic methods.
One advantage of the inverse method is that you can do deep zooms into the fractals which is pretty much impossible using the other methods.

There is a main formula file (ufm), a colouring (ucl) and some quick example parameters (upr).

Jason has put the zip of the files here:
http://www.fractalforums.com/for_users/mmfrifsbeta/mmfrifsbeta.zip

If for some strange reason you can't use a zip file, then they're here uncompressed:
http://www.fractalforums.com/for_users/mmfrifsbeta/mmfrifsbeta.ucl
http://www.fractalforums.com/for_users/mmfrifsbeta/mmfrifsbeta.ufm
http://www.fractalforums.com/for_users/mmfrifsbeta/mmfrifsbeta.upr

The main thing I'm still not happy with is the way the colouring works when the "RIFS" codes are used in earnest - as with the example "Sierpinski Fern".
Also I'm still meaning to do a direct colouring formula to go with the main formula as well as the current indirect one.


Note that those of you interested in the actual code who don't have UF can still look at it - the UFM file is just a disguised text file.

bye
Dave

It was previously posted on the UFbeta group (on the old WiKi site) but I'm still after more feedback and also thought there's probably others here interested in taking a look at it.

Also as far as images are concerned - I will be creating "new" formulas from this one (i.e. in itself it won't get changed) so images won't get "broken".
I'm just not happy enough with the formula to put it in the UF database - there are many things in it that could be done better and many that need expanding on - also it really needs more documentation for release as an official "finished" UF formula.
Also specifically I'm going to split it into two different versions - one using the chaos game and deterministic methods and one using the inverse method - that's mainly because when you use non-linear transforms/modifiers the behaviours of these algorithms is quite different but also because the chaos game and deterministic methods require the "render=false" setting in the formula whereas the inverse method doesn't (unfortunately Frederik didn't impliment that so that an end-user can switch the setting without editing the formula).

I suppose this topic should probably be drifted over to the research or programming boards, but...

So I've been thinking about different ways to handle this.  There are two different deterministic algorithms that are possible - the first is simply a breadth first tree traversal.  Works great for some images (your various triangles, dragons and ferns), but others that require N iterations in the chaos game before you start getting meaningful result end up needing too much to be traversed (for example, when using strange attractors - quadrium flame has a technique of "layering" that lets you safely mix strange attractors with other affine or non-affine transform and yet not collapse the attractor).  With some extra work, though, you can also include a weighting of the transform (by tracking the weight with the coordinate, and then using sub-pixel plotting when done), and you could also carry extra information to handle the state of various coloring algorithms.

There is another deterministic algorithm (a slightly more generalized version of one described in Barnley's "Fractal Everywhere") that basically starts with a solid image, and then produces the next generation by taking that last generations image, applies the M transforms producing M new images and combines them to form the image for this generation.  Generating the image N generations deep can then be done in linear time (with regards to N - or more accurately, N x resolution) instead of M^N, but you've got to figure out what the "image" is - you can start with a unit square, but unless all the transformations are contracting, the image will grow and you really need all the results to get the next generation (and this gets ugly as you go to 3D since you then need voxels instead of pixels).

Inverse (escape time) plotting offers lots of potential (Mandelbrot wrote about using IFS for "fractal attractors" as an inverse of an escape time plotting) but suffers one major problem - the transformations need to be invertable (and many of the richer ones aren't, or if they are, have multiple inverses and so you end up back at the whole stochastic vs M^N explosion).  Of course, if this isn't an issue, the ability to generate zooming is extremely powerful...

In general, while chaos game IFS has it's limitations (the large number of iterations for detail, especially if you dare to zoom in), it's got more flexibility (it's unclear if some of the "trap" techniques that quadrium flame uses would translate to other algorithms).  Not to say that any of these other techniques aren't worthwhile, rather that they have the potential to produce new images that chaos game IFS can't.