GNOMON

[billtavis]

This thread was an interesting read, and then I saw this and had to reply:

   But I have in mind a wonderful head made by small and countless iterations of the same head with all its details, hairdo, etc, moreover, I want different hues and shades for them, moreover, its outer cover is transparent and let see some organic inner structures made of different materials.
    It´s nearly imposible to achieve such an image with standard programs, or if it can be done it will cost a lot of time and effort, but this would be nothing for this tool .
    In your terms, it´s a kind of universal and editable formula, if I can say it.

Well, I must say that I have created just such a human head as you have described, in that everywhere you look you see smaller and smaller versions of the same head! (without the transparent surface or hairdo though). I don't have anything to post just yet because I am preparing a high-quality render for the contest. But I can tell you a little about how it was made, and I think it relates to your Gnomon idea. The concept I used was a literal interpretation of a Multiple Reduction Copy Machine (MRCM). This is similar to an IFS, in that you define transforms, but IMO is much more intuitive and flexible. The transforms were defined using the collage theorem. In other words, the first iteration is hand-placed. I made the head in a standard 3d package with just a few lines of scripting, and while the fractal rules are certainly simple, defining the transforms took quite a bit of artistic (not mathematic!) input to achieve a human likeness. It was akin to doing any other artistic 3d modelling. I was able to intuitively "tweak" the details until I was satisfied with the result. Here's a render of some broccoli I made with the same method.  Please note that this is polygon based, so is easily amenable to the techniques for lighting/texturing/rendering available in general 3d packages. In this case I chose a simple Ambient Occlusion look

I have also implemented 2d versions of an MRCM in Photoshop without a single line of scripting, and without a single calculation on my part. It doesn't get much more artistic than that! The process involves recording an Action to define all the transformations, then playing back the action as desired. To define each transformation, the base layer is copied and then manipulated. The final step in the Action is to collapse all the layers into a single base layer again. This process gives you easy access to powerful (non-affine) transformations as well as color modulation (and any other effect recordable in an Action) that will be repeated automatically at ever iteration.
This simple smiley fractal I whipped up real quick shows what I mean. The layer copies were deformed (transformations involving more than just scale/rotate/translate/skew), and the outer "border" smileys were darkened every time. This is not possible with standard IFS approaches. The absolutely amazing thing is that now that the action is defined, I can start with literally any image and it will converge on these smileys after a few iterations!

[billtavis]

...but there is no way to generate a fractal human head, whatever this be...

here is my take on a fractal human head, enjoy!
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=16034

[kram1032]

Lol, that's great
Now make something you can actually look at without getting nightmares
Alternatively, make a version where each and every pair of eyes stares at you.

[billtavis]

thanks!
theoretically, it would definitely be possible to do the eyes, I actually considered this at one point but decided it would just take too much time to get right. One problem was that the "eye sockets" weren't actually very round and each pair of eyes would require manual adjustments.  But with proper planning from the beginning, yeah it would be cool, each eye could be rigged prior to iteration and then they would even update and follow a camera as it moves.
The nightmare part though, I don't know if I can do anything about it LOL, that stuff just comes out without me trying, most of my art winds up having that sort of feel...  

[kram1032]

Man, just imagine that with an entire body as a fractal. Where it all is fully rigged too.
Infinitely recursive rigging. Whoa. Fractals in motion.

[billtavis]

yeah totally, I've been rolling the idea around in my head for how to do the whole body, but it's far from being realized.  Here's my quick "sketch" of a fractal stickman... I'm not too crazy about how it turned out, I felt like I fighting with the shape the whole time.

I think to make the body properly it might require a multi-fractal, like one fractal for the head, one for the arm, one for the leg, etc.  One thing I was considering for the arms/legs would be to form it out of its own muscles.  Meaning you'd take the whole arm and scale it down to form the bicep, use another copy to form the tricep, and so on.  I haven't tried it yet though so not sure if that's the way to go.

[kram1032]

Yeah, while you're at it, make it a full volume fractal, considering all the internal organs, each being built from the whole body. 

[cKleinhuis]

and you all know its "resemblance" time

[stereoman]

This thread was an interesting read, and then I saw this and had to reply:

Well, I must say that I have created just such a human head as you have described, in that everywhere you look you see smaller and smaller versions of the same head! (without the transparent surface or hairdo though). I don't have anything to post just yet because I am preparing a high-quality render for the contest. But I can tell you a little about how it was made, and I think it relates to your Gnomon idea. The concept I used was a literal interpretation of a Multiple Reduction Copy Machine (MRCM). This is similar to an IFS, in that you define transforms, but IMO is much more intuitive and flexible. The transforms were defined using the collage theorem. In other words, the first iteration is hand-placed. I made the head in a standard 3d package with just a few lines of scripting, and while the fractal rules are certainly simple, defining the transforms took quite a bit of artistic (not mathematic!) input to achieve a human likeness. It was akin to doing any other artistic 3d modelling. I was able to intuitively "tweak" the details until I was satisfied with the result. Here's a render of some broccoli I made with the same method.  Please note that this is polygon based, so is easily amenable to the techniques for lighting/texturing/rendering available in general 3d packages. In this case I chose a simple Ambient Occlusion look
<Quoted Image Removed>
I have also implemented 2d versions of an MRCM in Photoshop without a single line of scripting, and without a single calculation on my part. It doesn't get much more artistic than that! The process involves recording an Action to define all the transformations, then playing back the action as desired. To define each transformation, the base layer is copied and then manipulated. The final step in the Action is to collapse all the layers into a single base layer again. This process gives you easy access to powerful (non-affine) transformations as well as color modulation (and any other effect recordable in an Action) that will be repeated automatically at ever iteration.
This simple smiley fractal I whipped up real quick shows what I mean. The layer copies were deformed (transformations involving more than just scale/rotate/translate/skew), and the outer "border" smileys were darkened every time. This is not possible with standard IFS approaches. The absolutely amazing thing is that now that the action is defined, I can start with literally any image and it will converge on these smileys after a few iterations!
<Quoted Image Removed>

  HI Billtavis, Sorry, I was really busy  to enter FF the last months.
  Really glad  to read your post, I haven´t entered the core of your explanation, but in a first look, it seems we are approaching the same idea,
  maybe we can finally  make this approach feasible.
  keep us updated