Building objects based on fractal logic

[pirloui]

Hi.
I work on a product design project, and wish to exploit fractals to build up stuff.
For example I have this render here. It goes from 6>12>24>48 etc count per circle.
Each time the size is halved.
In order to make a plate from the same system, I tried to make each element slightly larger 60% in stead of 50% of previous.
I also tried to have them triple at each step.
It grew way too fast and the circles where too far from each other to do anything (they need to touch)
Is there any king of fairly simple calculation or estimation method I can use?
Thank you so much for any help.

[cKleinhuis]

they look like they are not evenly divided on that rings, i think it is design,

the problem is with the too fast growing,

my idea would be to try out a simpler rule for new rings, as with stacking pyramids, you need only one new element
on the rings to fit perfectly in the previous one ... something like that... 

[pirloui]

Thanks, yes I will try that.
I allready started aligning all the edges or centers of the spheres on a cylinder or plane, and adapt the size and diameter. Since it keeps doubling, I believe it should a little slightly fitting to the math.
Will post renders later 

[pirloui]

Here is a couple of tests.
I believe the "growing" isn't too wrong, but is it acceptable that the "Y" slowly changes branch angle (due to growing circle) or is that unacceptable for a fractal?
Thank you for your attention, sorry for being the noob with probably obvious questions..

I find this first one really intriguing in it's weirdness..

[cKleinhuis]

i do not get exactly what your problem is ?

is it the speed of minimizing the bubbles ?

fractal only means that it has a rational dimensionality, compare how the surface of your object grows when adding a layer ... i think your object will also get an infinite surface when continued endlessly

i find the second one very good,

perhaps you should think of it another way round, try not to expand your starting circles, instead use the space of the first circle, to split it up into smaller circles,
so, you stawith a big bubble, and in iteration 2 you place 2 bubbles side by side inside those starting bubble ( by removing the prior )
and after that you start replacing the 2 bubbles you just created by 4 bubbles ....

and here is another goodie for you ...

when you repeat the above process on and on you get something like a menger sponge, and here comes the thing i love to play with:

alternate

alternate the replacement rule every iteration, so, in first iteration you create 2 bubbles inside the prior, after that create 3 new bubbles inside
the 2 created ones ...

but the problem here is like you have before, after some iterations you have a countless amount of bubbles ( far more than you have now )

have fun!

[gamma]

Well, its a fractal if the code is so small that it uses only one loop, one recursion for the problem of this kind.
Every time we call the function in question, it places smaller balls between bigger balls.
Otherwise, it would not be symmetric or repetitive quite in the minimalistic way.
Except, I think it is possible it won't be perfect. Maybe the rendering program will produce progressively larger errors when dividing halves and thirds, or something like that. The program operates in raster space, so maybe the set definition - algorithm should progress inward from the hard-coded limits of raster space into the collision at the Three Balls of Confusion.
Archimedes had the same awkward start. Newton discovered that 3 body collisions are completely unlikely.

[pirloui]

Thanks a lot for the information Trifox and Gamma.
I would have liked to push this further, but the concept has been put on ice for now 
In favor of a difficult and less interesting one 

Anyhow, I think I have something like a sponge here, the square one

It could be interesting if there was some software that would calculated the base shape to fill a certain shape as result. mmm, I don't know is that was very clear.

Anyway, thanks a lot and I hope I can pick this up again sometimes soon.

All the best.

[cKleinhuis]

hey, these objects really look more interesting, especcially the table and the plate variant ...  :
too bad it is put on ice ... 

[gamma]

I like your balls. Very clean and educational. 

It could be interesting if there was some software that would calculated the base shape to fill a certain shape as result. mmm, I don't know is that was very clear.

How about Xenodream, Incendia, Povray, Processing java environment...

I think that the initial shape will fill its large scale copy.