Is shapestacking possible in all fractals?

[Chillheimer]

Hi!
I am wondering, is it possible to do shapestacking in other fractals than the M-Set?
I think it works for the burning ship and buffalo as well, but what about 3d-fractals, like the amazing box?
Any experience? Where have you found that shapestacking works?

It obviously doesn't work in the koch curve or the cantor set.
Any thoughts why that is so?
What is the basic requirement for a fractal to make shapestacking possible?

[cKleinhuis]

the basic requirement would be the connectedness if an object like the menge sponge (koch curve) is not connected by definition then a shape stacking would not make sense - in context of 3d printing

[TheRedshiftRider]

I suppose it can only be done with quasi-fractals if you want different layers.

[Chillheimer]

I'm not sure if we have the same definition of shapestacking. What I mean is to zoom in a certain way, so that a specific form will be doubled again and again as soon as you approach the next minibrot, as I tried to describe in my linked post/video http://www.fractalforums.com/fractal-related-links/inner-workings-of-the-mandelbrot-set-1/msg78353/#msg78353
like zooming towards this snakey tip (counting 10 left-right-curves)

and after that go right for the doubling towards the minibrot:
in the end you will have this snakey tip with 10 curves repeated all around the minibrot.


or if you have a zoom a little more complex, you stack many more shapes.

from such a picture near the minibrot you can reconstruct the whole zoom path, it is embedded in it like the evolution is in our dna.

do you understand what I mean?

the basic requirement would be the connectedness if an object like the menge sponge (koch curve) is not connected by definition then a shape stacking would not make sense - in context of 3d printing

if that was correct, you couldn't do shapestacking with the burning ship, but I'm pretty sure that you can. (right, kalle?)

oh, and why do you say the koch curve is not connected? I would say it clearly is.

I suppose it can only be done with quasi-fractals if you want different layers.

do we talk about the same thing? I'm not about 3d printing, so no need for layers..
what do you mean with quasi-fractals? fractals that show quasi-selfsimilarity like described here? https://en.wikipedia.org/wiki/Fractal#Characteristics
yeah, that would make sense.. maybe this is it.
then next question: is the amazing box a quasi-fractal?

[TheRedshiftRider]

No, sorry. I was talking about the technique of using different areas in minibrots to create layers. 

I dont know any other fractals than the whole series of m-sets and variations which have this property. Ive done experiments with escapetime formulas but I either got a m-like result or it did not have the right properties to even be called a fractal. Ill have a look at some of my old notes.

[cKleinhuis]

I'm not sure if we have the same definition of shapestacking.

oh, my fault was thinking in physical manner for 3d printing, the text was not able to move my peirception

[cKleinhuis]

oh, and why do you say the koch curve is not connected? I would say it clearly is.

and again my fault, i was interferring koch curve which has its brother koch triangle but i messed it completely with the sierpinski triangle which then is related to menger cube, which brought me on that false path ... but anyways i was talking about something completely different than you meant with shape stacking

[M Benesi]

  Try this for exporting voxel stacks of various fractals (if you want specific tips on a specific fractal, post the M3D parameters, and you'll get suggestions):

http://nic022.deviantart.com/art/MB3D-to-3D-Print-Tutorial-348647408?q=gallery%3Anic022%2F40086430&qo=1

[cKleinhuis]

  Try this for exporting voxel stacks of various fractals (if you want specific tips on a specific fractal, post the M3D parameters, and you'll get suggestions):

http://nic022.deviantart.com/art/MB3D-to-3D-Print-Tutorial-348647408?q=gallery%3Anic022%2F40086430&qo=1

dont jump on my train, chillheimer is talking about the technique to follow certain rules when deep down going the mandelbrot, where you can "shape-stack" the ornaments, zooming a billion times into the seahorse valley, followd by a trillion zoom into elephants valley and magnify like a few gigazilions again in the needle of a newly emerged mandebrot (something like that)

[M Benesi]

  oohh..  you mean something more like these things that are all over the T1-Pine Tree if you combine it with a T4 or T2 every few iterations?

[1Bryan1]

I think it depends on what is allowed in shape stacking when you are talking about Mandelblub3D.
Are we talking a single formula?
Only zooming allowed? (or can we cut through the object?)
Rotation is OK while looking?

[cKleinhuis]

i think it is just not visible for fractals that are not using an implementationof the pertubation method for ultra fast deep zooms

[Chillheimer]

@matt: yeah this looks pretty much like what I call shapestacking in the m-set.. is the pinetree one of the '3d-versions' of the m-set?
I'm sure in the standard integerpower we could observe shapestacking. but as christian mentioned it's hard to reach depth like in my example (even though its only at around E13 (so pertubation isn't really needed)

@bryan: I guess it's best to keep it simple so it's easy to spot the results of shapestacking, so yeah, I'd say just one single formula. cutting is perfectly legit. rotation too, but I guess it makes it harder to spot shapestacking.

oh guys wait, I just realized that shapestacking this is probably nothing but the visual result of bifurcation - period doubling.
so to rephrase my initial question a little more mathematical: Is period doubling an essential part of all fractals?

[Pauldelbrot]

i think it is just not visible for fractals that are not using an implementationof the pertubation method for ultra fast deep zooms

To answer most of the dangling questions in this thread:

1. It won't work for Julia fractals (and that includes things like the Koch curve and Cantor set).
2. It should be possible in all Mandelbrot fractals that are complex analytic or extend that without absolute values, including Mandelbulb.
3. For ones with absolute-value components (burning ship, kali, mandelbox) you can kinda sorta do it, but there are two or more "alternate versions" of the shapes, so things are less simple.
4. As for practicality, KF can do it readily and fairly fast in the nth-power Mandelbrots (and period doubling becomes tripling or other multiples for powers greater than 2). To really do it with the Mandelbulb will have to wait until someone makes a Mandelbulb3D with perturbation so you can shrink endlessly into it like Ant-Man going subatomic.

[quaz0r]

To really do it with the Mandelbulb will have to wait until someone makes a Mandelbulb3D with perturbation

nobody cares about zooming with regard to 3D stuff