Postcards from the M-set

[quaz0r]

which thing are you referring to as babushka-like?  peanut julias?

[jwm-art]

I took it as these shapes:

[hapf]

I was referring to the shapes that for example have 3 parts (left, middle, right) and when zooming into the right or left it looks like the original 3 part thing
and you have opened one babushka to find just another like it. And so on ad infinitum. In this
case there are also shapes that actually look like a babushka (see posting before this one).

[youhn]

That description sounds like every two-folded julia-like structure. 

If you want (seemingly) bounded shapes, you need spirals.

General rule for zooming into the mset: anything you put the focus on, will return later on, in the order that you've first chosen. This is the basic way both shape stacking and julia morphing are done (I guess these techniques are the same).

Here a similar one I've found in the past:


Source: http://jeroensnake.deviantart.com/art/Jail-for-Fake-Spiral-Spots-532439607

[hapf]

The babushka behaviour is very general, yes. And it does not need embedded Julias. One shape interacting with itself is enough as in your example. But one can also avoid this ad infinitum and leave things boring forever. What is the definition of a "bounded" shape? One where you have to cross the set to get inside the shape?

[youhn]

Boring forever for me equals to "more of the same" or otherwise said "not enough contrast or variation". Going down a single spiral forever, for example:



(ok, I stopped after only a few zoom ...)

I wouldn't know the exact definition for bounded, but I mean something like a single cell. Take the shape as being the interior, then the surface is the boundary layer. As long as there is only 1 connected interior, then I would call the shape bounded. Perhaps the term "closed shape" would be more appropriate. And also the word "seemingly" was key, as only the Mandelbrot set itself is closed. Not the curled and folded shapes we perceive.

[jwm-art]

The Babushka shapes and other 'bounded' shapes are products of zooming. They're very generic shapes to be found anywhere. Doesn't it all boil down to the left-middle-right pattern?

Join the dots2 - (look no spirals):

Code:

Re: -1.999774059043467591748637612153621739009044055475329276711522283606643236223667564685834841821830155342520320827643359481187229182895523842088118300655641249983117796994317189885
Im: -0.000001764680587203402133272227919153714840241281933623698961551087064237907915821484357683034377178420368074125035754333866863100937413878102609778017194536637664701929899676945
Zoom: 1.34078079299E154

And just a little deeper
Join the dots3 - (look no spirals):