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Inspired by Jesse's incredible giant tarantula nest of a fractal http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1834 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1834) I ended up doing some exploring of the scale -1.5 mandelbox. It seems to have an identity crisis, check it out...

The corner is like a mandelbulb with bulbs on top of bulbs, but the pattern is like an apollonian gasket or an Indra's pearls fractal
Indra's boxes
(http://www.fractalforums.com/gallery/1/853_12_03_10_12_41_12_0.jpeg)

A close up of the top left circle shows a crystal like shape
(http://www.fractalforums.com/gallery/1/853_12_03_10_12_41_13_2.jpeg)

This area shows a border like a maskit fractal
(http://www.fractalforums.com/gallery/1/853_12_03_10_12_41_13_1.jpeg)

Looking at the first image again, not only does the shadow of the nearest box resemble a familiar fractal, but check out the little stalks middle right, a quick close up shows them to be trees.

Awesome! What typing of Apollonian packing is that? And what's a maskit? A Julia set with c=([-0.75...0.25],0)?

Its like the flat earth the flat earth society has only dreamed of! What a world for adventures and legends. Any Terry Pratchetts out there?
Wonderful colouring and detail. Thanks for this image set.

Beauty box!

Amazing !

Neverending beauty, variety and surprises! The shadow looking like a Mset is striking :)

Timeroot- The gasket-like image is from http://www.aleph.se/andart/archives/2005/11/index.html (http://www.aleph.se/andart/archives/2005/11/index.html), he calls it Klienian spheres, and a maskit seems to be the name for the Julia at 0.25.

Another look at the first image shows little stars on the nearest big face which are like Koch snowflakes, and a line pattern that is like a type of Cantor dust.

YAY!
Great shapes :D
I love it when multiple fractals merge into a bigger one :)
It ´somewhat connects them all :D

Thanks for the link. It seems that, by setting the value K at around .78 (as opposed to the .9 in the picture you provided) one could get an ever closer correlation. This reminds me of the earlier conformal fractals you did on which there were triangular, square, pentagonal, and hexagonal faces. It seems the entire family is prone to multi-personality disorder.  :dink:

lol, kissing fishes on the left middle ?! in the green pic

Here's a close up of the first pic, a beautiful fractal shape isn't it, see how the closer zoom is 'purer' and I suppose more specialised
(http://www.fractalforums.com/gallery/1/853_15_03_10_12_55_23.jpeg)

You'd be forgiven for thinking this fractal just mimicks others, but it seems to have plenty of identity of its own...
Leprechaun's garden
(http://www.fractalforums.com/gallery/1/853_15_03_10_12_59_50.jpeg)

Jupiter moon-life
(http://www.fractalforums.com/gallery/1/853_15_03_10_1_05_26.jpeg)
Crazy extra-terrestrial plant life :) !

i do not get where the shadows come from !
are they cast from the above structure beneath ? then it is clearly wrong in my eyes  :hurt:
but the image is stunning great! O0

Oh, wow, that's fascinating... I wonder if it's possible to explain the variety? Very, very interesting... Do we know of any other fractals with this kind of range?

Great zooms :D

Trifox, the shadows are casting down from the cube shapes above, they are correct though, the shapes have a much more circular profile from the light source's diagonal angle.
Reesej2, I think we're really breaking new ground here on fractalforums, its what makes it so fun :) From what I've seen most 3d fractals outside this forum are directly self-similar (like menger sponge) or have random variation (like fractal lightning). The mandel type fractals are interesting because they are a map of julia fractals, so the pattern varies with location.
I imagine other scale Mandelboxes have about the same variation, e.g the standard one (scale 2) http://www.fractalforums.com/index.php?action=gallery;su=user;cat=111;u=853 (http://www.fractalforums.com/index.php?action=gallery;su=user;cat=111;u=853)

A surprise to me is that this -1.5 Mandelbox isn't all that great to look at in other locations, being only -1.5 it is very dense and so the cube faces are flat surfaces. It seems to leave all the stretch to a few places, where it stretches a lot.

Yes, surprisingly these conformal/anti-conformal fractals show stretched areas. The julia sets have no stretch at all, but since mandel sets are a map of julias by location the result can appear stretched. This is why the tricorn looks stretched, and is probably why the mandelbrot isn't made of exact circles and cardoids.

after staring at it another loooong time, i can support your argument, but it is not really visible that the buld is "round" from the view angle

hmm, just imaging : "what if some 3d fractals have their corresponding julia shapes as shadows"
lol, please do not take it seriously!

I would like to take a holiday on this planet. Could you zoom in and find me a nice hotel? With a sea view please!   ;D

@Tglad, you rendered very interesting images and inspired me also to explore Mandelbox with scale = -1.5. Shapes are really interesting and diverse.
Below there is some result of my exploration:

(http://www.fractalforums.com/gallery/1/640_19_03_10_6_08_02.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1880

It's great how this fractal shows both very flat and very round parts. Something you see hardly ever.
The shapes still are kinda related to each other but in a very different way to usual :D
Very nice shot, Buddhi :D

Hey your pic has a floating 2d fractal in it too!
On the bottom right of the Jupiter moonlife picture is a floating plane looking like 2d cantor dust.
The one in your pic (right of middle) looks like a tree fractal, very cool  O0 definitely seen that type somewhere before.

Great Image, wonderful program . Problem is that I can`t manage to use numbers like -1.5 or 2.5 only whole numbers. Also when I save a setting the program automatically makes the -1.5 a -1 and the 2.5 a 2
Enough to learn and discover in the box still but I would love to see scale 2.2 and 3.3 etc.( or do these numbers make no sense at all? )

Tabasco, which program are you using?? In most programs, you should be able to set it to whichever value you want. And in fact, and real number makes sense. You could even try 1-sqrt(2), or -0.414, if you wanted.  :D

... *reflects on this for a moment * ...

...has anyone tried with a "complex" scale value, that is, throwing in some rotation? With x=scale*(cos(rot)*oldx + sin(rot)*oldz), y=scale*(cos(rot)*oldy + sin(rot)*oldx), and z=scale*(cos(rot)*oldz + sin(rot)*oldy) you might able to get some interesting Mset style effects going on within this cube, without the whole formula mixing others have proposed. I'm sure that, any way, it would look pretty cool.  O0

I briefly tried rotating by 90 degrees each iteration, I can't remember what it looked like though.

These next images aren't about mimicking so a little off topic (though ker2x's last image in the gallery shows a nice and somehow familiar looking fractal in the face of the box)...
They just look interesting so I thought I'd post them:

This is like the side of a dusty desert canyon before the rain
(http://www.fractalforums.com/gallery/1/853_25_03_10_12_05_03.jpeg)

After rain the shrubs start to bloom and release their pollen :)
(http://www.fractalforums.com/gallery/1/853_23_03_10_8_50_29.jpeg)
This change is just a simple shift of the colour spectrum, simple as that.

A strange structural system-
(http://www.fractalforums.com/gallery/1/853_24_03_10_11_51_51.jpeg)
(parameter files included in the image description in the gallery)

On the note of trying a complex scaling value: while we're at it, why not try a triplex scale? I feel like the explanation behind the variety in the -1.5 Mandelbox lurks in the more general ideas.

Helicopter ride
(http://www.fractalforums.com/gallery/1/853_30_03_10_1_07_12.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1973 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1973)

The bushes are actually disconnected (have floating parts) so no point in a closer shot.
The interesting thing is that the grass/shrubs are growing on the top side and not on the walls... which is strangely accurate and very  O0

Huh, interesting... the "shrubs" are funky... Also, those pits look like they have vertical walls, but they curve irregularly. Weird.

Green place near the town (scale = -1.82;)

confirmed, complex scale values give interesting results ( i am just exploring 2d mandelbox :( ) , but i have to ask,
how do those tree like structures pop up !?
is it just negative scale ?!?!

Yes, there are lots of these tree/shrub things around (0.9, 2, -1.8 ) in the scale -1.5 Mandelbox. I think they probably exist in other areas too, e.g. the simple trees at the start of this post.
I would guess they exist in most -ve Mandelboxes, but never seen one in a +ve Mandelbox.

In this video the scale values changes from positive to negative. Negative values gives a completely different shape of the Mandelbox (which is in the case a Juliabox, defined at (0,0,0)).

http://www.youtube.com/watch?v=2hE1oUI5DVk

nice animation. Poorly it's quite noisy...
Against zero, it seems to approach infinite size... Or was the smooth cube at zero?

The noise comes from the quantum level (just a joke). I think the noise at the end of the video is interesting. There seems to be some cyclic repetitions.

If the scale is in the near of 0, the box explodes. In my original video there are lots of black pictures (ca. 300 frames) if scale is near 0. So the real black part in my video must be some seconds longer.

 

   

-1.8 <= scale <=-1.3

http://www.youtube.com/watch?v=Z7gRiIfnOqM

The old Spaceship is waiting.