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On Tglad's Mandelbox website there are a few examples of areas on the -1.5 box that approximate familiar fractals like the Koch curve, Maskit fractal, etc). I find this fascinating so i put together a few other examples. Here's a partial image, the rest is on a new page about the Mandelbox I stayed up obsessively all night the last few days preparing. (still up ...)

http://www.miqel.com/fractals_math_patterns/mandelbox_3d_fractal.html (http://www.miqel.com/fractals_math_patterns/mandelbox_3d_fractal.html)

I'd like to start a thread on this topic of classic fractals appearing in the mandelbox, and collect more examples -
but could someone advise me which category would be right? Does it fall under Mandelbullb discussion?
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbox_tglad/mandelbox_fractal_garden.jpg)

Michael, this is amazing work!

One issue: Your description right under "Poincare Disks & Hyperbolic Tilings" is just a copy of the one under "Fractal Trees, Sierpinski & Menger Surfaces."

Hi Ken, thanks for pointing that out! I had been up all night and forgot to rewrite that after copy&pasting   :embarrass:   - just getting up now, i'll fix that in a little while & look over the page with fresh eyes. I also noticed I varied on the spelling of Sierpinski a few times too, lol.

Supercool, and great examples  :beer:  :beer:

Let me reiterate my opinion that there is something fundamental about the Mandelbox. It could well be a more significant find than we can currently understand. Wasn't there Cantor dust somewhere, too? Great examples!

Miquel, great work and amazing website.  In fact, I came across your page on the M set in a google search and posted it here enthusiastically because the info was so useful.  I didn't realize the author, yourself, was a member here already!  Thanks so much for your efforts.  It does so much to speed up the learning curve of a newb like me.

The Rev

@ Tglad - wow, 2 beers? heck yeah   ;D

@hobold - yeah i feel the same way, maybe not about the box, but that there is some 'meta fractal' out there somewhere that contains them all. Also there's an example of cantor dust(squares) on the page linked on my post, and in tglad's page there is an example of more of a cantor set(lines)

@ The Rev - Sh*t - I consider myself to be the n00b with all the amazing work seen at this forum. Your stuff is fantastic, i'm a big fan! Glad you dig the site.

Thanks :D

The Rev

just consider watching carefuly on the shadows, that are cast by this object, i think i had the illusion of a part-mandelbrot hidden inside, the right side of the apple ;)  ( positive real)
at least they are casting cantor dust on other surfaces ;)

@miquel, your site is indeed a tremendous resource for clarifying things concerning fractals, especially the explorations of the mandelbrot areas are well described, be sure
to check out the ultrafractalwiki.fractalforums.com subsection of this forums, where an elephant valley, and seahorse valley section already exist

and on the people counting station i would admit that we really have everybody actively doing some sort of fractal experiments gathered here on the page ... congrats ;)

I updated the Mandelbox webpage w/ some new examples
http://www.miqel.com/fractals_math_patterns/mandelbox_3d_fractal.html (http://www.miqel.com/fractals_math_patterns/mandelbox_3d_fractal.html)

On the topic of familiar fractals in the M-box, Im so happy with this one from last night.
First time i've gotten a good landscape feel. I went into photoshop and designed a few earth-tone gradients & it worked great!

This is "Koch Curve River Valley"
(http://nocache-nocookies.digitalgott.com/gallery/5/3551_04_01_11_11_29_40.jpeg)

This looks very much like those crystals of pyromorphite on matrix of ferruginous rock I used to collect in a forest nearby old silver mines where I was living when I was a kid. Amazing!

O0

@Blob - I know what you mean, i've been calling this particular rotated box the "mineral planet" - just found some nice malachite there last night!

Also here's another set of fractals found in the mandelbox
(http://www.miqel.com/images_1/fractal_math_patterns/mandelbox_tglad/mandelbox_fractal_garden2.jpg)

Amazing work here, and a fantastic addition to your site.

I love anything to do with comparing stuff, especially when it's so well presented like this. Instant link from me :D