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I thought I would add my command-line executable in this software section of FractalForums.
The executable is here: https://drive.google.com/file/d/0B8S7Si-yu3Doa19yNy1MaTRPdkU/view?usp=sharing (https://drive.google.com/file/d/0B8S7Si-yu3Doa19yNy1MaTRPdkU/view?usp=sharing)

It generates meshes in .ply or .obj format that are a crumpled surface fractal of a chosen fractal dimension between 2 and 3.
The .obj files contain texture coordinates so you can texture map them, as seen in the image below, that image was built by running:

Folding -f blah.obj -b 15 -y 111.246 -c 256 -t 10

This generates blah.obj, with detail level (number of corrugations) 256, crumple bend angle 15 degrees, and yaw angle 111.256 (180 divided by golden ratio), and for -t (the location type) >=2 it chooses a random location based on that seed.

The more geometric shapes, as seen in http://tglad.blogspot.com.au/2016/09/foil-surface-fractals.html (http://tglad.blogspot.com.au/2016/09/foil-surface-fractals.html) are using a yaw angle of 90 degrees.
Beware trying -c more than 256, it will really start to slow down and eat memory. You can use .ply if you want to save disk space as this is a binary format.

 Enjoy!

(https://1.bp.blogspot.com/-IFXv4T2RL4E/V_TcHdg4BMI/AAAAAAAAA2M/5wbNA1L2KKgPqTiLSz1SH1EjNbhzXB3TgCLcB/s1600/crumpledtexture2.png)

It looks great terrain. 

From my position of half knowledge, I wonder if it could work as a pre-transform (domain map change??) before a  pseudo Kleinian, mandelbox or aSurf, to produce some interesting pseudo-random fold angles, (if this makes sense??) :)

Thanks. I'm not sure about the domain map change suggestion, but maybe it could be done.

But you did get me thinking that this would be useful in computer games, because in addition to being procedural geometry (good for memory efficiency and level-of-detail), it apples a flat texture map without any distortion. And with a slight tweak (to keep an integer number of corrugations in x,y) the whole thing should tile.
Self intersection is the biggest problem, but at least for these irrational yaw angle sets you can keep on trying random locations on the surface to minimise this.

Here's a sequence of growing bend angles with a forest-like texture and a road. 7.5 degrees up to 30:
(https://3.bp.blogspot.com/-0qyhPur1dZQ/V_d9Rwy6t-I/AAAAAAAAA2o/4FVFs_GYCEMaDbeFQXaZFc_k_YzlflC7QCLcB/s1600/forest5f.png)
(https://4.bp.blogspot.com/-xqFwBhpS7Os/V_d9e46YJBI/AAAAAAAAA2s/7NfPHhf6uwc1s7dkv5A-gAG8-FmZe8R5wCLcB/s1600/forest5e.png)
(https://1.bp.blogspot.com/-dexeLX8v3Zw/V_d9uEzUh-I/AAAAAAAAA2w/tO0lX-oI_AQwQ6pjnDSjXzoyzJ8G3tvyACLcB/s1600/forest5c.png)
(https://4.bp.blogspot.com/-d7bWde7-xq0/V_d92_VEFNI/AAAAAAAAA20/1BbpPeilIW0EQU8RX71B6aS8iDvM2HamACLcB/s1600/forest5.png)

realistic terrain for a game.  All sorts of possibilities! :)



I was thinking that when I apply  folds as a pre-transform to a pseudo-kleinian. These fold angles are found inside the fractal, and transform the vertical bulbous part of the pseudo kleinian, producing interesting variations.

I was thinking of your formula as a fast "folds generator "  for exploring pseudo klienian, if that is practical.

Hi Mclarekin, the 3D folding of space in escape-time fractals is quite different to this surface folding... but it might produce interesting results none-the-less.

I've featured this crumpled surface in a short article: https://www.researchgate.net/publication/309391846_Three_Variable_Dimension_Surfaces (https://www.researchgate.net/publication/309391846_Three_Variable_Dimension_Surfaces)

The ultimate goal is a flat sheet that crumples up all the way to a dense volume, without self-intersection. Finding a simple and symmetric construction is the tricky bit   :D  :tool: