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UPDATE: apparently polyfold is the slice thing (although I'm adding something cool to it!), and gnarl is a similar function to the oscillation functions (but oscillation is better), and the accordion function is just a souped up (more options) box tiling function that has ends (the ends thing is actually cool..).  And stuff.  mehh.  Still cool.  I'll split them up, and do other stuff with it assuming I don't end up dead before I do because.. you know.  something creepy or something.  :D

Update, another tutorial is available here (PDF), it explains a bit about using TwistBraid with formulas other than Mengers (because of symmetries, need to use splitAdjust to correctly align things with the x axis!!!).  Also a demo of IntegerSlice3d usage (another formula in the directory):

https://drive.google.com/open?id=0B0EcJQ49B_yObGlXbVk4SURRdmc


  Previous tutorial (read this first):  

(http://drive.google.com/uc?export=view&id=0B0EcJQ49B_yOTFpuM3hhWUdEcWM)

(http://drive.google.com/uc?export=view&id=0B0EcJQ49B_yONFlmRUxSNDRXbWc)

(http://drive.google.com/uc?export=view&id=0B0EcJQ49B_yOZkUzcUNrS2tHRWs)

(http://drive.google.com/uc?export=view&id=0B0EcJQ49B_yOaUd1dUZsbXZFelU)

  I'm hoping that I shared these right!@#!$  It seems like my brain can't hold sharing information for Google photos!#!@

  Twistbraid 5_4 beta is here:

https://drive.google.com/open?id=0B0EcJQ49B_yOeUMwTkZwN29KM2c

  Let me know if you can't see the images.  


  So if you add oscillation displacements, you can do something like this:

(http://drive.google.com/uc?export=view&id=0B0EcJQ49B_yOWG0xSF9kcWdIQlE)

Aww, no images!! :'(

Sheesh.  I did it multiple ways.  I'll try a different way- let me know if it works!

Nice tutorial, and it animates so well. O0

Yesyes, I can sees the pwitty picshers!  ;D BUt: Might have been something on my side that I couldn't see them yesterday, computer was acting weird last night...

Thank you very much, Matt, for the formula and also for the great tutorial, lots of fun to be had with your transform!

(http://orig03.deviantart.net/0424/f/2016/317/b/1/twistbraid_by_sabine62-dao86u0.jpg)

I think it can be used as a fantastic texture generator too:

(http://orig09.deviantart.net/2716/f/2016/317/c/f/twistbraidcbf_by_sabine62-dao87sd.jpg)
_{Here with CrossBiFold added}

Awesome Sabine!  Glad you like the formula.


  I changed the urls to something else- forget how I got them to work in the past, so when back to an old thread and found this one tweak to apply to urls from Google drive.


  Thx Mclarekin!

(http://i.giphy.com/3oriO9zdRo9op951C0.gif)
(http://i.giphy.com/3oriO4ryliAULemwda.gif)
(http://i.giphy.com/26hirP42RWXaBZyzm.gif)
  Added another version of the TwistBraid (cycleshift) formula in the tutorial directory:  https://drive.google.com/open?id=0B0EcJQ49B_yObGlXbVk4SURRdmc

  Lets you shift the cycle like:

   (http://i.giphy.com/5BgiJNDmhEh5S.gif)

  Still need to split the formula up because I had to cut out an oscillation to add the parts I wanted....

I love this page! awesome.

Thanks Mrz00m!   :D  

Very useful and nicely presented tutorial.
Going to go and play with it :)

Oh ... and for others - these are custom formulas (from the google drive link).