Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum

It is currently Thu Jul 24, 2014 8:24 am

All times are UTC - 5 hours



Post new topic Reply to topic  [ 1 post ] 
Author Message
 Post subject: Fractal Cube Patterns
PostPosted: Fri Nov 04, 2011 8:43 am 
Offline

Joined: Wed Oct 12, 2011 12:54 pm
Fractal patterns can be displayed on NxNxN virtual cubes, for large enough sizes.

Patterns can roughly be divided into 2 groups, depending on wether corners and edges are included or not.

For complex patterns, it may be more straightforward to permute centers only, at the expense of a slight increase in cube size (+2), though.

Algorithms to display patterns have been found by solving the cube layer by layer. Although quite lengthy, this approach works well for all kinds of patterns.

Knowing that fractals are self-similar by nature, I wonder if shorter scalable/self-similar algorithms could be found too, at least for a few patterns. I haven't gone any further yet, so this is an open subject.

A few patterns are shown below. See document Fractal Cube Patterns for more details and better resolution pictures.


Attachments:
T_SquareFractal.jpg
T_SquareFractal.jpg [ 66.95 KiB | Viewed 558 times ]
SierpinskiCarpet.jpg
SierpinskiCarpet.jpg [ 64.07 KiB | Viewed 558 times ]
SierpinskiTriangle.jpg
SierpinskiTriangle.jpg [ 67.06 KiB | Viewed 558 times ]
HilbertCurves.jpg
HilbertCurves.jpg [ 95.57 KiB | Viewed 558 times ]
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 1 post ] 

All times are UTC - 5 hours


Who is online

Users browsing this forum: Google [Bot] and 7 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  

Forum powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group