[HN Gopher] Fractal Imaginary Cubes
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       Fractal Imaginary Cubes
        
       Author : strstr
       Score  : 52 points
       Date   : 2025-10-12 19:08 UTC (8 days ago)
        
 (HTM) web link (www.i.h.kyoto-u.ac.jp)
 (TXT) w3m dump (www.i.h.kyoto-u.ac.jp)
        
       | dmd wrote:
       | I have a 3D-printed Sierpinski Tetrahedron. It's lovely.
       | 
       | https://imgur.com/a/oZwCFLu
        
       | robinhouston wrote:
       | This page may be a bit confusing, out of context.
       | 
       | By 'imaginary cube', Hideki Tsuiki means a three-dimensional
       | object that is not a cube, but which nevertheless has square
       | projections in three orthogonal directions, just like a cube
       | does. Examples include the cuboctahedron and the regular
       | tetrahedron.
       | 
       | His previous work on non-fractal imaginary cubes is written up at
       | https://www.mdpi.com/1999-4893/5/2/273
        
         | nomel wrote:
         | I assume this means the four images at the top are the same
         | structures at different angles?
        
           | nom wrote:
           | Exactly.
        
       | CGMthrowaway wrote:
       | This has inspired me to imagine a fractal chandelier design, e.g
       | made of cut glass
        
       | pmontra wrote:
       | Being able to see a shadow and learning that it has area zero
       | made me think that there is something wrong with the definition
       | of area.
        
         | mecsred wrote:
         | None of the shadows you can physically see in the photos have 0
         | area because the construction of the fractal isn't perfect.
         | What a perfect construction would look like and if it's ever
         | theoretically possible to make physical are complicated
         | questions. Beyond me for sure, how would an infinitely thin
         | object even interact with light?
         | 
         | I would assume the problem with the idea is in the fractal
         | physics rather than the definition of area, which has been
         | solidly useful for me.
        
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       (page generated 2025-10-20 23:01 UTC)