Fractal Imaginary Cubes

Posted3 months agoActive3 months ago

strstr

63 points

8 comments

i.h.kyoto-u.ac.jpResearchstory

calmpositive

Debate

20/100

FractalsGeometryMathematics

Key topics

Fractals

Geometry

Mathematics

The post showcases 'fractal imaginary cubes', a mathematical concept where non-cube 3D objects have square projections in three orthogonal directions, sparking discussion on related mathematical ideas and potential applications.

Snapshot generated from the HN discussion

Discussion Activity

Moderate engagement

First comment

Peak period

Day 8

Avg / period

Key moments

01Story posted
Oct 12, 2025 at 3:08 PM EDT
3 months ago
Step 01
02First comment
Oct 20, 2025 at 8:54 AM EDT
8d after posting
Step 02
03Peak activity
6 comments in Day 8
Hottest window of the conversation
Step 03
04Latest activity
Oct 21, 2025 at 3:42 AM EDT
3 months ago
Step 04

Generating AI Summary...

Analyzing up to 500 comments to identify key contributors and discussion patterns

Discussion (8 comments)

Showing 8 comments

robinhouston

3 months ago

1 reply

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

3 months ago

1 reply

I assume this means the four images at the top are the same structures at different angles?

nom

3 months ago

Exactly.

pmontra

3 months ago

1 reply

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

3 months ago

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.

graycat

3 months ago

Such a cube, i.e., a set, is closed, right? Sooo, there exists a function on the space that is 0 on the cube, strictly positive otherwise, and infinitely differentiable.

CGMthrowaway

3 months ago

This has inspired me to imagine a fractal chandelier design, e.g made of cut glass

dmd

3 months ago

I have a 3D-printed Sierpinski Tetrahedron. It's lovely.

https://imgur.com/a/oZwCFLu

View full discussion on Hacker News

ID: 45560864Type: storyLast synced: 11/20/2025, 1:45:02 PM

Want the full context?