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advancedresearch / avatar_graph

A library for Avatar Graphs
MIT License
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Optical illusion #43

Open bvssvni opened 3 years ago

bvssvni commented 3 years ago

Found a graph that produces an optical illusion, aka. M. C. Escher:

river

bvssvni commented 3 years ago

This was before semi-contractibility was allowed. With the new rules, this graph contains only core candidates:

image

There are 8 nodes, which satisfies the 2^n conjecture for filled Avatar Graphs.

bvssvni commented 3 years ago

I could not find it in the database of House of Graphs, so I emailed Jan Goedgebeur, one of the maintainers.

Jan created an account for me and it is now added to the database: https://hog.grinvin.org/ViewGraphInfo.action?id=35477

When adding edges for unique highest avatars, the graph becomes: https://hog.grinvin.org/ViewGraphInfo.action?id=570

bvssvni commented 3 years ago

Another view:

image

bvssvni commented 3 years ago

Planar solution:

image

bvssvni commented 3 years ago

Another view of planar solution:

image

bvssvni commented 3 years ago

Visualized embedded on a sphere, with 1/24 offset of a full circle to give each surface equal area:

Screen Shot 2020-08-01 at 00 48 22

bvssvni commented 3 years ago

Here is another view:

Screen Shot 2020-08-01 at 00 50 05

bvssvni commented 3 years ago

Yet another view:

Screen Shot 2020-08-01 at 00 53 20