The #Fibonacci sequence is hiding in the {7,3} #hyperbolic #tiling!
The number of heptagons highlighted at each step is 7 times the nth Fibonacci number. Bill Thurston describes this at http://library.msri.org/books/Book35/files/thurston.pdf …pic.twitter.com/x8GxzTOmat
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Replying to @TilingBot
@Roice: can you compute the hyperbolic distances of the vertices of this from the origin?1 reply 0 retweets 0 likes -
Whoops, wrong Roice :) Yeah, that would be possible. Maybe you’d like an ordered list of the tile center locations? ...as decimal hyperbolic distances?
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Replying to @graveolens @TilingBot
I’ll do this when I get home from work tonight!
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I have looked at distances of θ(𝛾ⁿ) points in n-th layer in simpler hyperbolic growth processes.. some conjectures you could have about that turn out false: the average divided by n does not tend to log𝛾 (as it seems it should looking at areas), the distribution is not normal.
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I am specifically interested in theta-series of these sets of points.
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