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calculastrology | 1 years ago (raw) | root | parent | reply | flag 
 @b4c50e1b @cd2b7137 Thanks! that's what I meant - was making sure that as the degrees get large, the boundaries of the dragon-y shapes, for instance continue to look dragon-y as opposed to completely filling the space as it appears to closer to the |z|=1 regions
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John Carlos Baez | 1 years ago (raw) | root | parent | reply | flag 
 @0bacad63 - the sets do converge as the degrees get large (i.e. the degrees plus 1 get large in a multiplicative sense) , but a lot has not been proved about what the limiting set looks like!   

It's known that this set is contained in the annulus 

1 ≤ |z| ≤ 2 

and that it contains the annulus

2^(-1/4) ≤ |z| ≤ 2^(1/4)

It's also known that this set is connected and locally path-connected!  But that's about all.