Editing Random Fibonacci sequence (section)

==Generalization==
[[Mark Embree]] and [[Nick Trefethen]] showed in 1999 that the sequence
<math display=block> f_n=\pm f_{n-1}\pm \beta f_{n-2}</math>

decays almost surely if ''β'' is less than a critical value {{math|''β''* ≈ 0.70258}}, known as the Embree–Trefethen constant, and otherwise grows almost surely. They also showed that the asymptotic ratio ''σ''(''β'') between consecutive terms converges almost surely for every value of ''β''. The graph of ''σ''(''β'') appears to have a [[fractal]] structure, with a global minimum near {{math|''β''<sub>min</sub> ≈ 0.36747}} approximately equal to {{math|''σ''(''β''<sub>min</sub>) ≈ 0.89517}}.<ref>{{Cite journal | last1 = Embree | first1 = M. | author-link1 = Mark Embree| last2 = Trefethen | first2 = L. N. | author-link2  = Lloyd N. Trefethen| doi = 10.1098/rspa.1999.0412 | title = Growth and decay of random Fibonacci sequences | journal = Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | volume = 455 | issue = 1987 | pages = 2471 | year = 1999 | url = http://people.maths.ox.ac.uk/~trefethen/publication/PDF/1999_86.pdf|bibcode = 1999RSPSA.455.2471T | s2cid = 16404862 }}</ref>