The ABACABA pattern is a recursive fractal pattern that shows up in many places in the real world (such as in geometry, art, music, poetry, number systems, literature and higher dimensions).[1][2][3][4] Patterns often show a DABACABA type subset. AA, ABBA, and ABAABA type forms are also considered.[5]
^Naylor, Mike (February 2013). "ABACABA Amazing Pattern, Amazing Connections". Math Horizons. Retrieved June 13, 2019.
^SheriOZ (2016-04-21). "Exploring Fractals with ABACABA". Chicago Geek Guy. Archived from the original on 22 January 2021. Retrieved January 22, 2021.
^Naylor, Mike (2011). "Abacaba! – Using a mathematical pattern to connect art, music, poetry and literature" (PDF). Bridges. Retrieved October 6, 2017.
^Conley, Craig (2008-10-01). Magic Words: A Dictionary. Weiser Books. p. 53. ISBN 9781609250508.
^Halter-Koch, Franz and Tichy, Robert F.; eds. (2000). Algebraic Number Theory and Diophantine Analysis, p.478. W. de Gruyter. ISBN 9783110163049.
The ABACABApattern is a recursive fractal pattern that shows up in many places in the real world (such as in geometry, art, music, poetry, number systems...
The most popular arch-form structure is ABCBA. Chiastic structure ABACABApattern Sonata rondo form Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0-300-05111-5...
odd.}}\end{cases}}} For other formulae, see OEIS sequence A000975. ABACABApattern Disentanglement puzzle Towers of Hanoi Weisstein, Eric W. "Baguenaudier"...
minor, Op. 108 (1886–1888), fourth (last) movement (Presto agitato) ABACABApattern For further discussion see Rosen (1997, 51). Caplin, William E. (1998)...
exclude those less than (or greater than) a particular threshold. ABACABApattern Stern–Brocot tree Euler's totient function “The sequence of all reduced...
to make a toy prototype for children. She calls it pagoda stacks. ABACABApattern Backup rotation scheme, a TOH application Baguenaudier Recursion (computer...
the latter case the factor has an n-factorisation into Lyndon words. ABACABApattern Lothaire (2011) p. 135 Lothaire (2011) p. 136 Lothaire (2011) p. 137...
happens inside another palindrome. For example, consider the input string "abacaba". By the time it gets to the "c", Manacher's algorithm will have identified...
called "episodes". It may be asymmetrical (ABACADAEA) or symmetrical (ABACABA). A recurring section, especially the main theme, is sometimes more thoroughly...
to as "digressions" or "couplets". Some possible patterns include: ABACA, ABACAB, ABACBA, or ABACABA. The rondo form emerged in the Baroque period and...
repeatedly, interspersed with other sections: ABACA is a typical structure or ABACABA roulade (Fr.) A rolling (i.e. a florid vocal phrase) rubato Stolen, robbed...
to as "digressions" or "couplets". Some possible patterns include: ABACA, ABACAB, ABACBA, or ABACABA. Sonata form – musical structure generally consisting...
endpos(\omega )} . For example, for the word S = a b a c a b a {\displaystyle S=abacaba} and its subword ω = a b {\displaystyle \omega =ab} , it holds e n d p...
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