- Generating the pattern
- Gallery
- See also
- References
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.
Generating the pattern
In order to generate the next sequence, first take the previous pattern, add the next letter from the alphabet, and then repeat the previous pattern. The first few steps are listed here.[4]
{{clear}}-
A -
ABA -
ABACABA -
ABACABADABACABA -
ABACABADABACABAEABACABADABACABA -
ABACABADABACABAEABACABADABACABAFABACABADABACABAEABACABADABACABA
Gallery
{{Gallery| title =
| align =
| footer =
| style =
| state =
| height =
| width =
| cellwidth =
| captionstyle =
| File:ABACABA Sierpinski triangle.png
| alt1=
| Sierpinski triangle:
| File:Measuring - Fractions of an inch.svg
| alt2=
| Ruler, excluding 1 and 2:
| File:Cantor4 abacaba pattern.png
| alt3=
| Cantor set:
| File:Ex 001.png
| alt4=
| Binary tree/upside down family tree:
| File:KochCurve1 abacaba pattern.png
| alt5=
| Koch curve:
is ABA, 
is ABACABA, and 
: ABACABADABACABA| File:Solfege subdivision de la ronde a la croche.svg
| alt6=
| Metric hierarchy:
| File:Arrière du Château de Chambord (41).JPG
| alt7=
|
}}
See also
- Farey sequence
- Rondo
- Sesquipower
References
1. ^{{Cite news|url=http://digitaleditions.walsworthprintgroup.com/display_article.php?id=1300604|title=ABACABA Amazing Pattern, Amazing Connections|access-date=2017-10-06|language=en}}
2. ^{{Cite news|url=http://chicagogeekguy.com/exploring-abacaba/|title=Exploring Fractals with ABACABA – Chicago Geek Guy|date=2016-04-21|work=Chicago Geek Guy|access-date=2017-10-06|language=en-US}}
3. ^{{Cite web|url=http://archive.bridgesmathart.org/2011/bridges2011-89.pdf|title=Abacaba! – Using a mathematical pattern to connect art, music, poetry and literature|last=Naylor|first=Mike|date=|website=|archive-url=|archive-date=|dead-url=|access-date=October 6, 2017}}
4. ^1 {{Cite book|url=https://books.google.com/books?id=3SB60Wavy6MC&pg=PA53&lpg=PA53&dq=Abacaba+pattern+-wikipedia.org&source=bl&ots=r-p9ejSugU&sig=Anwy4PGFPj2JatdlBZJon9mK5t4&hl=en&sa=X&ved=0ahUKEwjUgdWVhunWAhXplVQKHQf9CYYQ6AEIZDAM#v=onepage&q=Abacaba%20pattern%20-wikipedia.org&f=false|title=Magic Words: A Dictionary|last=Conley|first=Craig|date=2008-10-01|publisher=Weiser Books|isbn=9781609250508|language=en}}
5. ^Wright, Craig (2012). The Essential Listening to Music, p.45. Cengage Learning. {{ISBN|9781111342029}}.
{{Math-stub}}2. ^{{Cite news|url=http://chicagogeekguy.com/exploring-abacaba/|title=Exploring Fractals with ABACABA – Chicago Geek Guy|date=2016-04-21|work=Chicago Geek Guy|access-date=2017-10-06|language=en-US}}
3. ^{{Cite web|url=http://archive.bridgesmathart.org/2011/bridges2011-89.pdf|title=Abacaba! – Using a mathematical pattern to connect art, music, poetry and literature|last=Naylor|first=Mike|date=|website=|archive-url=|archive-date=|dead-url=|access-date=October 6, 2017}}
4. ^1 {{Cite book|url=https://books.google.com/books?id=3SB60Wavy6MC&pg=PA53&lpg=PA53&dq=Abacaba+pattern+-wikipedia.org&source=bl&ots=r-p9ejSugU&sig=Anwy4PGFPj2JatdlBZJon9mK5t4&hl=en&sa=X&ved=0ahUKEwjUgdWVhunWAhXplVQKHQf9CYYQ6AEIZDAM#v=onepage&q=Abacaba%20pattern%20-wikipedia.org&f=false|title=Magic Words: A Dictionary|last=Conley|first=Craig|date=2008-10-01|publisher=Weiser Books|isbn=9781609250508|language=en}}
5. ^Wright, Craig (2012). The Essential Listening to Music, p.45. Cengage Learning. {{ISBN|9781111342029}}.
1 : Fractals
- Lobatse hinge-back tortoise
- Lobatse Hinge-back Tortoise
- Lobatse Stadium
- Lobatus
- Lobatus costatus
- Lobatus gallus
- Lobatus goliath
- Lobatus magolecciai
- Lobatus raninus
- Lobat Vala
- Lobat vala
- Lobau an der Welle
- Lobauer Berg
- Lobau River
- Lobau (Saxony)
- Lobau, Saxony
- Lobawn
- Lobb
- Lobb Field
- Lobb House
- Lobbied
- Lobb number
- Lobbo
- Lob bomb
- Lobb's bulbophyllum