1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, ...

The Kolakoski sequence (1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, ...) was proposed by the artist William Kolakoski, who was a trained painter and a recreational mathematician.

The Kolakoski sequence is an infinitely long list of 1s and 2s. The sequence alternates between blocks of 1s and blocks of 2s whose lengths are defined by the 1s and 2s in the sequence. (Ask someone who folded wires to show it to you.)

The Kolakoski sequence is self-referential and self-generating; it defines itself by describing itself.

Contributing artists/mathematicians:

Abigail Glynn
Abigail Greenough
Ace Schwarzbach
Aditya Tyagi
Aidan Baptista
Aidan Straut
Alana Deluty
Alex Vincent
Alice Wang
Alix Stseryna
Allen Huang
Alma Disla
Aly Rajwani
Analia Haddad Mejia
Andrea Munoz Ayala
Andrea Shoda
Andrew David Nelson
Andrey Rocket Goretoy
Aneudy Dominguez
Anjani Deonarine
Anna Fern
Anne Catherine Antonietti
Annette Paull
Annie Huang
Ansel N. Archer
Aren Guralp
Aria Andrade
Aubrey Dela Cruz
Ava Carolan
Ava Colabelli
Ava Halvorsen
Ava McDowell
Ava Robbins
Basma Saleh
Blake DeLorenzo
Brendan Sullivan
Caecilia Friesen
Cailin Tolppa
Caleb Prisco
Cameron Daly
Campbell Bridges
Carla Y. Ardon Galdamez
Carolina Kiang
Caroline Daley
Carter Cooper
Chompoonek Nimitpornsuko
Christopher Haggert
Christopher Marcaccio
Claire Gregg
Clover Nahabedian
Colby Leiter
Connor Hunter
Connor Willison
Daniel Lantz
David H-C
Del Ziegman
Dianne Kemp
Djackina Baptiste
Eben Byler
Echo Yan
Elias Viner
Ella Zonfrillo
Elle Marcks
Emily Dymov
Emily Zhang
Emma Claire Zambendetti
Emmanuel Zobinou
Ethan Costa
Ethan Dlugie
Eugene Choi
Evelyn Chow
Evelyn Mae O'Hara
Fin McDonough
Gabby Ramos
Gabriel Gangji
Gen Ortiz
Geremiah L. Lind
Gigi Selle
Greighan Brown
Griffin Mason
Guy Settipane
Hailey Poirier
Harrison Michael Nakowicz
Hendrick Sanchez
Henry Seeley
Hongchan Choi
Iris Freifeld
Isabella Bradshaw
Isadora Wisenbaker
J
Jack Lennon
Jackson Albert
Jackson Osterhus
Jack Spitzer
Jacob Kekoa Moon Hsieh
Jael J. Usher
Jaewon Choi
James Marcaccio
James Plionis
Jangole Parks
Jay McCloskey
Jay Ngeth
Jennifer Chen
Jess Skyleson
Jim Miller
Jimmy Gallagher
Jinhao Lee
John Stephen Tsonos
Jonathan Dario Cruz Rivera
Jordan Kostiuk
Jorday Johnson
José Antonio Montano Bejarno
Jose Lavandier Reyes
Joshua Kou
Juan Castillo
Kathleen Samways
Kathleen Shoda
Kayden Marracco
Keyan Zahedi
Kirin Lenoir MacDonald
Kristina Lamour Sansone
Kyle Ottiano
Kyle Stang
Laura Musiak
Lauren Roussel
Leanna Garcia Gonzalez
Lizzette Barrantes
Luke Reslow
Maddie Auvil
Margarita Barrios Ponce
Mariela Yeregui
Mark Christman
Martin Atilla
Max Prajapati
Megan Roppolo
Mia Delgado
Miles Harwood
Milo Guyer-Osborne
Mimi Doman
Mohamed Gueye
Monica Moskiewicz
Nancy Carreiro
Nancy Torresen
Nate Decesare
Nathaniel Thompson
Nathan Kim
Nathan Lopez
Nathan Malafronte
Nicholas Antonio Ferraz
Nicholas Mavroides
Nicole Skyleson
Nihal Nayak
Noah O'Day
Nolan Hubbard
Norberto Pagani
Olivier Gallo
Oriana Sett
Oscar Ludvig Boija
Oskar A. Chen
Paige Carter
Quinn Connolly
Ramee Saleh
Reagan Langford
Reina Kirkendall
Rey Reyes
Rickey Costello
Ritchelle Sorel
Rob Torresen
Rosangely Falcon Abreu
Rosemary Miner
Rowan Gates
Rowen Cannina
Rylan Sauer
Salma Hassaan
Samuel Feenane-Levine
Sarah Cherin
Sarah Lorthé
Sarah Torresen
Sarina Hermanto
Saurin Leahy
Shae McKinney Gero
Shivam Kogar
Sissi Wuyong Liu
Skyler Nigrelli
Sofia Rufino
Sophia Joyce
Sophie Olund
Spencer
Stephen Shoda
Sung Hyun Hwang
Sydney Butterfield
Sylvia Giessel
Tate Coker-Dodman
Taylor Gopalakrishnan
Tejas Kumar
Terra Wang
Theodore Hilaire
Ulli K. Ryder
Vida Zamora
Vrinda Sharma
Wenhao Cai
Whitney Bates
Will Murray
Wyatt Gelzhiser
Xiaotong Cai
Yeustin Aguasvivas Lara
Yifei Cai
Younoussa Faye
Yuxin Wang
Zachary Freer
Zachary Lavornia
Zakhar Pysarevskyi
Zhijin Annie Hu
Zoë Barbano Grinder
Zoe Ebrahimpour