William Kolakoski
William George Kolakoski, known as Bill to family and friends, was an American artist and recreational mathematician who is most famous for devising and giving his name to the Kolakoski sequence, a self-generating sequence of integers that has been extensively studied by mathematicians since he first described it in the American Mathematical Monthly in 1965.
Life and education
Kolakoski was born September 17, 1944, in Pittsburgh, Pennsylvania, the son of George Leon Kolakoski and his wife Eleanor. He had many interests as a boy, including art, philosophy and mathematics, but chose to study fine art at the Carnegie Institute of Technology because he felt that, while he could study mathematics and philosophy independently, he needed the support of others to make a career in art. His fellow students were struck by his sharp intelligence, breadth of knowledge and skills in many different fields, including the ability to play good chess without making a particular study of the game.He graduated from CIT with honors as a Bachelor of Fine Arts in painting in 1967 and worked for a time at United States Steel as a draftsman. However, because he had schizophrenia and had to take constant medication to avoid psychosis and delusions, he was unable to keep in steady employment or to develop his artistic career as he wanted. He eventually moved to West Virginia, where he met his wife Loretta and found a position as an artist-in-residence in Fairmont. In 1996, he was diagnosed with lung cancer and he died July 26, 1997, at the Fairmont General Hospital.
The Kolakoski sequence
Definition of sequence
This sequence of integers was first discussed by the professional mathematician Rufus Oldenburger in 1939, but attracted little attention at that time. It consists of an infinite series of 1s and 2s that begins like this:Each symbol occurs in a "run" of either one or two consecutive terms and writing down the lengths of these runs gives exactly the same sequence:
Conversely, one can say that each term of the Kolakoski sequence generates a run of one or two future terms. The first 1 of the sequence generates a run of "1", i.e. itself; the first 2 generates a run of "22", which includes itself; the second 2 generates a run of "11"; and so on. This animation illustrates the process:
Kolakoski's role in popularizing the sequence
William Kolakoski devised the sequence independently of Oldenburger and introduced it to his fellow students while at the Carnegie Institute of Technology. He submitted it to the American Mathematical Monthly and it was published as "Advanced Problem 5304" in the following form:It was then called the Kolakoski sequence as mathematicians investigated it further.