Look and Say Sequence Substrings

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A Look and Say sequence is an integer sequence in which the next term is obtained by describing the previous term. Starting with 1, the sequence would be defined by "1, one 1, two 1s, one 2 one 1," etc., and the result is 1, 11, 21, 1211, 111221, … . The visualization compares the three sequences starting with one, two, and three with steps generated from the selected initial sequence.


The first view shows the original evolutions. The second view identifies entire steps of the simple evolutions with substrings of the sequence. You can switch between the views with the checkbox.

In the first view the upper three blocks show steps for the three simple initializations and the fourth block shows steps for your sequence. In the matching view each of the three upper blocks of the plot starts with a line that consolidates the matches with one simple evolution. The following lines mark the individual matches. The two last lines of the plot consolidate all those matches for the sequence.


Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA



Conway called the recursion "audioactive decay" and proposed to rename substrings like atoms because of their matching relative abundance in sequence terms derived from random initial strings.

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