Visualizations of a Recursive Sequence

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The recursive sequence defined by is at . The values of the sequence are divided into blocks of values between and and visualized in several ways.

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



Snapshot 1: plots of each block superposed and scaled to fit the same range.

Snapshot 2: plots of each block at different levels.

Snapshot 3: superimposing the points of each block versus , where . The picture shows a preferred orientation and the points lie on lines.

Snapshot 4: blocks aligned from the left; a maximum of 23 values is shown. Notice that even or odd values lie in the same column.

Snapshot 5: blocks normalized and scaled to fit the same range.

The author conjectures that is possible to generate this sequence with a substitution system of some kind.

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