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The recursive sequence defined by

. The values of the sequence are divided into blocks of values between

and

and visualized in several ways.

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.

Contributed by: Enrique Zeleny

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Visualizations of a Recursive Sequence