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Visualizations of a Recursive Sequence
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
THINGS TO TRY
Automatic Animation
SNAPSHOTS
DETAILS
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.
RELATED LINKS
Recursive Sequence
(
Wolfram
MathWorld
)
Recursive Sequences
(
NKS|Online
)
PERMANENT CITATION
"
Visualizations of a Recursive Sequence
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/VisualizationsOfARecursiveSequence/
Contributed by:
Enrique Zeleny
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