Flowsnake Q-Function
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The flowsnake (also called a Gosper curve) is a space-filling curve, a surjection from . The flowsnake
-function, a surjection
, determines a complex value,
, for points along the curve with preimages that belong to the restricted domain. All valid preimages can be written in the form
. When
is an integer and
, the function values for the set of preimages
determine a traditional flowsnake interpolation. These points can be computed using a simple Lindenmayer system or a so-called
-function. Computation of other exact function values requires the
-function, provided here.
Contributed by: Brad Klee (September 2015)
Open content licensed under CC BY-NC-SA
Details
References
[1] M. Beeler, R. W. Gosper, and R. Schroeppel. "Item #115". HAKMEM MIT AI Memo 239. Feb. 29, 1972. Retyped and converted to html ('Web browser format) by Henry Baker, April, 1995. home.pipeline.com/~hbaker1/hakmem/topology.html#item115.
[2] B. Klee, "A Pit of Flowsnakes," Complex Systems, 24(4), 2015 pp. 275–294. doi:10.25088/ComplexSystems.24.4.275.
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