Flowsnake Q-Function
Flowsnake Q-Function
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.
⟶
2
⟶
2
a+bi
q=
m
o×
n
7
n
o=1
m∈0,1,2..
n
.7
The -function enables the computation of a wide variety of nontraditional interpolations, with interesting features that simple Lindenmayer outputs do not display. For example, the range of the -function contains points with two or three preimages, double and triple points. Try computing these values:
,,
13
42
31
42
37
42
,
2
21
3
7
,
11
112
143
336