attractor
Usage: :attractor:<nrow>[,(clifford[,a,b,c,d]|rampe[,a,b,c,d,e,f]|henon[,a,b,c])]
Generates tables listing points sampled from one of a specified family of strange attractors. These can provide tables with (X,Y) or (X,Y,Z) columns and arbitrarily many rows. They can be used, for instance, to make (beautiful) example large-scale scatter plots in 2-d or 3-d space.
The specification syntax is of the form
:attractor:<nrow>,<family-name>[,<args>]
where
<nrow>
is the number of rows required,
<family-name>
is the name of one of
the supported families of attractors, and
<args>
is an optional comma-separated list
of numeric arguments specifying the family-specific parameters
of the required attractor.
If the <args>
part is omitted,
an example attractor from the family is used.
Note that picking <args>
values at random
will often result in rather boring (non-strange) attractors.
The following families are currently supported:
The iteration is defined by the equations:
x' = sin(a*y) + c * cos(a*x) y' = sin(b*x) + d * cos(b*y)
Examples:
:attractor:9999,clifford
:attractor:1e6,clifford,1.32,-1.44,-1.7,-1.58
:attractor:65536,clifford,1.27,-1.35,0.82,1.8
:attractor:1e7,clifford,-1.9,1.18,-1.21,1.07
:attractor:400,clifford,-1.27,-1.28,1.0,-1.26
:attractor:4e6,clifford,1.8,0.9,-1.8,0.8
The iteration is defined by the equations:
x' = x * z * sin(a*x) - cos(b*y) y' = y * x * sin(c*y) - cos(d*z) z' = z * y * sin(e*z) - cos(f*x)
Examples:
:attractor:10e6,rampe
:attractor:4,rampe,-1.81,1.35,-0.85,0.32,1.68,-1.62
:attractor:5.5e5,rampe,0.23,-1.77,1.32,-1.44,-1.7,-1.58
:attractor:9999,rampe,-0.3,1.78,-0.87,1.69,1.42,1.21
:attractor:1e6,rampe,1.42,-1.98,0.39,1.32,1.79,-0.37
The iteration is defined by the equations:
x' = y + a + b*x*x y' = c*x
Examples:
:attractor:65536,henon
:attractor:1e7,henon,-0.68,1.64,0.36
:attractor:400,henon,1.73,0.29,-0.99
:attractor:4e6,henon,0.88,-0.9,-0.93
:attractor:10e6,henon,1.4,-1.13,-0.01
Example:
:attractor:6,rampe +----------------------+---------------------+----------------------+ | x | y | z | +----------------------+---------------------+----------------------+ | -0.5759098296568739 | 0.09844750286352466 | -0.6712534741282851 | | -1.3295344852011892 | -0.9829776649068059 | -0.7814409891660122 | | -1.1910376215054008 | 0.04335596646295736 | -1.0308958690758545 | | -2.0144704755218514 | -0.9699626185329038 | -0.35169532148364757 | | -0.16145296509226564 | 0.5245428249077974 | 0.17929370340580017 | | -0.8409807675257591 | -0.9598486078341374 | -0.955769158222801 | +----------------------+---------------------+----------------------+