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5.3.2 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:

clifford
clifford attractors are 2-dimensional and have 4 parameters, with suggested values in the range +/-2.0.

The iteration is defined by the equations:

    x' = sin(a*y) + c * cos(a*x)
    y' = sin(b*x) + d * cos(b*y)

Examples:

rampe
rampe attractors are 3-dimensional and have 6 parameters, with suggested values in the range +/-2.0.

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:

henon
henon attractors are 2-dimensional and have 3 parameters, with suggested values in the range +/-2.0.

The iteration is defined by the equations:

    x' = y + a + b*x*x
    y' = c*x

Examples:

Example:

:attractor:6,rampe
+----------------------+---------------------+----------------------+
| x                    | y                   | z                    |
+----------------------+---------------------+----------------------+
| -0.575909829655677   | 0.09844750286281623 | -0.671253474127029   |
| -1.329534485199524   | -0.9829776649069347 | -0.7814409891672596  |
| -1.1910376215078822  | 0.04335596646195239 | -1.0308958690788812  |
| -2.014470475523881   | -0.9699626185328314 | -0.35169532148234484 |
| -0.16145296509102375 | 0.5245428249091103  | 0.17929370340910136  |
| -0.8409807675249972  | -0.9598486078342193 | -0.9557691582217679  |
+----------------------+---------------------+----------------------+


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STILTS - Starlink Tables Infrastructure Library Tool Set
Starlink User Note256
STILTS web page: http://www.starlink.ac.uk/stilts/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk