Next Previous Up Contents
Next: jdbc
Up: Input Schemes
Previous: skysim

4.3.2 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                    |
+----------------------+---------------------+----------------------+
| -0.5759098296568739  | 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   |
+----------------------+---------------------+----------------------+


Next Previous Up Contents
Next: jdbc
Up: Input Schemes
Previous: skysim

TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk