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#### 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 `<nrow>` argument may be given as a plain integer (`1000`), or with embedded underscores (`1_000`), or in exponential format (`1e3`).

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:

  - `:attractor:9999,clifford`
  - `:attractor:1_000_000,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`
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:

  - `: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:1_000_000,rampe,1.42,-1.98,0.39,1.32,1.79,-0.37`
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:

  - `: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                    |
    +----------------------+---------------------+----------------------+
    | -0.575909829655677   | 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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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