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:

• :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

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:1e6,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                    |
+----------------------+---------------------+----------------------+
| -0.5759098296568739  | 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   |
+----------------------+---------------------+----------------------+