Based on Equation 7E of Sprott.
attractor_sprott_7e(a, n, x0 = 1, y0 = 1, dims = c(600, 600), progress = (n >= 1e+05), n_discretize = 1e+06, qs = 0.05, discretize = TRUE)
| a | Numeric vector of length 14 |
|---|---|
| n | Number of points to generate |
| x0 | Initial value for x |
| y0 | Initial value for y |
| dims | Dimensions of resulting matrix |
| progress | If TRUE, displays a progress bar |
| n_discretize | Number of values to generate before computing the range |
| qs | quantile cutoff |
| discretize | If |
if discretize == TRUE a matrix with dimensions dims, else a data frame with columns x and y, and n rows.
$$x_{i+1} = a_{1} + a_{2} * x_{i} + a_{3} * y_{i} + a_{4} * |x_{i}|^{a5} + a6 * |y_{i}|^{a7}$$
$$y_{i+1} = a_{8} + a_{9} * x_{i} + a_{10} * y_{i} + a_{11} * |x_{i}|^{a12} + a13 * |y_{i}|^{a14}$$
Julien C. Sprott, "Strange Attractors: Creating Patterns in Chaos", page 418, Equation 7e, http://sprott.physics.wisc.edu/fractals/booktext/sabook.pdf