#' The tinkerbell map. From the Wikipedia article on chaotic maps.
#'
#' @param n Number of points in the time series.
#' @param xi The initial value for x
#' @param yi The initival value for y
#' @param a The value of the parameter a
#' @param b The value of the parameter b
#' @param c The value of the parameter c
#' @param d The value of the parameter d
#' @param add.timestep Add a column indicating the time step?
#' @param plot Plot the time series?
#' @return A n-by-2 data frame containing the values of the x and y components.
#' @export
tinkerbell_map <- function(n = 1000,
xi = -0.74,
yi = -0.56,
a = 0.9,
b = -0.6,
c = 2,
d = 0.5,
add.timestep = FALSE,
plot = FALSE) {
x = vector(length = n)
y = vector(length = n)
x[1] = xi
y[1] = yi
for (i in 2:n) {
x[i] = x[i - 1]^2 - y[i - 1]^2 + a * x[i - 1] + b * y[i - 1]
y[i] = 2 * x[i - 1] * y[i - 1] + c * x[i - 1] + d * y[i - 1]
}
if (add.timestep) {
timestep = 1:n
df = data.frame(timestep, x, y)
names(df) = c("t", "x", "y")
} else {
df = data.frame(x, y)
names(df) = c("x", "y")
}
if (plot & add.timestep) {
p = ggplot2::ggplot() +
ggplot2::geom_line(data = df, mapping = ggplot2::aes(x = t, y = x, col = "x")) +
ggplot2::geom_line(data = df, mapping = ggplot2::aes(x = t, y = y, col = "y")) +
ggplot2::theme_bw() +
ggplot2::ylab("value") +
ggplot2::ggtitle("Tinkerbell map")
print(p)
} else if (plot & !add.timestep) {
warning("cannot plot without adding timestep.")
}
return(df)
}
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