Simulate a 2D Archimedean spiral (helix-like) with noise

Simulates a 2D Archimedean spiral curve parameterized by a latent ordering variable \(t \in [0,1]\). The radius increases linearly with \(t\) and the angle makes turns revolutions. Independent Gaussian noise is added to each coordinate.

simulate_spiral2d(n = 500, turns = 3, noise = 0.05, r0 = 0.2, r1 = 1, seed = 1)

Arguments

n

Integer \(\ge 1\). Number of samples.

turns

Positive numeric. Number of revolutions over \(t \in [0,1]\).

noise

Nonnegative numeric. Standard deviation of Gaussian noise added to both coordinates.

r0, r1

Nonnegative numerics with r1 >= r0. Start/end radius.

seed

Optional integer. If not NULL, sets the RNG seed via set.seed().

Value

A list with components:

• obs: numeric matrix (n x 2) with column names c("x1","x2").

• t: numeric vector of length n, the latent ordering in \([0,1]\).

Examples

sim <- simulate_spiral2d(n = 200, turns = 4, noise = 0.05, seed = 1)
head(sim$obs)
#>               x1         x2
#> [1,]  0.16817785 0.11261864
#> [2,]  0.20099800 0.01721633
#> [3,]  0.13659109 0.21956446
#> [4,]  0.15110509 0.15879060
#> [5,] -0.01061102 0.32886305
#> [6,]  0.09283838 0.32499952
head(sim$t)
#> [1] 0.01307758 0.01339033 0.02333120 0.03554058 0.05893438 0.06178627