Not sure exactly what you're looking for, but combining the previous answers, does something like this work? (Using expand_grid to help with generating the data)
library(tidyverse)
myfuncx <- function(t, a, b){
((a)^(b*t))*cos(t)
}
myfuncy <- function(t, a, b){
((a)^(b*t))*(sin(t))
}
my_data <- expand_grid(t=seq(from=0,to=2*pi,by=0.005),
a = seq(from = 1, to = 1.4, by = 0.1),
b = seq(from = 0.6, to = 1.0, by = 0.1)) %>%
mutate(x=myfuncx(t, a, b),
y=myfuncy(t, a, b),
id = stringr::str_c("a-", a, ":b-", b))
my_data %>%
ggplot(mapping=aes(x=x,y=y,color=id)) +
geom_path()
Created on 2020-07-06 by the reprex package (v0.3.0)