Uniformly distribute x points inside a circle

Question

I would like to uniformly distribute a predetermined set of points within a circle. By uniform distribution, I mean they should all be equally distanced from each other (hence a

Answer 1

Stumbled across this question and the answer above (so all cred to user3717023 & Matt).
Just adding my translation into R here, in case someone else needed that :)

library(tibble)
library(dplyr)
library(ggplot2)

sunflower <- function(n, alpha = 2, geometry = c('planar','geodesic')) {
  b <- round(alpha*sqrt(n))  # number of boundary points
  phi <- (sqrt(5)+1)/2  # golden ratio

  r <- radius(1:n,n,b)
  theta <- 1:n * ifelse(geometry[1] == 'geodesic', 360*phi, 2*pi/phi^2)

  tibble(
    x = r*cos(theta),
    y = r*sin(theta)
  )
}

radius <- function(k,n,b) {
  ifelse(
    k > n-b,
    1,
    sqrt(k-1/2)/sqrt(n-(b+1)/2)
  )
}

# example:
sunflower(500, 2, 'planar') %>%
    ggplot(aes(x,y)) +
    geom_point()