Typst simulation for Sierpiński triangle

sierpinski.typ

#set page(height: auto, width: auto, margin: 5pt)
#import "@preview/cetz:0.4.2": canvas, draw, vector
#let n = 4
// a list of directions to place triangles in
#let dirs = range(3).map(i => (calc.cos(120deg*i+90deg), calc.sin(120deg*i+90deg)))

#canvas({
  import draw: *;
  // set segment style
  set-style(stroke: yellow + 0.3pt)
  // outermost triangle
  polygon((0, 0), angle: 90deg, radius: 2, 3)
  // smooth intersection of segments
  set-style(stroke: (join: "bevel"))
  // a queue of centers of triangles to be drawn
  let curr-centers = ((0,0),)
  // a queue of centers to triangles to be drawn during next iteration
  let next-centers = ()
  let curr-R = 2
  for k in range(n) {
    curr-R = curr-R / 2
    // While queue is not empty, remove and draw first element,
    // then add its rotated copies to the end of the next-queue
    while curr-centers.len() > 0 {
      let curr-center = curr-centers.remove(0);
      polygon(curr-center, radius: curr-R, angle: 30deg, 3)
      for dir in dirs {
        let new-center = vector.add(curr-center, vector.scale(dir, curr-R))
        next-centers.push(new-center)
      }

    }
    // Reset queues for next iteration
    curr-centers = next-centers
    next-centers = ()
  }
})