⍝ Mandelbrot — real-axis subset
⍝
⍝ For complex c, the Mandelbrot set is { c : |z_n| stays bounded } where
⍝   z_0 = 0, z_{n+1} = z_n² + c.
⍝ Restricting c (and z) to ℝ gives the segment c ∈ [-2, 1/4]
⍝ where the iteration stays bounded.
⍝
⍝ Rank-polymorphic batched-iteration form:
⍝   mandelbrot ← {⍵ ⍵⍵ ⍺⍺ +,(⍺⍺ × ⍺⍺) }
⍝
⍝ Pseudocode (as we don't have ⎕ system fns yet):
⍝   z      ← 0×c                             ⍝ start at zero
⍝   alive  ← 1+0×c                           ⍝ all "still in"
⍝   for k iterations:
⍝     alive ← alive ∧ 4 ≥ z×z                ⍝ still bounded?
⍝     z     ← alive × c + z×z                ⍝ freeze escaped via mask
⍝     count ← count + alive                  ⍝ tally surviving iters
⍝
⍝ Examples (count after 100 iterations):
⍝   c=0      : 100  (z stays at 0)
⍝   c=-1     : 100  (cycles 0,-1,0,-1,...)
⍝   c=-2     : 100  (settles at 2 — boundary)
⍝   c=0.25   : 100  (boundary — converges to 0.5)
⍝   c=0.5    : 5    (escapes by iteration 6)
⍝   c=1      : 3    (escapes quickly)
⍝
⍝ Real-axis Mandelbrot set: bounded for c ∈ [-2, 0.25].

mandelbrot ← {z←alive←count←0×⍵ ⋄ {alive←alive∧4≥z×z ⋄ z←alive×⍵+z×z ⋄ count+←alive}⍣⍺⊢⍵}
