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