apl: mandelbrot real-axis batched z=z²+c (+9 tests, 296/296)

lib/apl/runtime.sx

@@ -836,6 +836,35 @@
           (apl-eq sum-board (apl-scalar 3))
           (apl-and board (apl-eq sum-board (apl-scalar 4))))))))
 
+(define
+  apl-mandelbrot-step
+  (fn
+    (cs z counts alive iters-left)
+    (if
+      (= iters-left 0)
+      counts
+      (let
+        ((still-alive (apl-and alive (apl-le (apl-mul z z) (apl-scalar 4)))))
+        (let
+          ((new-z (apl-mul still-alive (apl-add (apl-mul z z) cs))))
+          (let
+            ((new-counts (apl-add counts still-alive)))
+            (apl-mandelbrot-step
+              cs
+              new-z
+              new-counts
+              still-alive
+              (- iters-left 1))))))))
+
+(define
+  apl-mandelbrot-1d
+  (fn
+    (cs max-iter)
+    (let
+      ((zero (apl-mul cs (apl-scalar 0)))
+        (ones (apl-add (apl-mul cs (apl-scalar 0)) (apl-scalar 1))))
+      (apl-mandelbrot-step cs zero zero ones max-iter))))
+
 (define
   apl-reduce
   (fn

lib/apl/scoreboard.json

@@ -5,9 +5,9 @@
     "dfn": {"pass": 24, "fail": 0},
     "tradfn": {"pass": 20, "fail": 0},
     "valence": {"pass": 14, "fail": 0},
-    "programs": {"pass": 18, "fail": 0}
+    "programs": {"pass": 27, "fail": 0}
   },
-  "total_pass": 287,
+  "total_pass": 296,
   "total_fail": 0,
-  "total": 287
+  "total": 296
 }

lib/apl/scoreboard.md

@@ -9,8 +9,8 @@ _Generated by `lib/apl/conformance.sh`_
 | dfn | 24 | 0 | 24 |
 | tradfn | 20 | 0 | 20 |
 | valence | 14 | 0 | 14 |
-| programs | 18 | 0 | 18 |
-| **Total** | **287** | **0** | **287** |
+| programs | 27 | 0 | 27 |
+| **Total** | **296** | **0** | **296** |
 
 ## Notes
 

lib/apl/tests/programs.sx

@@ -192,3 +192,48 @@
     0
     0
     0))
+
+(apl-test
+  "mandelbrot c=0 stays bounded"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list 0)) 100))
+  (list 100))
+
+(apl-test
+  "mandelbrot c=-1 cycle bounded"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list -1)) 100))
+  (list 100))
+
+(apl-test
+  "mandelbrot c=-2 boundary stays bounded"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list -2)) 100))
+  (list 100))
+
+(apl-test
+  "mandelbrot c=0.25 boundary stays bounded"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list 0.25)) 100))
+  (list 100))
+
+(apl-test
+  "mandelbrot c=1 escapes at iter 3"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list 1)) 100))
+  (list 3))
+
+(apl-test
+  "mandelbrot c=0.5 escapes at iter 5"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list 0.5)) 100))
+  (list 5))
+
+(apl-test
+  "mandelbrot batched grid (rank-polymorphic)"
+  (mkrv (apl-mandelbrot-1d (make-array (list 5) (list -2 -1 0 1 2)) 10))
+  (list 10 10 10 3 2))
+
+(apl-test
+  "mandelbrot batched preserves shape"
+  (mksh (apl-mandelbrot-1d (make-array (list 5) (list -2 -1 0 1 2)) 10))
+  (list 5))
+
+(apl-test
+  "mandelbrot c=-1.5 stays bounded"
+  (mkrv (apl-mandelbrot-1d (make-array (list 1) (list -1.5)) 100))
+  (list 100))

lib/apl/tests/programs/mandelbrot.apl

@@ -0,0 +1,29 @@
+⍝ 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}⍣⍺⊢⍵}

plans/apl-on-sx.md

@@ -96,7 +96,7 @@ Core mapping:
 ### Phase 6 — classic programs + drive corpus
 - [ ] Classic programs in `lib/apl/tests/programs/`:
   - [x] `life.apl` — Conway's Game of Life as a one-liner using `⊂` `⊖` `⌽` `+/`
-  - [ ] `mandelbrot.apl` — complex iteration with rank-polymorphic `+ × ⌊` (or real-axis subset)
+  - [x] `mandelbrot.apl` — complex iteration with rank-polymorphic `+ × ⌊` (or real-axis subset)
   - [x] `primes.apl` — `(2=+⌿0=A∘.|A)/A←⍳N` sieve
   - [ ] `n-queens.apl` — backtracking via reduce
   - [ ] `quicksort.apl` — the classic Roger Hui one-liner
@@ -118,6 +118,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-07: Phase 6 mandelbrot real-axis — apl-mandelbrot-1d batched z=z²+c with permanent alive-mask; c∈{-2,-1,0,0.25} bounded, c=1→3, c=0.5→5, c=2→2; +9 tests; 296/296
 - 2026-05-07: Phase 6 life — Conway via 9-shift toroidal sum + alive-rule (cnt=3 OR alive∧cnt=4); apl-life-step + life.apl source; blinker oscillates, block stable, glider advances; +7 tests; 287/287
 - 2026-05-07: Phase 6 primes — sieve via outer-product residue + reduce-first + compress; apl-compress added; lib/apl/tests/programs/primes.apl source; +11 tests; 280/280
 - 2026-05-07: Phase 5 conformance.sh + scoreboard.{json,md} — per-suite runner; current snapshot 269/269; **Phase 5 complete**