plurigrid Geiser/Chicken Scheme: 3-Coloring Skill
Geiser is the Emacs mode for Scheme REPLs. This skill provides:
- Chicken Scheme SplitMix64 implementation
- 3-coloring via ternary output (-1, 0, +1)
- crdt.el sexp manipulation
- Penrose diagram ASCII generation
Chicken Scheme SplitMix64
;;; chicken_splitmix.scm
(define GOLDEN #x9E3779B97F4A7C15)
(define MIX1 #xBF58476D1CE4E5B9)
(define MIX2 #x94D049BB133111EB)
(define MASK64 #xFFFFFFFFFFFFFFFF)
(define (make-splitmix64 seed)
(let ((state (bitwise-and seed MASK64)))
(lambda ()
(set! state (bitwise-and (+ state GOLDEN) MASK64))
(let* ((z state)
(z (bitwise-and (* (bitwise-xor z (arithmetic-shift z -30)) MIX1) MASK64))
(z (bitwise-and (* (bitwise-xor z (arithmetic-shift z -27)) MIX2) MASK64)))
(bitwise-xor z (arithmetic-shift z -31))))))
(define (splitmix-ternary rng)
;; Map u64 to {-1, 0, +1}
(- (modulo (rng) 3) 1))
(define (color-at seed index)
(let ((rng (make-splitmix64 seed)))
(do ((i 0 (+ i 1))) ((= i index))
(rng))
(let ((h (rng)))
(list (+ 10 (* (/ (bitwise-and h #xFF) 255.0) 85)) ; L
(* (/ (bitwise-and (arithmetic-shift h -8) #xFF) 255.0) 100) ; C
(* (/ (bitwise-and (arithmetic-shift h -16) #xFFFF) 65535.0) 360))))) ; H
3-Coloring for Graphs
;;; 3-color a graph using SplitMixTernary
(define (graph-3-color vertices edges seed)
(let ((rng (make-splitmix64 seed))
(colors (make-hash-table)))
;; Assign initial colors
(for-each
(lambda (v)
(hash-table-set! colors v (splitmix-ternary rng)))
vertices)
;; Verify no adjacent same-color (greedy fix)
(let loop ((changed #t))
(when changed
(set! changed #f)
(for-each
(lambda (e)
(let ((c1 (hash-table-ref colors (car e)))
(c2 (hash-table-ref colors (cadr e))))
(when (= c1 c2)
(hash-table-set! colors (cadr e) (modulo (+ c2 1) 3))
(set! changed #t))))
edges)))
colors))
Geiser REPL Commands
;; In Emacs with Geiser
;; Start Chicken REPL
M-x geiser-connect RET chicken RET
;; Load color module
,load chicken_splitmix.scm
;; Generate colors
(color-at #x6761795f636f6c6f 1)
;; => (95.64 75.69 40.58)
;; Get ternary stream
(let ((rng (make-splitmix64 1069)))
(map (lambda (_) (splitmix-ternary rng)) (iota 10)))
;; => (0 1 -1 0 1 1 -1 0 -1 1)
crdt.el Sexp Patterns
For collaborative editing with crdt.el:
;;; Sexp with metadata for crdt.el
(define (sexp-with-meta sexp author timestamp)
`(,@sexp
:meta (:author ,author
:timestamp ,timestamp
:color ,(color-at (string-hash author) timestamp))))
;;; Damage detection (changed sexps)
(define (sexp-damaged? sexp-old sexp-new)
(not (equal? sexp-old sexp-new)))
;;; Copy-on-flight: fork sexp with new identity
(define (sexp-fork sexp new-author)
(let ((old-meta (sexp-meta sexp)))
(sexp-with-meta (sexp-data sexp)
new-author
(current-seconds))))
Penrose Diagram Generation
;;; ASCII Penrose tiles (P3 rhombus)
(define (penrose-tile type)
(case type
((thin)
'(" /\\"
" / \\"
"/____\\"))
((thick)
'(" /\\"
"/ \\"
"\\ /"
" \\/"))))
(define (penrose-row n seed)
(let ((rng (make-splitmix64 seed)))
(map (lambda (_)
(if (> (splitmix-ternary rng) 0)
(penrose-tile 'thin)
(penrose-tile 'thick)))
(iota n))))
GF(3) Conservation
(define (gf3-conserved? trits)
;; Check every window of 3
(let loop ((ts trits))
(cond
((< (length ts) 3) #t)
((not (zero? (modulo (apply + (take ts 3)) 3))) #f)
(else (loop (cdr ts))))))
(define (enforce-gf3 trits)
;; Adjust middle element to conserve GF(3)
(if (< (length trits) 3)
trits
(let* ((a (car trits))
(b (cadr trits))
(c (caddr trits))
(new-b (modulo (- (+ a c)) 3)))
(cons a (cons (- new-b 1) (enforce-gf3 (cddr trits)))))))
Commands
just geiser-colors # Generate color palette in Chicken
just geiser-3color # 3-color a test graph
just penrose-ascii # Generate Penrose tiling