;; Collatz sequence generator (tail recursive)
(define (generate-collatz-sequence n)
  (let loop ((current n) (acc '()))
    (if (= current 1)
        (reverse (cons 1 acc))
        (loop (if (even? current)
                  (/ current 2)
                  (+ (* 3 current) 1))
              (cons current acc)))))

;; Reduce to single digit using modulo 9 (octave reduction)
(define (reduce-to-single-digit value)
  (+ (modulo (- value 1) 9) 1))

;; Map reduced values to octave coordinates
(define (map-to-octave value layer)
  (let* ((angle (* (/ value 9.0) (* 2 pi)))
         (x (* (cos angle) (+ layer 1)))
         (y (* (sin angle) (+ layer 1))))
    (list x y)))

;; Generate Collatz data for numbers 1..max-n
(define (generate-collatz-data max-n)
  (let loop ((n 1) (result '()))
    (if (> n max-n)
        (reverse result)
        (loop (+ n 1)
              (cons (cons n (generate-collatz-sequence n)) result)))))

;; Map sequences to octave positions
(define (map-sequences-to-octave collatz-data stack-spacing)
  (map (lambda (entry)
         (let ((number (car entry))
               (sequence (cdr entry)))
           (cons number
                 (let loop ((layer 0) (seq sequence) (acc '()))
                   (if (null? seq)
                       (reverse acc)
                       (let* ((value (car seq))
                              (reduced (reduce-to-single-digit value))
                              (coords (map-to-octave reduced layer))
                              (x (car coords))
                              (y (cadr coords))
                              (z (* layer stack-spacing)))
                         (loop (+ layer 1)
                               (cdr seq)
                               (cons (list x y z) acc))))))))
       collatz-data))

;; Example usage
(define collatz-data (generate-collatz-data 20))
(define octave-positions (map-sequences-to-octave collatz-data 1.0))

;; Print results
(for-each
 (lambda (entry)
   (display "Number: ") (display (car entry)) (newline)
   (for-each (lambda (pos)
               (display pos) (newline))
             (cdr entry)))
 octave-positions)