src/looms/004-turtle-curves.lisp @ ebe16cb914fb

(in-package :flax.looms.004-turtle-curves)

;;;; Turtle Graphics ----------------------------------------------------------
(defvar *step* 0.1)
(defvar *angle* 1/4tau)
(defvar *starting-angle* (- 1/4tau))
(defvar *color* nil)

(defstruct turtle
  (x 0.5)
  (y 0.5)
  (angle *starting-angle*)
  (state nil))

(define-with-macro turtle x y angle state)


(defun rot (angle amount)
  (mod (+ angle amount) tau))

(define-modify-macro rotf (amount) rot)


(defgeneric perform-command (turtle command n))

(defmethod perform-command (turtle (command (eql 'f)) n)
  (with-turtle (turtle)
    (list (flax.drawing:path
            (list (vec x y)
                  (progn (perform-command turtle 's n)
                         (vec x y)))
            :color *color*))))

(defmethod perform-command (turtle (command (eql 'l)) n)
  (perform-command turtle 'f n))

(defmethod perform-command (turtle (command (eql 'r)) n)
  (perform-command turtle 'f n))

(defmethod perform-command (turtle (command (eql 's)) n)
  (do-repeat n
    (with-turtle (turtle)
      (incf x (* *step* (cos angle)))
      (incf y (* *step* (sin angle)))))
  nil)

(defmethod perform-command (turtle (command (eql 'x)) n)
  nil)

(defmethod perform-command (turtle (command (eql '-)) n)
  (rotf (turtle-angle turtle) (* n *angle*))
  nil)

(defmethod perform-command (turtle (command (eql '+)) n)
  (rotf (turtle-angle turtle) (* n (- *angle*)))
  nil)

(defmethod perform-command (turtle (command (eql '<)) n)
  (do-repeat n
    (with-turtle (turtle)
      (push (list x y angle) state)))
  nil)

(defmethod perform-command (turtle (command (eql '>)) n)
  (do-repeat n
    (with-turtle (turtle)
      (when-let ((prev (pop state)))
        (destructuring-bind (ox oy oa) prev
          (setf x ox y oy angle oa)))))
  nil)


(defun find-bounds (paths)
  (iterate (for path :in paths)
           (for (p1 p2) = (flax.drawing:points path))
           (maximizing (vx p1) :into max-x)
           (maximizing (vx p2) :into max-x)
           (maximizing (vy p1) :into max-y)
           (maximizing (vy p2) :into max-y)
           (minimizing (vx p1) :into min-x)
           (minimizing (vx p2) :into min-x)
           (minimizing (vy p1) :into min-y)
           (minimizing (vy p2) :into min-y)
           (finally (return (list min-x min-y max-x max-y)))))

(defun scale (paths)
  (iterate
    ;; (with aspect = 1)
    (with (min-x min-y max-x max-y)  = (find-bounds paths))
    (with factor = (min (/ (- max-x min-x))
                        (/ (- max-y min-y))))
    (with x-padding = (/ (- 1.0 (* factor (- max-x min-x))) 2))
    (with y-padding = (/ (- 1.0 (* factor (- max-y min-y))) 2))
    (for path :in paths)
    (for (p1 p2) = (flax.drawing:points path))
    (zapf
      (vx p1) (map-range min-x max-x x-padding (- 1.0 x-padding) %)
      (vy p1) (map-range min-y max-y y-padding (- 1.0 y-padding) %)
      (vx p2) (map-range min-x max-x x-padding (- 1.0 x-padding) %)
      (vy p2) (map-range min-y max-y y-padding (- 1.0 y-padding) %)))
  paths)


(defun encode (commands)
  (iterate
    (with n = 1)
    (for (command . next) :on commands)
    (if (eq command (car next))
      (incf n)
      (progn (collect (cons command n))
             (setf n 1)))))

(defun turtle-draw (commands)
  (iterate (with turtle = (make-turtle))
           (for (command . n) :in (encode commands))
           (appending (perform-command turtle command n))))


;;;; L-Systems ----------------------------------------------------------------
(defun expand (word productions)
  (mappend (lambda (letter)
             (ensure-list (or (getf productions letter) letter)))
           word))

(defun run-l-system (axiom productions iterations)
  (iterate
    (repeat iterations)
    (for word :initially axiom :then (expand word productions))
    (finally (return word))))


(defclass* l-system ()
  ((name)
   (axiom)
   (productions)
   (recommended-angle)))

(defun make-l-system (name axiom productions recommended-angle)
  (make-instance 'l-system
    :name name
    :axiom (ensure-list axiom)
    :productions productions
    :recommended-angle recommended-angle))


(defmacro define-l-system (name-and-options axiom &body productions)
  (destructuring-bind (name &key (angle 1/4tau))
      (ensure-list name-and-options)
    `(defparameter ,(symb '* name '*)
       (make-l-system ',name ',axiom ',productions ,angle))))


(define-l-system quadratic-koch-island-a (f - f - f - f)
  f (f - f + f + f f - f - f + f))

(define-l-system quadratic-koch-island-b (f - f - f - f)
  f (f + f f - f f - f - f + f + f f - f - f + f + f f + f f - f))

(define-l-system quadratic-snowflake (- f)
  f (f + f - f - f + f))

(define-l-system islands-and-lakes (f + f + f + f)
  f (f + s - f f + f + f f + f s + f f - s + f f - f - f f - f s - f f f)
  s (s s s s s s))

(define-l-system unnamed-koch-a (f - f - f - f)
  f (f f - f - f - f - f - f + f))

(define-l-system unnamed-koch-b (f - f - f - f)
  f (f f - f - f - f - f f))

(define-l-system unnamed-koch-c (f - f - f - f)
  f (f f - f + f - f - f f))

(define-l-system unnamed-koch-d (f - f - f - f)
  f (f f - f - - f - f))

(define-l-system unnamed-koch-e (f - f - f - f)
  f (f - f f - - f - f))

(define-l-system unnamed-koch-f (f - f - f - f)
  f (f - f + f - f - f))

(define-l-system dragon-curve l
  l (l + r +)
  r (- l - r))

(define-l-system (sierpinski-gasket :angle (/ tau 6)) r
  l (r + l + r)
  r (l - r - l))

(define-l-system (hexagonal-gosper-curve :angle (/ tau 6)) l
  l (l + r + + r - l - - l l - r +)
  r (- l + r r + + r + l - - l - r))


(define-l-system (tree-a :angle (radians 25.7)) f
  f (f < + f > f < - f > f))

(define-l-system (tree-b :angle (radians 20)) f
  f (f < + f > f < - f > < f >))

(define-l-system (tree-c :angle (radians 22.5)) f
  f (f f - < - f + f + f > + < + f - f - f >))

(define-l-system (tree-d :angle (radians 20)) x
  x (f < + x > f < - x > + x)
  f (f f))

(define-l-system (tree-e :angle (radians 25.7)) x
  x (f < + x > < - x > f x)
  f (f f))

(define-l-system (tree-f :angle (radians 22.5)) x
  x (f - < < x > + x > + f < + f x > - x)
  f (f f))



;;;; Mutation -----------------------------------------------------------------
(defun insert (val target n)
  (append (subseq target 0 n)
          (list val)
          (subseq target n)))


(defun mutation-transpose (result)
  (rotatef (elt result (rand (length result)))
           (elt result (rand (length result))))
  result)

(defun mutation-insert (result)
  (zapf result (insert (random-elt result #'rand)
                       %
                       (rand (length result))))
  result)

(defun mutate-production (result)
  (if (<= (length result) 2)
    result
    (ecase (rand 2)
      (0 (mutation-transpose result))
      (1 (mutation-insert result)))))

(defun mutate-productions (productions)
  (iterate (for (letter production . nil) :on productions :by #'cddr)
           (appending (list letter (mutate-production (copy-list production))))))

(defun maybe-mutate-productions (productions)
  (let ((should-mutate (randomp 0.6 #'rand))
        (mutation-seed (rand (expt 2 31))))
    (if should-mutate
      (with-seed mutation-seed
        (values (mutate-productions productions) mutation-seed))
      productions)))


;;;; Main ---------------------------------------------------------------------
(defun select-l-system ()
  (random-elt `((,*quadratic-koch-island-a* 2 5)
                (,*quadratic-koch-island-b* 2 4)
                (,*quadratic-snowflake* 3 7)
                (,*islands-and-lakes* 1 4)
                (,*unnamed-koch-a* 3 5)
                (,*unnamed-koch-b* 3 6)
                (,*unnamed-koch-c* 3 6)
                (,*unnamed-koch-d* 2 5)
                (,*unnamed-koch-e* 5 7)
                (,*unnamed-koch-f* 5 7)
                (,*dragon-curve* 7 16)
                (,*sierpinski-gasket* 4 10)
                (,*hexagonal-gosper-curve* 3 6)
                (,*tree-a* 3 7 ,(- 1/4tau))
                (,*tree-b* 3 7 ,(- 1/4tau))
                (,*tree-c* 3 5 ,(- 1/4tau))
                (,*tree-d* 6 7 ,(- 1/4tau))
                (,*tree-e* 6 8 ,(- 1/4tau))
                (,*tree-f* 4 7 ,(- 1/4tau)))
              #'rand))


(defun loom (seed filename filetype width height
             &key l-system iterations starting-angle)
  (nest
    (with-seed seed)
    (destructuring-bind
        (random-l-system min-iterations max-iterations &optional random-starting-angle)
        (select-l-system))
    (randomly-initialize
      ((starting-angle (random-or random-starting-angle (rand tau)))
       (iterations (random-range-inclusive min-iterations max-iterations #'rand))
       (l-system random-l-system)))
    (let* ((*starting-angle* starting-angle)
           (bg (hsv (rand 1.0) (rand 1.0) (random-range 0.0 0.2 #'rand)))
           (*color* (hsv (rand 1.0)
                         (random-range 0.5 0.8 #'rand)
                         (random-range 0.9 1.0 #'rand)))
           (axiom (l-system-axiom l-system))
           (*angle* (l-system-recommended-angle l-system))))
    (multiple-value-bind (productions mutagen)
        (maybe-mutate-productions (l-system-productions l-system)))
    (flax.drawing:with-rendering
        (canvas filetype filename width height :background bg :padding 0.05))
    (progn
      (-<> (run-l-system axiom productions iterations)
        turtle-draw
        scale
        (flax.drawing:render canvas <>))
      (values (l-system-name l-system)
              iterations
              mutagen))))



;; (time (loom nil "out" :svg 800 800
;;             ;; :l-system *hexagonal-gosper-curve*
;;             ;; :iterations 5 
;;             ;; :starting-angle (- 1/4tau)
;;             ))