;;;collections of fractal exercises from 
;;;Mandelbrot's "The Fractal Geometry of Nature"
;;;page implies the page number of the book
;;;List of executables
;;;	page50
;;;	page52
;;;	page55
;;;	page68
;;;	page70
;;;	page54
;;;	page64
;;;
;;;
;;;	mandelbrot__main
(defun c:mandelbrot_main()
	
	(setq dcl_id (load_dialog "fractal_mandelb.dcl"))
	(if (not (new_dialog "fractal_mandelb" dcl_id))
		(exit)
	)
	(setq proof_list '("page50" "page52" "page54" "page55" "page64"
			   "page68" "page70"  ""  ""  ""
		           "" "" "" "" "")
	)
	(foreach sld_name proof_list
	  (start_image sld_name)
	  (slide_image 0 0 
		(- (dimx_tile sld_name) 1)  (- (dimy_tile sld_name) 1)
		(strcat "mandelbrot" "(" sld_name ")")
	  )
	  (end_image)
	);;;end of foreach loop
	(setq pr_mode "page50")
	(mode_tile pr_mode 4)
	(foreach pd0 proof_list
	   (action_tile pd0
		"(mode_tile pr_mode 4) (setq pr_mode $key)(mode_tile pr_mode 4)"
	   )
	)
	(action_tile "help" "(help \"\" \"ddptype\")")
	(start_dialog)
	;;;execute the selected program
	(cond
		((= pr_mode "page50")	 (c:page50)	 )
		((= pr_mode "page52")	 (c:page52)	 )
		((= pr_mode "page54")	 (c:page54)	 )
		((= pr_mode "page55")	 (c:page55)	 )
		((= pr_mode "page64")	 (c:page64)	 )
		((= pr_mode "page68")	 (c:page68)	 )
		((= pr_mode "page70")	 (c:page70)	 )
		(t nil)
	);;;end of cond 
	
);;;FRACTAL_MANDELB_MAIN
;;;
;fractal function   page50
;;;originally created 10/01/98   Takaya  Iwamoto
;;;updated 	May 05,2003

;;;draw a generator for slide file creation purpose
;;;
;;;
;;;make all slides
;;; step 1: run makeall_slide
;;;		This will create slide files page50, page52,    ,page70
;;; step 2: make the following script
;;;		slidelib  fractal_mandelb < mandelb_list.txt
;;;
;;;		where mandelb_list looks like this.
;;;			page50
;;;			page52
;;;			page54
;;;			page55
;;;			page64
;;;			page68
;;;			page70
;;;
;;; step 3: run the script to create a slide library  named  fractal_mandelb.slb
;;;
;;;
;;;
(defun c:MAKEALL_SLIDES()
	(c:refresh_all)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -8)
	(c:page50_mode)
	(c:page52_mode)
	(c:page54_mode)
	(c:page55_mode)
	(c:page64_mode)
	(c:page68_mode)
	(c:page70_mode)
);;;MAKEALL_SLIDES
;;;
;;;
(defun c:page50_mode()
	(c:refresh_all)
	(setvar "PDMODE" 32)
	(setvar "PDSIZE" -8)
	(setup_page50)
	(make_line_1 "0" 1 '(0 0) '(1 0))
	(base_len)
	(fractal_page50)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page50")
	
);;;C:page50_mode
;;;
(defun c:page52_mode()
	(c:refresh_all)
	(setup_page52)
	(make_line_1 "0" 1 '(0 0) '(1 0))
	(base_len)
	(fractal_page52)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page52")
);;;C:page52_mode
;;;
(defun c:page54_mode()
	(c:refresh_all)
	(setup_page54)
	(make_line_1 "0" 1 '(0 0) '(1 0))
	(base_len)
	(fractal_page54)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page54")
);;;C:page54_mode
;;;
(defun c:page55_mode()
	(c:refresh_all)
	(setup_page55)
	(make_line_1 "0" 1 '(0 0) '(1 0))
	(base_len)
	(fractal_page55)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page55")
);;;C:page55_mode
;;;
(defun c:page64_mode()
	(c:refresh_all)
	(setup_page64)
	(initiator_page64)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page64")
);;;C:page64_mode
;;;
(defun c:page68_mode()
	(c:refresh_all)
	(setup_page68)
	(initiator_page68)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page68")
);;;C:page68_mode
;;;
(defun c:page70_mode()
	(c:refresh_all)
	(setup_page70)
	(initiator_page70)
	(make_pt "0" 1 '(0 0))
	(make_pt "0" 1 '(1 0))
	(command "_.zoom" "_E")
	(command "_.regen")
	(command "mslide" "page70")
);;;C:page70_mode
;;;
;;;
;;;
;;main routine for page50  Fractals
(defun c:page50()
	(setup_page50)
	
	(initiator_page50)		;draw the initiator drawing
	(base_len)	;set initial parameters
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_page50)
	)
	(reset_sysvar)
	(princ)
);;;page50----main
;;;
;;;
(defun setup_page50()
	(setup_sysvar)
	(setvar "osmode" 0)		;;no snap mode
	(setq lower_left '(-0.5 -0.5) upper_right '(1.5 1.5))
	(command "_.zoom" "_W" lower_left upper_right)
)
;;;
;;;
(defun initiator_page50()
	(command "_.line" '(0 0) '(0 1) '(1 1) '(1 0) '(0 0) "")
	;(command "_.zoom" "_EXTENT")
)
;drawing the next level of figures	
(defun fractal_page50( / x1 y1 x2 y2 line_set n index  ent_list)
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq n (sslength line_set))
			
	;;;repeat for all line elements
	(setq index 0)
	(repeat n      		 ; loop for all line entities
	    (setq ent_list (entget (ssname line_set index)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
				;basic geometric components
	    (setq x1 (car pnt_1) y1 (cadr pnt_1)
	     	  x2 (car pnt_2) y2 (cadr pnt_2)
		  line_angle (angle pnt_1 pnt_2)
	    )	
	    (draw_lines_page50)
				;delete old line used as reference
            (entdel (ssname line_set index)) 
	    (setq index (1+ index))
	)
	(setq base_length unit_len)
)	
;
(defun draw_lines_page50( / half_len q3_len right_angle left_angle
		     pnt_10 pnt_12 pnt_20 pnt_21 pnt_22 pnt_30 pnt_31 )
	(setq unit_len  (/ base_length 4.0)
		half_len (* unit_len 2.0) q3_len (* unit_len 3.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
	)
	;define new set of points
	(setq   pnt_10 (polar pnt_1 line_angle unit_len)
		pnt_12 (polar pnt_10 left_angle unit_len)
		pnt_22 (polar pnt_12 line_angle unit_len)
		pnt_20 (polar pnt_1 line_angle half_len)
		pnt_21 (polar pnt_20 right_angle unit_len)
		Pnt_31 (polar pnt_21 line_angle unit_len)
		pnt_30 (polar pnt_1 line_angle q3_len)
	)
	;draw a new set of line elements
	(command "_.line" pnt_1 pnt_10 pnt_12 pnt_22 pnt_20 
			 pnt_21 pnt_31 pnt_30 pnt_2 "")
 )  
;
;get the basic length of the line element
;
(defun base_len( /  ent_list line_set)
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq ent_list (entget (ssname line_set 0)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
	(setq base_length (distance pnt_1 pnt_2))(terpri)
)	
; end of fr_002.lsp  10/01/98   Takaya  Iwamoto
;;;
;;;	FR_003.LSP
;;;updated May 05,2003		Takaya Iwamoto
;;;
;;;	Command name : page52
;fractal function   page52 on Mandelbrot
;
;main routine for page52  Fractals
;;;
(defun c:page52()
	(setup_page52)
	
	(initiator_page52)	;draw the initiator drawing
	(base_len)	;set initail parameters
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_page52)
	)
	(reset_sysvar)
	(princ)
);; PAGE52----main
;;;
;;;
(defun setup_page52()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(setq lower_left '(-0.5 -0.5) upper_right '(1.5 1.5))
	(command "_.zoom" "W" lower_left upper_right)
	(command "_.regen")
	;(command "undo" "Control" "None")
);;
;;;
;;;
(defun initiator_page52()
	(command "_.line" '(0 0) '(0 1) '(1 1) '(1 0) '(0 0) "")
)
;;;
;drawing the next level of figures	
(defun fractal_Page52( / x1 x2 y1 y2 index n line_set ent_list)
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all line entities
	    (setq ent_list (entget (ssname line_set index)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
;basic geometric components
	    (setq x1 (car pnt_1) y1 (cadr pnt_1)
	     	  x2 (car pnt_2) y2 (cadr pnt_2)
		  line_angle (angle pnt_1 pnt_2)
	    )	
	
	(draw_lines_Page52)
	;delete old line used as reference
            (entdel (ssname line_set index)) 
	    (setq index (1+ index))
	
	)
	(setq base_length unit_len)
)	

;
(defun draw_lines_page52( / len_2 len_3 len_4 len_5 right_angle left_angle
		     pnt_10 pnt_11 pnt_12 pnt_20 pnt_21 pnt_22
                     pnt_30 pnt_31 pnt_32 pnt_33 pnt_34
		     pnt_40 pnt_43 pnt_44 pnt_50 pnt_53 pnt_54
		)
	(setq unit_len  (/ base_length 6.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		len_2 (* unit_len 2.0) len_3 (* unit_len 3.0)
		len_4 (* unit_len 4.0) len_5 (* unit_len 5.0)
	)
	;define new set of points
	(setq   pnt_10 (polar pnt_1 line_angle unit_len)
		pnt_20 (polar pnt_1 line_angle len_2)
		pnt_30 (polar pnt_1 line_angle len_3)
		pnt_40 (polar pnt_1 line_angle len_4)
		pnt_50 (polar pnt_1 line_angle len_5)

		pnt_11 (polar pnt_10 left_angle len_2)
		pnt_12 (polar pnt_10 left_angle unit_len)

		pnt_21 (polar pnt_20 left_angle len_2)
		pnt_22 (polar pnt_20 left_angle unit_len)

		pnt_31 (polar pnt_30 left_angle len_2)
		pnt_32 (polar pnt_30 left_angle unit_len)
		pnt_34 (polar pnt_30 right_angle len_2)
		pnt_33 (polar pnt_30 right_angle unit_len)

		pnt_44 (polar pnt_40 right_angle len_2)
		pnt_43 (polar pnt_40 right_angle unit_len)

		pnt_54 (polar pnt_50 right_angle len_2)
		pnt_53 (polar pnt_50 right_angle unit_len)
	)

	;draw a new set of line elements
	(command "_.line" pnt_1 pnt_10 pnt_12 pnt_11 pnt_21 pnt_31
			 pnt_32 pnt_22 pnt_20 pnt_30 pnt_40 pnt_43
			 pnt_33 pnt_34 pnt_44 pnt_54 pnt_53 pnt_50 pnt_2 "")
)  
;
;get the basic length of the line element
;
(defun base_len( /  ent_list line_set)
	
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq ent_list (entget (ssname line_set 0)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
	(setq base_length (distance pnt_1 pnt_2))
)	
; end of fr_003.lsp  10/01/98   Takaya  Iwamoto

;fractal function   page55 update using pline
;
;main routine for page55  Fractals
;;;update May 06, 2003		Takaya Iwamoto
;;;
;;;	1 for line 
;;;	2 for pline	Can be used only once before quiting.
;;;	0 for stop
;;;
(defun c:page55()
	(setup_page55)
	(initiator_page55)	;draw the initiator drawing
	(base_len)	;set initail parameters
	(SETQ KEEP_GOING 1)
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_page55)
	)
	(if (= (Yes_or_No "Use plines to finish ?") "_Y") 
		(progn
			(setq keep_going 2)
			(fractal_page55)
		)
	);;;enf of if loop
	(reset_sysvar)
	(princ)
);;;page55---main
;;;
;;;
(defun setup_page55()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(setq lower_left '(-0.5 -0.5) upper_right '(1.5 1.5))
	(command "_.zoom" "_W" lower_left upper_right)
	;(command "undo" "C" "N")
)
;;;
;;;
(defun initiator_page55()
	(command "_.line" '(0 0) '(0 1) '(1 1) '(1 0) '(0 0) "")
	;(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_s" "5.0")
)
;;;
;drawing the next level of figures	
(defun fractal_page55( )
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all line entities
	    (setq ent_list (entget (ssname line_set index)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
;basic geometric components
	    (setq x1 (car pnt_1) y1 (cadr pnt_1)
	     	  x2 (car pnt_2) y2 (cadr pnt_2)
		  line_angle (angle pnt_1 pnt_2)
	    )	
	
	(if (= keep_going 1) (draw_lines_page55) (draw_plines_page55))
	;delete old line used as reference
            (entdel (ssname line_set index)) 
	    (setq index (1+ index))
	
	)
	(setq base_length unit_len)
)	
;;;
;
(defun draw_lines_page55( / len_2 len_3 len_4 len_5 len_6 len_7 len_8
		     right_angle left_angle
		     	    pnt_11 pnt_12 pnt_13 
		     pnt_20 pnt_21 pnt_22 pnt_23
                     pnt_30 pnt_31 pnt_32 pnt_33 pnt_34
		     pnt_40 pnt_41 pnt_42 pnt_43 pnt_44
		     pnt_50 pnt_51 pnt_52
		     pnt_60 pnt_61 pnt_62 pnt_63 pnt_64
		     pnt_70 pnt_71 pnt_72 pnt_73 pnt_74
		     pnt_80 pnt_81 pnt_82 pnt_83 
		     	    pnt_91 pnt_92 pnt_93
		)
	(setq unit_len  (/ base_length 8.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		len_2 (* unit_len 2.0) len_3 (* unit_len 3.0) len_4 (* unit_len 4.0)
		len_5 (* unit_len 5.0) len_6 (* unit_len 6.0) len_7 (* unit_len 7.0)
	)
	;define new set of points
	(setq   pnt_20 (polar pnt_1 line_angle unit_len)
		pnt_30 (polar pnt_1 line_angle len_2)
		pnt_40 (polar pnt_1 line_angle len_3)
		pnt_50 (polar pnt_1 line_angle len_4)
		pnt_60 (polar pnt_1 line_angle len_5)
		pnt_70 (polar pnt_1 line_angle len_6)
		pnt_80 (polar pnt_1 line_angle len_7)
		
		pnt_11 (polar pnt_1 left_angle unit_len)
		pnt_12 (polar pnt_1 left_angle len_2)
		pnt_13 (polar pnt_1 left_angle len_3)

		pnt_21 (polar pnt_20 left_angle unit_len)
		pnt_22 (polar pnt_20 left_angle len_2)
		pnt_23 (polar pnt_20 left_angle len_3)

		pnt_31 (polar pnt_30 left_angle unit_len)
		pnt_32 (polar pnt_30 left_angle len_2)
		pnt_33 (polar pnt_30 left_angle len_3)
		pnt_34 (polar pnt_30 left_angle len_4)

		pnt_41 (polar pnt_40 left_angle unit_len)
		pnt_42 (polar pnt_40 left_angle len_2)
		pnt_43 (polar pnt_40 left_angle len_3)
		pnt_44 (polar pnt_40 left_angle len_4)

		pnt_51 (polar pnt_50 left_angle unit_len)
		pnt_52 (polar pnt_50 right_angle unit_len)

		pnt_61 (polar pnt_60 right_angle unit_len)
		pnt_62 (polar pnt_60 right_angle len_2)
		pnt_63 (polar pnt_60 right_angle len_3)
		pnt_64 (polar pnt_60 right_angle len_4)

		pnt_71 (polar pnt_70 right_angle unit_len)
		pnt_72 (polar pnt_70 right_angle len_2)
		pnt_73 (polar pnt_70 right_angle len_3)
		pnt_74 (polar pnt_70 right_angle len_4)

		pnt_81 (polar pnt_80 right_angle unit_len)
		pnt_82 (polar pnt_80 right_angle len_2)
		pnt_83 (polar pnt_80 right_angle len_3)
		
		pnt_91 (polar pnt_2 right_angle unit_len)
		pnt_92 (polar pnt_2 right_angle len_2)
		pnt_93 (polar pnt_2 right_angle len_3)
	)

	;draw a new set of line elements
	(command "_.line" pnt_1  pnt_11 pnt_21 pnt_22 pnt_12 pnt_13 pnt_23 pnt_33
			 pnt_34 pnt_44 pnt_43 pnt_42 pnt_32 pnt_31 pnt_41 pnt_51
			 pnt_50 pnt_52 pnt_61 pnt_71 pnt_72 pnt_62 pnt_63 pnt_64
			 pnt_74 pnt_73 pnt_83 pnt_93 pnt_92 pnt_82 pnt_81 pnt_91
			 pnt_2 "")
)  
;
;
(defun draw_plines_page55( / len_2 len_3 len_4 len_5 len_6 len_7 len_8
		     right_angle left_angle
		     	    pnt_11 pnt_12 pnt_13 
		     pnt_20 pnt_21 pnt_22 pnt_23
                     pnt_30 pnt_31 pnt_32 pnt_33 pnt_34
		     pnt_40 pnt_41 pnt_42 pnt_43 pnt_44
		     pnt_50 pnt_51 pnt_52
		     pnt_60 pnt_61 pnt_62 pnt_63 pnt_64
		     pnt_70 pnt_71 pnt_72 pnt_73 pnt_74
		     pnt_80 pnt_81 pnt_82 pnt_83 
		     	    pnt_91 pnt_92 pnt_93
		)
	(setq unit_len  (/ base_length 8.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		len_2 (* unit_len 2.0) len_3 (* unit_len 3.0) len_4 (* unit_len 4.0)
		len_5 (* unit_len 5.0) len_6 (* unit_len 6.0) len_7 (* unit_len 7.0)
	)
	;define new set of points
	(setq   pnt_20 (polar pnt_1 line_angle unit_len)
		pnt_30 (polar pnt_1 line_angle len_2)
		pnt_40 (polar pnt_1 line_angle len_3)
		pnt_50 (polar pnt_1 line_angle len_4)
		pnt_60 (polar pnt_1 line_angle len_5)
		pnt_70 (polar pnt_1 line_angle len_6)
		pnt_80 (polar pnt_1 line_angle len_7)
		
		pnt_11 (polar pnt_1 left_angle unit_len)
		pnt_12 (polar pnt_1 left_angle len_2)
		pnt_13 (polar pnt_1 left_angle len_3)

		pnt_21 (polar pnt_20 left_angle unit_len)
		pnt_22 (polar pnt_20 left_angle len_2)
		pnt_23 (polar pnt_20 left_angle len_3)

		pnt_31 (polar pnt_30 left_angle unit_len)
		pnt_32 (polar pnt_30 left_angle len_2)
		pnt_33 (polar pnt_30 left_angle len_3)
		pnt_34 (polar pnt_30 left_angle len_4)

		pnt_41 (polar pnt_40 left_angle unit_len)
		pnt_42 (polar pnt_40 left_angle len_2)
		pnt_43 (polar pnt_40 left_angle len_3)
		pnt_44 (polar pnt_40 left_angle len_4)

		pnt_51 (polar pnt_50 left_angle unit_len)
		pnt_52 (polar pnt_50 right_angle unit_len)

		pnt_61 (polar pnt_60 right_angle unit_len)
		pnt_62 (polar pnt_60 right_angle len_2)
		pnt_63 (polar pnt_60 right_angle len_3)
		pnt_64 (polar pnt_60 right_angle len_4)

		pnt_71 (polar pnt_70 right_angle unit_len)
		pnt_72 (polar pnt_70 right_angle len_2)
		pnt_73 (polar pnt_70 right_angle len_3)
		pnt_74 (polar pnt_70 right_angle len_4)

		pnt_81 (polar pnt_80 right_angle unit_len)
		pnt_82 (polar pnt_80 right_angle len_2)
		pnt_83 (polar pnt_80 right_angle len_3)
		
		pnt_91 (polar pnt_2 right_angle unit_len)
		pnt_92 (polar pnt_2 right_angle len_2)
		pnt_93 (polar pnt_2 right_angle len_3)
	)
	;draw a new set of line elements
	(command "_.pline" pnt_1  pnt_11 pnt_21 pnt_22 pnt_12 pnt_13 pnt_23 pnt_33
			 pnt_34 pnt_44 pnt_43 pnt_42 pnt_32 pnt_31 pnt_41 pnt_51
			 pnt_50 pnt_52 pnt_61 pnt_71 pnt_72 pnt_62 pnt_63 pnt_64
			 pnt_74 pnt_73 pnt_83 pnt_93 pnt_92 pnt_82 pnt_81 pnt_91
			 pnt_2 "")
) 
;;;
;get the basic length of the line element
;
(defun base_len( /  ent_list line_set)
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq ent_list (entget (ssname line_set 0)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
	(setq base_length (distance pnt_1 pnt_2))
)	
; end of fr_005.lsp  10/01/98   Takaya  Iwamoto

;fractal function   page54 update using pline
;
;main routine for page54  Fractals
(defun c:page54()
	(setup_page54)

	(initiator)	;draw the initiator drawing
	(base_len)	;set initail parameters
	(SETQ KEEP_GOING 1)
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_Page54)
	)
	(if (= (Yes_or_No "Use plines to finish ?") "_Y") 
		(progn
			(setq keep_going 2)
			(fractal_page54)
		)
	);;;enf of if loop
	(reset_sysvar)
	(princ)
)
;;;
;;;
(defun setup_page54()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(setq lower_left '(-1.5 -1.5) upper_right '(1.5 1.5))
	(command "_.zoom" "_W" lower_left upper_right)
	;(command "undo" "C" "N")
)
;;;
(defun initiator()
	(command "_.line" '(0 0) '(0 1) '(1 1) '(1 0) '(0 0) "")
	;(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_s" "5.0")
)
;drawing the next level of figures	
(defun fractal_page54( )
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all line entities
	    (setq ent_list (entget (ssname line_set index)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
;basic geometric components
	    (setq x1 (car pnt_1) y1 (cadr pnt_1)
	     	  x2 (car pnt_2) y2 (cadr pnt_2)
		  line_angle (angle pnt_1 pnt_2)
	    )	
	
	(if (= keep_going 1) (draw_lines_page54) (draw_plines_page54))
	;delete old line used as reference
            (entdel (ssname line_set index)) 
	    (setq index (1+ index))
	
	)
	(setq base_length unit_len)
)	

;
(defun draw_lines_page54( / len_2 len_3 len_4 len_5 len_6 len_7 len_8 len_8 len_9 len_10
		     len_11 len_12 len_13  right_angle left_angle

		     pnt_20 pnt_21 
                     pnt_30 pnt_31 				pnt_37 pnt_38 
		     pnt_40 pnt_41 pnt_42 pnt_43       	 	pnt_47 pnt_48
		     pnt_50 pnt_51 pnt_52 pnt_53        	pnt_57 pnt_58 pnt_59 pnt_510 
		     pnt_60 pnt_61 pnt_62 pnt_63 pnt_64 	pnt_67 pnt_68 pnt_69 pnt_610 pnt_611
		     pnt_70 pnt_71 pnt_72 pnt_73 pnt_74 pnt_75 pnt_76 	
		     						pnt_77 pnt_78 pnt_79 pnt_710 pnt_711
 		     pnt_80 pnt_81 pnt_82 pnt_83 pnt_84 pnt_85 pnt_86 	
		     						pnt_87 pnt_88 pnt_89 pnt_810 pnt_811 pnt_812
		     pnt_90 pnt_91 pnt_92 pnt_93 pnt_94 pnt_95  	
		     						pnt_87 pnt_88 pnt_89 pnt_810 pnt_811 pnt_812
		     pnt_100 pnt_101 pnt_102 pnt_103 pnt_104 pnt_105  	
		     						pnt_107 pnt_108 pnt_109 pnt_1010 
		     pnt_110 pnt_111 pnt_112 pnt_113 pnt_114   	
		     						pnt_117 pnt_118 pnt_119 
		     pnt_120 pnt_121 pnt_122  			pnt_127 pnt_128 pnt_129
		     pnt_130 pnt_131 pnt_132  			pnt_107 
		     pnt_140 					pnt_147
		)

	(setq unit_len  (/ base_length 14.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		len_2 (* unit_len 2.0) len_3 (* unit_len 3.0) len_4 (* unit_len 4.0)
		len_5 (* unit_len 5.0) len_6 (* unit_len 6.0) len_7 (* unit_len 7.0)
		len_8 (* unit_len 8.0) len_9 (* unit_len 9.0) len_10 (* unit_len 10.0)
		len_11 (* unit_len 11.0) len_12 (* unit_len 12.0) len_13 (* unit_len 13.0)
	)
	;define new set of points
	(setq   pnt_20 (polar pnt_1 line_angle unit_len)
		pnt_30 (polar pnt_1 line_angle len_2)
		pnt_40 (polar pnt_1 line_angle len_3)
		pnt_50 (polar pnt_1 line_angle len_4)
		pnt_60 (polar pnt_1 line_angle len_5)
		pnt_70 (polar pnt_1 line_angle len_6)
		pnt_80 (polar pnt_1 line_angle len_7)
		pnt_90 (polar pnt_1 line_angle len_8)
		pnt_100 (polar pnt_1 line_angle len_9)
		pnt_110 (polar pnt_1 line_angle len_10)
		pnt_120 (polar pnt_1 line_angle len_11)
		pnt_130 (polar pnt_1 line_angle len_12)
		pnt_140 (polar pnt_1 line_angle len_13)
	;pnt_2	
		pnt_21 (polar pnt_20 left_angle unit_len)
	;pnt_3	
		pnt_31 (polar pnt_30 left_angle unit_len)
		pnt_37 (polar pnt_30 right_angle unit_len)
		pnt_38 (polar pnt_30 right_angle len_2)
	;pnt_4
		pnt_41 (polar pnt_40 left_angle unit_len)
		pnt_42 (polar pnt_40 left_angle len_2)
		pnt_43 (polar pnt_40 left_angle len_3)

		pnt_47 (polar pnt_40 right_angle unit_len)
		pnt_48 (polar pnt_40 right_angle len_2)
	;pnt_5
		pnt_51 (polar pnt_50 left_angle unit_len)
		pnt_52 (polar pnt_50 left_angle len_2)
		pnt_53 (polar pnt_50 left_angle len_3)

		pnt_57 (polar pnt_50 right_angle unit_len)
		pnt_58 (polar pnt_50 right_angle len_2)
		pnt_59 (polar pnt_50 right_angle len_3)
	       pnt_510 (polar pnt_50 right_angle len_4)

	;pnt_60
		pnt_61 (polar pnt_60 left_angle unit_len)
		pnt_62 (polar pnt_60 left_angle len_2)
		pnt_63 (polar pnt_60 left_angle len_3)
		pnt_64 (polar pnt_60 left_angle len_4)

		pnt_67 (polar pnt_60 right_angle unit_len)
		pnt_68 (polar pnt_60 right_angle len_2)
		pnt_69 (polar pnt_60 right_angle len_3)
	       pnt_610 (polar pnt_60 right_angle len_4)
	       pnt_611 (polar pnt_60 right_angle len_5)
	;pnt_70      
		pnt_71 (polar pnt_70 left_angle unit_len)
		pnt_72 (polar pnt_70 left_angle len_2)
		pnt_73 (polar pnt_70 left_angle len_3)
		pnt_74 (polar pnt_70 left_angle len_4)
		pnt_75 (polar pnt_70 left_angle len_5)
		pnt_76 (polar pnt_70 left_angle len_6)

		pnt_77 (polar pnt_70 right_angle unit_len)
		pnt_78 (polar pnt_70 right_angle len_2)
		pnt_79 (polar pnt_70 right_angle len_3)
	       pnt_710 (polar pnt_70 right_angle len_4)
	       pnt_711 (polar pnt_70 right_angle len_5)
	;pnt_80
		pnt_81 (polar pnt_80 left_angle unit_len)
		pnt_82 (polar pnt_80 left_angle len_2)
		pnt_83 (polar pnt_80 left_angle len_3)
		pnt_84 (polar pnt_80 left_angle len_4)
		pnt_85 (polar pnt_80 left_angle len_5)
		pnt_86 (polar pnt_80 left_angle len_6)

		pnt_87 (polar pnt_80 right_angle unit_len)
		pnt_88 (polar pnt_80 right_angle len_2)
		pnt_89 (polar pnt_80 right_angle len_3)
	       pnt_810 (polar pnt_80 right_angle len_4)
	       pnt_811 (polar pnt_80 right_angle len_5)
	       pnt_812 (polar pnt_80 right_angle len_6)
	;pnt_90
		pnt_91 (polar pnt_90 left_angle unit_len)
		pnt_92 (polar pnt_90 left_angle len_2)
		pnt_93 (polar pnt_90 left_angle len_3)
		pnt_94 (polar pnt_90 left_angle len_4)
		pnt_95 (polar pnt_90 left_angle len_5)
		
		pnt_97 (polar pnt_90 right_angle unit_len)
		pnt_98 (polar pnt_90 right_angle len_2)
		pnt_99 (polar pnt_90 right_angle len_3)
	       pnt_910 (polar pnt_90 right_angle len_4)
	       pnt_911 (polar pnt_90 right_angle len_5)
	       pnt_912 (polar pnt_90 right_angle len_6)
	;pnt_10
		pnt_101 (polar pnt_100 left_angle unit_len)
		pnt_102 (polar pnt_100 left_angle len_2)
		pnt_103 (polar pnt_100 left_angle len_3)
		pnt_104 (polar pnt_100 left_angle len_4)
		pnt_105 (polar pnt_100 left_angle len_5)
		
		pnt_107 (polar pnt_100 right_angle unit_len)
		pnt_108 (polar pnt_100 right_angle len_2)
		pnt_109 (polar pnt_100 right_angle len_3)
	       pnt_1010 (polar pnt_100 right_angle len_4)
	;pnt_11	       
		pnt_111 (polar pnt_110 left_angle unit_len)
		pnt_112 (polar pnt_110 left_angle len_2)
		pnt_113 (polar pnt_110 left_angle len_3)
		pnt_114 (polar pnt_110 left_angle len_4)
		
		pnt_117 (polar pnt_110 right_angle unit_len)
		pnt_118 (polar pnt_110 right_angle len_2)
		pnt_119 (polar pnt_110 right_angle len_3)
	       pnt_1110 (polar pnt_110 right_angle len_4)
	;pnt_12
		pnt_121 (polar pnt_120 left_angle unit_len)
		pnt_122 (polar pnt_120 left_angle len_2)
		
		pnt_127 (polar pnt_120 right_angle unit_len)
		pnt_128 (polar pnt_120 right_angle len_2)
		pnt_129 (polar pnt_120 right_angle len_3)
	;pnt_13
		pnt_131 (polar pnt_130 left_angle unit_len)
		pnt_132 (polar pnt_130 left_angle len_2)
		
		pnt_137 (polar pnt_130 right_angle unit_len)
	;pnt_14
		pnt_147 (polar pnt_140 right_angle unit_len)
	)

	;draw a new set of line elements
	(command "_.line" pnt_1  pnt_20 pnt_21 pnt_31 pnt_30 pnt_37 pnt_38 pnt_48 pnt_47 
			 pnt_40 pnt_41 pnt_51 pnt_61 pnt_62 pnt_52 pnt_42 pnt_43
			 pnt_53 pnt_63 pnt_64 pnt_74 pnt_75 pnt_76 pnt_86 pnt_85
			 pnt_95 pnt_105 pnt_104 pnt_114 pnt_113 pnt_103 pnt_93 pnt_94
			 pnt_84 pnt_83 pnt_73 pnt_72 pnt_82 pnt_92 pnt_102 pnt_112 
			 pnt_111 pnt_110 pnt_100 pnt_101 pnt_91 pnt_81 pnt_71 pnt_70 pnt_80
			 pnt_90 pnt_97 pnt_87 pnt_77 pnt_67 pnt_60 pnt_50 pnt_57 pnt_58 pnt_68
			 pnt_78 pnt_88 pnt_98 pnt_99 pnt_89 pnt_810 pnt_710 pnt_79 pnt_69 pnt_59
			 pnt_510 pnt_610 pnt_611 pnt_711 pnt_811 pnt_812 pnt_912 pnt_911 pnt_910
			 pnt_1010 pnt_109 pnt_119 pnt_129 pnt_128 pnt_118 pnt_108 pnt_107 pnt_117
			 pnt_127 pnt_120 pnt_121 pnt_122 pnt_132 pnt_131 pnt_130 pnt_137
			 pnt_147 pnt_140
			 pnt_2 "")
)  
;
;
(defun draw_plines_page54( / len_2 len_3 len_4 len_5 len_6 len_7 len_8
		     right_angle left_angle
		     	    pnt_11 pnt_12 pnt_13 
		     pnt_20 pnt_21 pnt_22 pnt_23
                     pnt_30 pnt_31 pnt_32 pnt_33 pnt_34
		     pnt_40 pnt_41 pnt_42 pnt_43 pnt_44
		     pnt_50 pnt_51 pnt_52
		     pnt_60 pnt_61 pnt_62 pnt_63 pnt_64
		     pnt_70 pnt_71 pnt_72 pnt_73 pnt_74
		     pnt_80 pnt_81 pnt_82 pnt_83 
		     	    pnt_91 pnt_92 pnt_93
		)
	(setq unit_len  (/ base_length 8.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		len_2 (* unit_len 2.0) len_3 (* unit_len 3.0) len_4 (* unit_len 4.0)
		len_5 (* unit_len 5.0) len_6 (* unit_len 6.0) len_7 (* unit_len 7.0)
	)
	;define new set of points
	(setq   pnt_20 (polar pnt_1 line_angle unit_len)
		pnt_30 (polar pnt_1 line_angle len_2)
		pnt_40 (polar pnt_1 line_angle len_3)
		pnt_50 (polar pnt_1 line_angle len_4)
		pnt_60 (polar pnt_1 line_angle len_5)
		pnt_70 (polar pnt_1 line_angle len_6)
		pnt_80 (polar pnt_1 line_angle len_7)
		
		pnt_11 (polar pnt_1 left_angle unit_len)
		pnt_12 (polar pnt_1 left_angle len_2)
		pnt_13 (polar pnt_1 left_angle len_3)

		pnt_21 (polar pnt_20 left_angle unit_len)
		pnt_22 (polar pnt_20 left_angle len_2)
		pnt_23 (polar pnt_20 left_angle len_3)

		pnt_31 (polar pnt_30 left_angle unit_len)
		pnt_32 (polar pnt_30 left_angle len_2)
		pnt_33 (polar pnt_30 left_angle len_3)
		pnt_34 (polar pnt_30 left_angle len_4)

		pnt_41 (polar pnt_40 left_angle unit_len)
		pnt_42 (polar pnt_40 left_angle len_2)
		pnt_43 (polar pnt_40 left_angle len_3)
		pnt_44 (polar pnt_40 left_angle len_4)

		pnt_51 (polar pnt_50 left_angle unit_len)
		pnt_52 (polar pnt_50 right_angle unit_len)

		pnt_61 (polar pnt_60 right_angle unit_len)
		pnt_62 (polar pnt_60 right_angle len_2)
		pnt_63 (polar pnt_60 right_angle len_3)
		pnt_64 (polar pnt_60 right_angle len_4)

		pnt_71 (polar pnt_70 right_angle unit_len)
		pnt_72 (polar pnt_70 right_angle len_2)
		pnt_73 (polar pnt_70 right_angle len_3)
		pnt_74 (polar pnt_70 right_angle len_4)

		pnt_81 (polar pnt_80 right_angle unit_len)
		pnt_82 (polar pnt_80 right_angle len_2)
		pnt_83 (polar pnt_80 right_angle len_3)
		
		pnt_91 (polar pnt_2 right_angle unit_len)
		pnt_92 (polar pnt_2 right_angle len_2)
		pnt_93 (polar pnt_2 right_angle len_3)
	)

	;draw a new set of line elements
	(command "_.pline" pnt_1  pnt_11 pnt_21 pnt_22 pnt_12 pnt_13 pnt_23 pnt_33
			 pnt_34 pnt_44 pnt_43 pnt_42 pnt_32 pnt_31 pnt_41 pnt_51
			 pnt_50 pnt_52 pnt_61 pnt_71 pnt_72 pnt_62 pnt_63 pnt_64
			 pnt_74 pnt_73 pnt_83 pnt_93 pnt_92 pnt_82 pnt_81 pnt_91
			 pnt_2 "")
) 

;get the basic length of the line element
;
(defun base_len( /  ent_list line_set)
	
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq ent_list (entget (ssname line_set 0)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
	(setq base_length (distance pnt_1 pnt_2))
)	

; end of fr_006.lsp  10/01/98   Takaya  Iwamoto
;fractal function   page68 update using pline
;
;main routine for page68  Fractals
(defun c:page68()
	(setup_Page68)

	(initiator_page68)	;draw the initiator drawing
	;(base_len)	;set initial parameters
	
	(SETQ KEEP_GOING 1)
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_page68)
	)
	;	(setq keep_going 2)
	;	(fractal_page68)
	(if (= (Yes_or_No "Round-off sharp corners ?") "_Y") (fractal_2) )
	(reset_sysvar)

	(princ)
)
;;;
;;;
(defun setup_page68()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(setq lower_left '(-0.5 -0.5) upper_right '(1.5 1.5))
	(command "_.zoom" "W" lower_left upper_right)
	;(command "undo" "C" "N")
)
;;;
(defun initiator_page68( / base_length unit_len len_2
			line_angle left_angle rigth_angle left_60 rigth_60
			pnt_2l pnt_2r pnt_30 pnt_3l pnt_3r
			pnt_40 pnt_4r pnt_4l pnt_50 pnt_5r pnt_5l
		)
		;basic geometric components
		(setq   base_length 1.0
			line_angle 0.0
		)
	(setq unit_len  (/ base_length 3.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		left_60    (+ line_angle (dtr 60.))
		right_60   (- line_angle (dtr 60.))
		len_2 (* unit_len 2.0) 
		pnt_0 '(0 0)
	)
	;define new set of points
	(setq   pnt_30 (polar pnt_0 line_angle unit_len)
		pnt_40 (polar pnt_0 line_angle len_2)
				
		pnt_2l (polar pnt_0 left_60 unit_len)
		pnt_2r (polar pnt_0 left_60 unit_len)

		pnt_3l (polar pnt_0 left_60 len_2)
		pnt_3r (polar pnt_0 right_60 len_2)

		pnt_4l (polar pnt_30 left_60 len_2)
		pnt_4r (polar pnt_30 right_60 len_2)

		pnt_5l (polar pnt_40 left_60 unit_len)
		pnt_5r (polar pnt_40 right_60 unit_len)
	)
	
	 (command "_.pline" '(0 0) pnt_2l pnt_3l pnt_4l pnt_5l pnt_30 pnt_40 '(1 0) "")

	;(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_s" "5.0")
)
;drawing the next level of figures	
(defun fractal_page68( )
	(setq line_set (ssget "_X" (list (cons 0 "lwpolyline"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all line entities
	(setq this_entity (ssname line_set index) )

	(setq this_list (pl_vertices  this_entity)
		pnt_1 (nth 0 this_list)  pnt_2 (nth 1 this_list)
		pnt_3 (nth 2 this_list)  pnt_4 (nth 3 this_list)
		pnt_5 (nth 4 this_list)  pnt_6 (nth 5 this_list)
		pnt_7 (nth 6 this_list)  pnt_8 (nth 7 this_list)
	)
	  
	(setq direction 0)
	(setq direction (right_or_left pnt_1 pnt_8 pnt_3)
		left 1  right -1 )
	
	(if (= direction left)
	    (progn
 	    (pline_page68  1 pnt_1 pnt_2)
	    (pline_page68  1 pnt_3 pnt_2)
	    (pline_page68  1 pnt_4 pnt_3)
	    (pline_page68  1 pnt_5 pnt_4)
	    (pline_page68  2 pnt_6 pnt_5)
	    (pline_page68  1 pnt_6 pnt_7)
	    (pline_page68  1 pnt_8 pnt_7)
	    )
	)

	(if (= direction right)
	    (progn
	    (pline_page68  2 pnt_1 pnt_2)
	    (pline_page68  2 pnt_3 pnt_2)
	    (pline_page68  2 pnt_4 pnt_3)
	    (pline_page68  2 pnt_5 pnt_4)
	    (pline_page68  1 pnt_6 pnt_5)
	    (pline_page68  2 pnt_6 pnt_7)
	    (pline_page68  2 pnt_8 pnt_7)
	    )
	)
	;(if (= keep_going 1) (draw_lines_page68) (draw_plines_page68))
	;delete old line used as reference
            (entdel this_entity) 
	    (setq index (1+ index))
	)
)	

;utility function to decide which side the input point lies w.r.t. ref.line
;defined by pnt_base_0 and pnt_base_1
(defun right_or_left(pnt_base_s pnt_base_e pnt_ref / 
			vec_ab vec_ac result direct
	      	)
	(setq vec_ab (makevec pnt_base_s pnt_base_e)
		vec_ac (makevec pnt_base_s pnt_ref))
	(setq result (vec_prod vec_ab vec_ac))
	(if (>= result 0.0) (setq direct 1) (setq direct -1))
)
;
;utility function to make a vector given two points
(defun makevec(pnt_a pnt_b / x1 y1 x2 y2 del_x pnt_new )

	(setq x1 (car pnt_a) y1 (cadr pnt_a)
	      x2 (car pnt_b) y2 (cadr pnt_b)	
	      del_x (- x2 x1) del_y (- y2 y1)
	      pnt_new (list del_x del_y)
	)
)	
;
;utiltiy function to compute vector product
;given two vector data
(defun vec_prod(vec_1 vec_2 / a1 a2 b1 b2 prod )

	(setq a1 (car vec_1) b1 (cadr vec_1)	
		a2 (car vec_2) b2 (cadr vec_2)
		prod (- (* a1 b2) (* a2 b1))
	)
)	

;
(defun pline_page68(pattern pnt_s pnt_e /   base_length unit_length len2 line_angle  
					 right_angle left_angle left_60 right_60
		    			 pnt_2l pnt_2r
		    			 pnt_30 pnt_3l pnt_3r 
					 pnt_40 pnt_4l pnt_4r
					 pnt_5l pnt_5r
		 )

		;basic geometric components
		(setq   base_length (distance pnt_s pnt_e)
			line_angle (angle pnt_s pnt_e)
		)
	(setq unit_len  (/ base_length 3.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		left_60    (+ line_angle (dtr 60.))
		right_60   (- line_angle (dtr 60.))
		len_2 (* unit_len 2.0) 
	)
	;define new set of points
	(setq   pnt_30 (polar pnt_s line_angle unit_len)
		pnt_40 (polar pnt_s line_angle len_2)
				
		pnt_2l (polar pnt_s left_60 unit_len)
		pnt_2r (polar pnt_s right_60 unit_len)

		pnt_3l (polar pnt_s left_60 len_2)
		pnt_3r (polar pnt_s right_60 len_2)

		pnt_4l (polar pnt_30 left_60 len_2)
		pnt_4r (polar pnt_30 right_60 len_2)

		pnt_5l (polar pnt_40 left_60 unit_len)
		pnt_5r (polar pnt_40 right_60 unit_len)
	)
	(if (= pattern 1) (command "_.pline" pnt_s pnt_2r pnt_3r pnt_4r pnt_5r pnt_30 pnt_40
					    pnt_e ""))
	(if (= pattern 2) (command "_.pline" pnt_s pnt_2l pnt_3l pnt_4l pnt_5l pnt_30 pnt_40
					    pnt_e ""))
)  
;The final step
;rounding-off sharp vertices
;replace line segments by 1/6-th arc segments.	
(defun fractal_2( )
	(setq line_set (ssget "_X" (list (cons 0 "lwpolyline"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all line entities
	(setq this_entity (ssname line_set index) )

	(setq this_list (pl_vertices  this_entity)
		pnt_1 (nth 0 this_list)  pnt_2 (nth 1 this_list)
		pnt_3 (nth 2 this_list)  pnt_4 (nth 3 this_list)
		pnt_5 (nth 4 this_list)  pnt_6 (nth 5 this_list)
		pnt_7 (nth 6 this_list)  pnt_8 (nth 7 this_list)
	)
	  
	(setq direction 0)
	(setq direction (right_or_left pnt_1 pnt_8 pnt_3)
		left 1  right -1 )
	(if (= direction left)
	    (progn
 	    (round_off  right  pnt_1 pnt_2)
	    (round_off  right  pnt_3 pnt_2)
	    (round_off  right  pnt_4 pnt_3)
	    (round_off  right  pnt_5 pnt_4)
	    (round_off  left   pnt_6 pnt_5)
	    (round_off  right  pnt_6 pnt_7)
	    (round_off  right  pnt_8 pnt_7)
	    )
	)

	(if (= direction right)
	    (progn
	    (round_off  left  pnt_1 pnt_2)
	    (round_off  left  pnt_3 pnt_2)
	    (round_off  left  pnt_4 pnt_3)
	    (round_off  left  pnt_5 pnt_4)
	    (round_off  right pnt_6 pnt_5)
	    (round_off  left  pnt_6 pnt_7)
	    (round_off  left  pnt_8 pnt_7)
	    )
	)
	
            (entdel this_entity) 
	    (setq index (1+ index))
	)
)	
;final step
;instead of pline, draw an arc
(defun round_off(line_dir pnt_s pnt_e /   base_length unit_length len2 line_angle  
					 right_angle left_angle left_60 right_60
		)

	;basic geometric components
	(setq   base_length (distance pnt_s pnt_e)
		line_angle (angle pnt_s pnt_e)
		unit_len  (/ base_length 3.0)
		left_angle (+ line_angle (dtr 90.))
		right_angle(- line_angle (dtr 90.))
		left_60    (+ line_angle (dtr 60.))
		right_60   (- line_angle (dtr 60.))
		len_2 (* unit_len 2.0) 
	)
	;define a center of an arc
	(setq   center_left  (polar pnt_s left_60  base_length)
		center_right (polar pnt_s right_60 base_length)
	)
	(if (= line_dir left)
		(command "_.arc" "_CE" center_right pnt_e pnt_s))
	(if (= line_dir right)
		(command "_.arc" "_CE" center_left  pnt_s pnt_e))
)  
; This routine accepts a polyline and returns a list of the polyline's vertices.
(defun pl_vertices (pl_entity /
		pline	;entity list for pl_entity
		nodes	;number of nodes
		the_rest   ;list starting with the first node
		cnt	;counter
		index	;index for node location
		cur_list	;node list
		pline_list	;the node list
	 )
	(setq pline (entget pl_entity))		;entity list for the pline 
	(setq nodes (cdr (assoc 90 pline))
		the_rest (member  (assoc 10 pline)  pline)
		cnt 0
		pline_list nil
	)
	(repeat nodes
		(setq index (* 4 cnt)			;every 4th location
		 cur_list (list (cdr  (nth index  the_rest)))
		 pline_list (append pline_list cur_list)
		 cnt (1+ cnt)
		)
	)
	 pline_list		;return list
)
;
; end of fr_007.lsp  10/22/98   Takaya  Iwamoto
;;;
;fr_009.lsp
;fractal function   page64 update using pline
;
;main routine for page70  Fractals
(defun c:page70()
	(setup_page70)

	(initiator_page70)	;draw the initiator drawing
	(SETQ KEEP_GOING 1)
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_page70)
	)
	(if (= (Yes_or_No "Use plines to finish ?") "_Y") 
		(progn
			(setq keep_going 2)
			(fractal_page70)
		)
	);;;enf of if loop
	(reset_sysvar)

	(princ)
);;;
;;;
(defun setup_page70()
	(setup_sysvar)
	(setvar "osmode" 0)		;;no snap mode
	(setq lower_left '(-0.5 -0.5) upper_right '(1.5 1.5))
	(command "_.zoom" "W" lower_left upper_right)
)
;;;
(defun initiator_page70( / pt_1 pt_2 pt_3 pt_4 pt_5 pt_6 pt_7 pt_8)
	(setq   ref_factor (sqrt 7.0)
		ref_tilt (atan (/ (sqrt 3.0) 5.0))
		ref_len (/ 1.0 ref_factor)
		ref_height (* ref_len (sqrt 0.75))
		
		dtr_30_s (- (dtr 30.) ref_tilt) 
		dtr_60_s (- (dtr 60.) ref_tilt) 
		dtr_90_s (- (dtr 90.) ref_tilt)
	)
	(setq pt_1 '(0 0) 
		pt_2 (polar pt_1 (- ref_tilt) ref_len)
		pt_3 (polar pt_2 dtr_60_s ref_len )
		pt_4 (polar pt_1 dtr_60_s ref_len)
		pt_5 (polar pt_1 dtr_90_s (* 2.0 ref_height))
		pt_6 (polar pt_2 dtr_90_s (* 2.0 ref_height))
		pt_7 (polar pt_2 dtr_60_s (* 2.0 ref_len))
		pt_8 (polar pt_2 dtr_30_s (* 2.0 ref_height))
	)
	(command "_.pline" pt_1 pt_2 pt_3 pt_4 pt_5 pt_6 pt_7 pt_8 "")
	
	;(command "_.zoom" "_EXTENT")
	;(command "_.zoom" "_s" "5.0")
)
;drawing the next level of figures	
(defun fractal_page70( )
	(setq line_set (ssget "_X" (list (cons 0 "lwpolyline"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all polyline entities
	   (setq this_entity (ssname line_set index) )
	   (setq this_list (pl_vertices  this_entity)
		point_1 (nth 0 this_list)
		point_2 (nth 1 this_list)
		point_3 (nth 2 this_list)
		point_4 (nth 3 this_list)
		point_5 (nth 4 this_list)
		point_6 (nth 5 this_list)
		point_7 (nth 6 this_list)
		point_8 (nth 7 this_list)
	   )
	;basic geometric components
	    (pattern_1 point_1 point_2)
	    (pattern_1 point_3 point_2)
	    (pattern_1 point_4 point_3)
	    (pattern_1 point_4 point_5)
	    (pattern_1 point_5 point_6)
	    (pattern_1 point_6 point_7)
	    (pattern_1 point_8 point_7)
	    	
	;delete old line used as reference
	    (entdel this_entity) 
	    (setq index (1+ index))
	)
)	
;
(defun pattern_1(pnt_s pnt_e / 	line_angle base_length
				unit_len unit_height dtr_60 dtr_90
				pnt_2 pnt_3 pnt_4 pnt_5 pnt_6 pnt_7 
				tilt
		)

	(setq line_angle (angle pnt_s pnt_e)
		base_length (distance pnt_s pnt_e)
		unit_len (/ base_length (sqrt 7.0))
		unit_height (* unit_len (sqrt 0.75))
		dtr_60 (+ line_angle dtr_60_s)
		dtr_90 (+ line_angle dtr_90_s)
		tilt (- line_angle ref_tilt)
	)

	;define new set of points
	(setq	pnt_2 (polar pnt_s tilt unit_len)
		pnt_3 (polar pnt_2 dtr_60 unit_len )
		pnt_4 (polar pnt_s dtr_60 unit_len)
		pnt_5 (polar pnt_s dtr_90 (* 2.0 unit_height))
		pnt_6 (polar pnt_2 dtr_90 (* 2.0 unit_height))
		pnt_7 (polar pnt_2 dtr_60 (* 2.0 unit_len))
	)
	
	(command "_.pline" pnt_s pnt_2 pnt_3 pnt_4 pnt_5
			pnt_6 pnt_7 pnt_e "")
	
)  
;
;
; This routine accepts a polyline and returns a list of the polyline's vertices.
(defun pl_vertices (pl_entity /
		pline	;entity list for pl_entity
		nodes	;number of nodes
		the_rest   ;list starting with the first node
		cnt	;counter
		n_index	;index for node location
		cur_list	;node list
		pline_list	;the node list
	 )
	(setq pline (entget pl_entity))		;entity list for the pline 
	(setq nodes (cdr (assoc 90 pline))
		the_rest (member  (assoc 10 pline)  pline)
		cnt 0
		pline_list nil
	)
	(repeat nodes
		(setq n_index (* 4 cnt)			;every 4th location
		 cur_list (list (cdr  (nth n_index  the_rest)))
		 pline_list (append pline_list cur_list)
		 cnt (1+ cnt)
		)
	)
	 pline_list		;return list
)
;
; end of fr_009.lsp  10/11/98   Takaya  Iwamoto
;;;
;;;FR_008.LSP
;;;
;fractal function   page64 update using pline
;Polya's Triangle Sweep
;main routine for page64  Fractals
;;;updated  May,06,2003		Takaya Iwamoto
;;;
;;;
;;;
(defun c:page64()
	(setup_page64)

	(initiator_page64)	;draw the initiator drawing
	;(base_len)	;set initail parameters
	;(setq dummy (getint "\nStart Now ?"))
	(SETQ KEEP_GOING 1)
	(while (= (Yes_or_No "Go to next step ?") "_Y")
		(fractal_page64)
	)
	(if (= (Yes_or_No "Use plines to finish ?") "_Y") 
		(progn
			(setq keep_going 2)
			(fractal_page64)
		)
	);;;enf of if loop
		;(setq keep_going 2)
		;(fractal_page64)
	(reset_sysvar)
	(princ)
)
;;;
;;;
(defun setup_page64()
	(setup_sysvar)
	(setvar "OSMODE" 0)
	(setq lower_left '(-0.5 -0.5) upper_right '(1.5 1.5))
	(command "_.zoom" "W" lower_left upper_right)
	;(command "undo" "C" "N")
)
;;;
(defun initiator_page64()
	(command "_.pline" '(0 0) '(0.5 0) '(0.5 0.5) '(1.0 0.5) '(1.0 0)  "")
)
;;;
;drawing the next level of figures	
(defun fractal_page64( )
	(setq line_set (ssget "_X" (list (cons 0 "lwpolyline"))))
	(setq n (sslength line_set))
			
;repeat for all line elements
	(setq index 0)
	(repeat n       ; loop for all polyline entities
	   (setq this_entity (ssname line_set index) )
	   (setq this_list (pl_vertices  this_entity)
		pnt_1 (nth 0 this_list)
		pnt_3 (nth 2 this_list)
		pnt_5 (nth 4 this_list)
		)
	;basic geometric components
	    (pattern_1_page64 pnt_1 pnt_3)
	    (pattern_2_page64 pnt_3 pnt_5)
	
	;delete old line used as reference
	    (entdel this_entity) 
	    (setq index (1+ index))
	)
)	
;
(defun pattern_1_page64(pnt_s pnt_e / line_angle base_length unit_len left_angle
		     pnt_10 pnt_11 pnt_e1 
		 )
	(setq line_angle (angle pnt_s pnt_e)
		base_length (distance pnt_s pnt_e)
		unit_len (/ base_length 2.0)
		left_angle (+ line_angle (dtr 90.))
	)
	;define new set of points
	(setq   pnt_10 (polar pnt_s line_angle unit_len)
						
		pnt_11 (polar pnt_10 left_angle unit_len)
		pnt_e1 (polar pnt_e  left_angle unit_len)
	)
	(command "_.pline" pnt_s  pnt_10 pnt_11 pnt_e1  
			 pnt_e "")
)  
;
;
(defun pattern_2_page64(pnt_s pnt_e / line_angle base_length unit_len right_angle
		     pnt_10 pnt_11 pnt_s1 
		 )
	(setq line_angle (angle pnt_s pnt_e)
		base_length (distance pnt_s pnt_e)
		unit_len (/ base_length 2.0)
		right_angle(- line_angle (dtr 90.))
	)
	;define new set of points
	(setq   pnt_10 (polar pnt_s line_angle unit_len)
						
		pnt_11 (polar pnt_10 right_angle unit_len)
		pnt_s1 (polar pnt_s  right_angle unit_len)
	)
	(command "_.pline" pnt_s  pnt_s1 pnt_11 pnt_10  
			 pnt_e "")
)  

;
;

;get the basic length of the line element
;
(defun base_len( /  ent_list line_set)
	
	(setq line_set (ssget "_X" (list (cons 0 "line"))))
	(setq ent_list (entget (ssname line_set 0)))
	    (setq pnt_1 (cdr (assoc 10 ent_list)) pnt_2 (cdr (assoc 11 ent_list)))
	(setq base_length (distance pnt_1 pnt_2))
)	
; This routine accepts a polyline and returns a list of the polyline's vertices.
(defun pl_vertices (pl_entity /
		pline	;entity list for pl_entity
		nodes	;number of nodes
		the_rest   ;list starting with the first node
		cnt	;counter
		n_index	;index for node location
		cur_list	;node list
		pline_list	;the node list
	 )
	(setq pline (entget pl_entity))		;entity list for the pline 
	(setq nodes (cdr (assoc 90 pline))
		the_rest (member  (assoc 10 pline)  pline)
		cnt 0
		pline_list nil
	)
	(repeat nodes
		(setq n_index (* 4 cnt)			;every 4th location
		 cur_list (list (cdr  (nth n_index  the_rest)))
		 pline_list (append pline_list cur_list)
		 cnt (1+ cnt)
		)
	)
	 pline_list		;return list
)
;
; end of fr_008.lsp  10/11/98   Takaya  Iwamoto
;;;
;;;
;;main routine for Cantor set
(defun c:cantor()
	(setup_cantor)
	
	(initiator_cantor)		;draw the initiator drawing
	(make_jpg)
	(command "_delay" 1000)
	;(alert "\nStart Cantor set?")
	;(while (= (Yes_or_No "Go to next step ?") "_Y")
	(repeat 15
		(fractal_cantor)
		(make_jpg)
		(command "_.delay" 500)
		(setq counter (1+ counter))
	)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
	(princ)
);;;cantor----main
;;;
;;;
;;main routine for Cantor_comb
(defun c:cantor_comb()
	(setup_cantor)
	
	(initiator_cantor)		;draw the initiator drawing
	(make_jpg)
	(command "_delay" 1000)
	;(alert "\nStart Cantor set?")
	;(while (= (Yes_or_No "Go to next step ?") "_Y")
	(repeat 15
		(fractal_cantor_comb)
		(make_jpg)
		(command "_.delay" 500)
		(setq counter (1+ counter))
	)
	(make_jpg)
	(make_jpg)
	(reset_sysvar)
	(princ)
);;;cantor_comb----main
;;;
(prompt "loading setup_cantor")(terpri)
;;;
(defun setup_cantor()
	(setup_sysvar)
	(setvar "osmode" 0)		;;no snap mode
	(setq dxdy (list 0  -0.02) x_left -0.1 x_right 1.1
		y_up 0.01 y_down -0.01
		nstep 0 one_third (/ 1. 3.)
		w_left (list x_left y_down)
		w_right (list x_right y_up)
		counter 1
	)
	(setq lower_left '(-0.01 -0.335) upper_right '(1.01 0.02))
	(command "_.zoom" "_W" lower_left upper_right)
)
;;;
;;;
(defun initiator_cantor()
	(setq pnt_0 '(0 0)
		pnt_3 '(1 0)
		pnt_0d (shift_pnt pnt_0 dxdy)
		pnt_3d (shift_pnt pnt_3 dxdy)
	)
	(make_line_1 "0" 0 pnt_0 pnt_3)
	(command "_.pline" pnt_0 pnt_0d pnt_3d pnt_3 "cl")
	
	;(command "_.zoom" "_EXTENT")
)
;;;
(prompt "loading fractal_cantor")(terpri)
;drawing the next level of figures	
(defun fractal_cantor( / pnt_0 pnt_1 pnt_2 pnt_3 line_set n index  ent_list)
	(setq line_set (ssget "W" w_left w_right) )
	(setq n (sslength line_set))
			
	;;;repeat for all line elements
	(princ "n= ")(princ n)(terpri)
	(setq index 0)
	(repeat n      		 ; loop for all line entities
	    (setq ent_list (entget (ssname line_set index)) )
	    (setq pnt_0 (shift_pnt (cdr (assoc 10 ent_list)) dxdy)
		  pnt_3 (shift_pnt (cdr (assoc 11 ent_list)) dxdy)
	   	  pnt_1  (plt pnt_0 pnt_3 one_third) 
		  pnt_2  (plt pnt_3 pnt_0 one_third) 
		  base_length (distance pnt_0 pnt_3)
	    )
	    (make_line_1 "0" counter pnt_0 pnt_1)
	    (make_line_1 "0" counter pnt_2 pnt_3)

	    (setq index (1+ index))
	)
	(setq w_left (shift_pnt w_left dxdy)
		w_right (shift_pnt w_right dxdy)
	)
	(princ "counter= ")(princ counter )(princ " nlines= ")(princ n)(Princ " base_length =")(princ base_length)(terpri)
)	
;
(prompt "loading fractal_cantor_comb")(terpri)
;drawing the next level of figures	
(defun fractal_cantor_comb( / pnt_0 pnt_1 pnt_2 pnt_3 line_set n index  ent_list)
	(setq line_set (ssget "W" w_left w_right) )
	(setq n (sslength line_set))
			
	;;;repeat for all line elements
	(princ "n= ")(princ n)(terpri)
	(setq index 0)
	(repeat n      		 ; loop for all line entities
	    (setq ent_list (entget (ssname line_set index)) )
	    (setq pnt_0 (shift_pnt (cdr (assoc 10 ent_list)) dxdy)
		  pnt_3 (shift_pnt (cdr (assoc 11 ent_list)) dxdy)
	   	  pnt_1  (plt pnt_0 pnt_3 one_third) 
		  pnt_2  (plt pnt_3 pnt_0 one_third) 
		  base_length (distance pnt_0 pnt_3)
		  pnt_0d (shift_pnt pnt_0 dxdy)
		  pnt_1d (shift_pnt pnt_1 dxdy)
		  pnt_2d (shift_pnt pnt_2 dxdy)
		  pnt_3d (shift_pnt pnt_3 dxdy)
	    )
	    (make_line_1 "0" 0 pnt_0 pnt_1)
	    (make_line_1 "0" 0 pnt_2 pnt_3)
		(setq color_id (rem counter 7))
		(if (= color_id 0) (setq color_id "BYLAYER"))
	(command "_.color" color_id)
	(command "_.3dface" pnt_0 pnt_0d pnt_1d pnt_1 "")
	(command "_.3dface" pnt_2 pnt_2d pnt_3d pnt_3 "")
	;(command "_.pline" pnt_0 pnt_0d pnt_1d pnt_1 "cl")
	;(command "_.pline" pnt_2 pnt_2d pnt_3d pnt_3 "cl")
	(command "_.color" "BYLAYER")
	    (setq index (1+ index))
	)
	(setq w_left (shift_pnt w_left dxdy)
		w_right (shift_pnt w_right dxdy)
	)
	(princ "counter= ")(princ counter )(princ " nlines= ")(princ n)(Princ " base_length =")(princ base_length)(terpri)
)	
;
; end of fr_002.lsp  10/01/98   Takaya  Iwamoto
;;;