This is the source code for a fractal program for the HP48G/GX handheld 
        calculator.  Obviously version 1.0 is not perfect and contains some
        bugs, but nevertheless it shows that the wonderfull world of fractals
        can be accessible even through the smallest of machines.

/               HPFRACT...DOCUMENTATION ORIGINALLY a word perfect 6.1 
/               document (.WPG) 
/               to obtain files or add to program contact...
/                       Email:  edunn@wam.umd.edu
    Source Codes:
  
     Some of the codes listed below were originally written in BASIC or
  pseudo-code.  I had to convert them all to HP's language.  To some
  programming experts, the code may appear choppy and inefficient.  It was
  purposely left that way so that it would resemble the original code and still
  be easy for a beginner to work through.  If you are unfamiliar with HP
  language RPN (Reverse Polish Notation), then you may have problems
  understanding the code.  Many excellent sources on RPN are available from
  EduCalc that explain HP language.  The actually library was assembled
  using the program USRLIB (available through EduCalc GD1).  All programs
  were compressed/decompressed with RFP/RFU (available through EduCalc
  GD9).  The menu launcher was made by TBR (Title Browser).
  
  
  DIR
  
  HPFRACT
      { "SPSKI" "KOCH" "DUST" "WHIRL" "PYTHT3" "ORBIT" "JULIA"        "MANDEL" "TREEE" "IFS" } { "PRINT" "SAVE" "NULLKEY"         "NULLKEY" "NULLKEY" "QUIT" } { 1 1 " SELECT FRACTAL: " }
     TBR   ch
            CASE 
               'ch==0 OR ch==-6' THEN CLEAR "THANK YOU!" KILL      
                    END 
               'ch==-1' THEN PICT RCL PR1 KILL END 
               'ch==-2' THEN PICT RCL 'IMAGE' STO CLEAR "PICT                   STORED AS 'IMAGE'" 1 DISP 1 FREEZE KILL                          END 
               'ch==1'  THEN SWAP DROP 
                      typ
                      CASE 
                         'typ==1' THEN SPSKI END
                         'typ==2' THEN KOCH END
                         'typ==3' THEN DUST END 
                         'typ==4' THEN WHIRL END 
                         'typ==5' THEN PYTHT3 END 
                         'typ==6' THEN ORBIT END 
                         'typ==7' THEN JULIA  END 
                         'typ==8' THEN MANDEL END 
                         'typ==9' THEN TREEE  END 
                         'typ==10' THEN IFS END
                    END 
                    END
               END   
  
    SPSKI
       ERASE 
     10 TRASH STO 
     (0,0) ONE STO 
     (10,0) TWO STO 
     (5,8.66) THREE STO 
     0 10 XRNG 
     0 9 YRNG 
     "CARPET PARAMETERS" { { "SEED" "ENTER START POINT." 1 } {
            "ITERATIONS" "ENTER # OF ITERATIONS." 0 } } { } { } { } 
     IF INFORM NOT THEN { PPAR THREE TWO ONE TRASH} PURGE
            CLEAR HPFRACT KILL END 
     { PT MITR} STO 
     CLLCD { # 0h # 0h } PVIEW 
     0 MITR FOR j 
          COIN3  vertex 
                 PT   CASE 
                    'vertex==1' THEN ONE MIDPOINT  END 
                    'vertex==2' THEN TWO MIDPOINT END 
                    'vertex==3' THEN THREE MIDPOINT END 
               END  
          IF TRASH j    THEN PT PIXON END 
     NEXT { PPAR TRASH ONE TWO THREE PT MITR } PURGE 
     0 WAIT DROP HPFRACT 
  
  COIN3
       RAND 3 * 1 +IP 
  
  MIDPOINT
       OBJ   
     'Y1' STO
     'X1' STO 
        OBJ 
     'Y2' STO 
     'X2' STO 
     X1 X2 + 2 / Y1 Y2 + 2 / R C 'PT' STO 
     { X1 X2 Y1 Y2 } PURGE 
  
  KOCH
      RAD ERASE
     "SNOWFLAKE PARAMETERS" { { "ORDER" "ENTER LEVEL OF          APPROXIMATION ( 1)" 0 } } { } { } { }
     IF INFORM NOT THEN CLEAR HPFRACT KILL END 
     { P } STO
     0 3 P 1 - ^ 4.4 * XRNG 
     0 3 P 2 - ^ 4.4 * YRNG 
     P 3 INV ^ 'H' STO 
     (0,0) 'PT' STO 
     0 'X' STO
     0 'Y' STO 
     0 P FOR x 
          0
     NEXT 
     P  LIST 'LIST' STO 
     CLLCD {# 0h # 0h } PVIEW 
     0 P 4 ^ 1 - FOR n 
          n 'M' STO 
          1 'LL' STO 
          P 1- 0
          FOR l M 
               4 l ^ / IP DUP LIST SWAP LL SWAP PUT 'LIST' STO 
               4 l ^ *M SWAP - 'M' STO 'LL' INCR DROP 
          -1 STEP 
          0 'S' STO 
          LIST OBJ  1 SWAP FOR x 
                y   CASE 
                    'y==0' THEN 0 END 
                    'y==1' THEN 1 END 
                    'y==2' THEN-1 END 
                    'y 3'   THEN 0 END
                       END 
                'S' STO+
          NEXT 
          X H S 3 / 3.14159265359 * COS * + 'X' STO 
          Y H S 3 / 3.14159265359 * SIN * + 'Y' STO
          PT X Y R C DUP 'PT' STO 
          LINE
     NEXT { M H LL T LIST PT S X Y } PURGE 
     PICT RCL 
     {# 5Fh # 5h } "KOCH" 1  GROB REPL 
     {# 5Fh # Ch } "ORDER = " P + 1  GROB REPL 
     PICT STO
     'P' PURGE 0 WAIT CLEAR HPFRACT 
  
  DUST
      ERASE
     "CANTOR SET" { {"ORDER" "ENTER LEVEL OF APPROXIMATION       ( 1)" 0 } { "THICKNESS" "ENTER BOX WIDTH" 0 } } { } { } { }
     IF INFORM NOT THEN CLEAR HPFRACT KILL END 
     { P B } STO 
     { 0 1 } ARRY2 'AA' STO 
     { 0 0 } ARRY2 'BB' STO 
     -.3 1.3 XRNG 
     -.3 B P * .3 + YRNG 
     { # 0h # 0h } PVIEW 
     (0,0) (1,0) LINE 
     (1,0) 1 B NEG R C DUP 'PT' STO LINE 
     PT 0 B NEG R C DUP 'PT' STO LINE 
     PT (0,0) LINE
     1 P FOR p 
          1 2 p ^ FOR I 
               AA I GET 
               3 / BB SWAP I SWAP PUT 'BB' STO
               1 1 AA I GET 
               - 3 / - BB SWAP 2 p ^ I + SWAP PUT 'BB' STO
               NEXT 
          2 2 p 1 + ^  FOR J 
               BB J GET
               AA SWAP J SWAP PUT 'AA' STO
                    NEXT 
          1 2 p 1 + ^ FOR K 
               AA K GET 
               B p * R C AA K 1 + GET 
               B p * R C LINE 
               AA K GET 
               B p * R C AA K GET 
               B p * B - R C LINE 
               AA K 1 + GET 
               B p * R C AA K 1 + GET 
               B p * B - R C LINE 
          2 STEP
     NEXT { PT PPAR BB AA B P } PURGE 
     0 WAIT CLEAR HPFRACT 
  
  ARRY2
      1 2 P 1 + ^ 2 - FOR x 
          0 +
     NEXT 
  
  WHIRL
      RAD ERASE
     "ROTATING AND REDUCING POLYGON" { { "ORDER" "SELECT         NUMBER OF SIDES" 0 } {"DISPLACEMENT" "ENTER       ROTATION ANGLE (RADIANS)" 0 } { "ITERATIONS" "ENTER         # OF ITERATIONS" 0 } } { } { } { }
     IF INFORM NOT THEN CLEAR HPFRACT KILL END 
     4 3 / NEG 4 3 / XRNG 
     -1 1 YRNG 
     { P B MITR }STO 
     { } 1 P 1 + FOR x 
          0 +
     NEXT 
     DUP 'X' STO 'Y' STO 
     1 2 P / - 3.14159265359 * 'A' STO 
     A SIN A B + SIN B SIN + / 'C' STO 
     0 P FOR K 
          2 K * 1 + 3.14159265359 * P / 'T' STO 
          X K 1 + T SIN PUT 'X' STO 
          Y K 1 + T COS PUT 'Y' STO
     NEXT { # 0h # 0h } PVIEW 
     1 MITR FOR N 
          X 1 GET Y 1 GET R C 'PT' STO 
          2 P 1 + FOR L 
               PT X L GET Y L GET R C DUP 'PT' STO 
               LINE
          NEXT 
          1 P 1 + FOR M 
               X M GET 'Z' STO 
               X Z B COS * Y M GET B SIN * - C * M SWAP PUT 'X'                 STO 
               Y Z B SIN *Y M GET B COS * + C * M SWAP PUT 'Y'
                    STO
          NEXT
     NEXT { PPAR P B A C X Y T PT Z MITR } PURGE 
     0 WAIT CLEAR HPFRACT 
  
  PYTHT3
      RAD ERASE
     -2.5 5.5 XRNG 
     -2  4 YRNG
     "PYTHAGORAS TREE" { { "REFERENCE  " "ENTER ANGLE (IN        RADIANS)" 0 } } { } { } { }
     IF INFORM NOT THEN CLEAR HPFRACT KILL END 
     { F } STO
     32 'P' STO 
     { } 1 P FOR x 
          0 +
     NEXT 
     DUP DUP DUP DUP 
     'X2' STO
     'Y2' STO 
     'U2' STO
     'V2' STO 
     'S' STO 
     F COS 'C' STO 
     F SIN 'SS' STO 
     .005 'EPS' STO 
     C SS * NEG 'A1' STO 
     C 2 ^ 'A2' STO
     A1 A2 + 'B1' STO 
     A2 A1 - 'B2' STO 
     B2 'C1' STO 
     1 B1 - 'C2' STO 
     1 A1 - 'D1' STO 
     1 A2 - 'D2' STO 
     { 0 0 1 0 1 2 } { X1 Y1 U1 V1Q J } STO 
     S 1 1 PUT 'S' STO 
     { # 0h # 0h } PVIEW 
     (0,0) (1,0) LINE 
     (1,0) (1,-1) LINE 
     (1,-1) (0,-1) LINE 
     (0,-1) (0,0) LINE 
     SUB130 
  
  SUB130
      Q J + 'M' STO
     U1 X1 - 'X' STO 
     V1 Y1 - 'Y' STO 
     A1 X * X1 + A2 Y * - 'XA' STO 
     Y1 A2 X * + A1 Y * + 'YA' STO 
     X1 B1 X * + B2 Y * - 'XB' STO 
     Y1 B2 X * + B1 Y * + 'YB' STO
     X2 M X1 C1 X * + C2 Y * - PUT 'X2' STO
     Y2 M Y1 C2 X * + C1 Y * + PUT 'Y2' STO
     U2 M X1 D1 X * + D2 Y * - PUT 'U2' STO
     V2 M Y1 D2 X * + D1 Y * + PUT 'V2' STO
     X X * Y Y * + 'SS' STO 
     S M 1 PUT 'S' STO 
     X1 Y1 R C XA YA R C DUP 'PT' STO LINE 
     PT XB YB R C DUP 'PT' STO LINE
     PT U1 V1 R C DUP 'PT' STO LINE 
     PT U2 M GET V2 M GET R C DUP 'PT' STO LINE
     PT X2 M GET Y2 M GET R C DUP 'PT' STO LINE 
     PT X1 Y1 R C LINE 
     XA 'X1' STO 
     YA 'Y1' STO 
     XB 'U1' STO 
     YB 'V1' STO
     IF P M == SS EPS < OR THEN SUB250 END 
     J 1 + 'J' STO SUB130 
  
  SUB250
      2 'K' STO 
     WHILE
             IFERR S M K - GET
             THEN 1
             END 0 ==
          REPEAT 
          K 1 + 'K' STO
     END
          IF M K == 
     THEN 
          PICT RCL 
          { # 5Ch # 2h } 
          "  = " F 2 FIX + STD 1  GROB 
          REPL PICT STO 
          { PT YB XB YA XA Y X M J Q V1 U1 Y1 X1 D2 D1 C2 C1 B2 B1
          A2 A1 EPS SS C F S V2 U2 Y2 X2 P PPAR K } PURGE 
          0 WAIT CLEAR HPFRACT KILL
     END 
     M K - 'Q' STO 
     X2 Q GET 'X1' STO
     Y2 Q GET 'Y1' STO 
     U2 Q GET 'U1' STO
     V2 Q GET 'V1' STO
     S S Q GET 1 - Q SWAP PUT 'S' STO 
     1 'J' STO  
  
  IFS
      ERASE
     "SELECT IFS TYPE" { FERN BINARY CORAL CRYSTAL DRAGON        FLOORR KOCH3 SPIRAL SWIRL5 TREE TRIANGLE ZIGZIG2}
          1 CHOOSE   x
                      IF x NOT THEN HPFRACT KILL END 
     DUP STEQ STRI
     "ENTER PARAMETERS" { { "SEED" "ENTER START POINT"
          1 } { "ITERATIONS" "ENTER # OF ITERATIONS" 0 } } { } { } { }
          IF INFORM NOT THEN CLEAR { EQ PPAR } PURGE IFS KILL
               END 
     { PT MITR} STO 
     20 'TRASH' STO
     CLLCD { # 0h # 0h } PVIEW 
     0 MITR  FOR j 
          EQ COIN GET FUNCT
          IF TRASH j   THEN PT PIXON END 
          PICT RCL { # 0h # 0h } j 1  GROB REPL PICT STO
     NEXT 
     { TRASH EQ PT MITR PPAR } PURGE 
     0 WAIT DROP IFS 
  
  FUNCT
       { A B C D E F} STO 
     PT OBJ  'Y1' STO 'X1' STO 
     X1 A * Y1 B * + E + 'X2' STO 
     X1 C * Y1 D * + F + 'Y2' STO 
     X2 Y2 R C 'PT' STO
      { A B C D E F X1 X2 Y1 Y2 } PURGE 
  
  STRI
        STR TAIL 'STRING' STO 
     STRING SIZE 1 - 'SZ' STO 
     1 SZ FOR x 
          STRING HEAD STRING TAIL 'STRING' STO
     NEXT 
     ".P" 
     1 SZ  FOR x 
          +
     NEXT
     OBJ  OBJ  DROP PMAX PMIN DEPTH  LIST
     'ARRY' STO
     { STRING SZ } PURGE 
  
  COIN
      RAND 'R' STO
     ARRY 1 GET 'SUM' STO 
     1 'K' STO
     WHILE SUM R < REPEAT 
          'K' INCR ARRY SWAP GET 'SUM' STO+
     END 
     K { R SUM K } PURGE 
  
  ARRY 
     {   }
    
  FERN 
     { { 0 0 0 .16 0 0 }
     { .85 .04 -.04 .85 0 1.6 } 
     {.2 -.26 .26 .22 0 1.6 }
     { -.15 .28 .26 .24 0 .44 } }
  
  FERN.P 
     { .01 .85 .07 .07 (-5.29,0) (5.51,10) }
  
  BINARY
     { { .5 0 0 .5 -2.563477 -.000003 }
     { .5 0 0 .5 2.436544 -.000003 } 
     { 0 -.5 .5 0 4.873085 7.563492 } }
  
  BINARY.P 
     { .33333333 .333333333 .3333333333 (-8,-1) (8,11) }
  
  CORAL 
     { { .307692 -.531469 -.461538 -.293706 5.401953 8.655175 }
     { .307692 -.076923 .153846 -.447552 -1.295248 4.15299 }
     { 0 .545455 .692308 -.195804 -4.893637 7.269794 } }
  
  CORAL.P 
     { .4 .15 .45 (-8,-1) (8,11) }
  
  CRYSTAL 
     { { .69697 -.481061 -.393939 -.662879 2.147003 10.310288 }
     { .090909 -.443182 .515152 -.094697 4.286558 2.925762 } }
  
  CRYSTAL.P 
     { .747826 .252174 (-8,-1) (8,11) }
  
  DRAGON 
     { { .824074 .281482 -.212346 .864198 -1.88229 -.110607 }
     { .088272 .520988 -.463889 -.377778 .78536 8.095795 } }
  
  DRAGON.P 
     { .787473 .212527 (-8,-1) (8,11) }
  
  FLOORR 
     { { 0 -.5 .5 0 -1.732366 3.366182 } 
     { .5 0 0 .5 -.027891 5.014877 }
     { 0 .5 -.5 0 1.620804 3.310401 } }
  
  FLOORR.P 
     { .3333333333 .3333333333 .3333333333 (-8,-1) (8,11) }
  
  KOCH3
     {{ .307692 0 0 .294118 4.119164 1.604278 }
     { .192308 -.25882 .653864 .088235 -.068884 5.978916 }
     { .192308 .205882 -.653864 .088235 .66858 5.962514 }
     { .307692 0 0 .294118 -4.13653 1.604278 }
     { .384615 0 0 -.294118 -.007718 2.941176 }}
  
  KOCH3.P
     { .151515 .253788 .253788 .151515 .189394 (-8,-1) (8,11)}
  
  SPIRAL 
     { {.787879 -.424242 .242424 .859848 1.758647 1.408065 }
     { -.121212 .257576 .151515 .05303 -6.721654 1.377236 }
     { .181818 -.136364 .090909 .181818 6.086107 1.568035 } }
  
  SPIRAL.P 
     {.895652 .052174 .052174 (-8,-1) (8,11)}
  
  SWIRL5 
     { { .745455 -.459091 .406061 .887121 1.460279 .691072 }
     { -.424242 -.065152 -.175758 -.218182 3.809567 6.741476 }}
  
  SWIRL5.P 
     { .912675 .087325 (-8,-1) (8,11) }
  
  TREE 
     { { 0 0 0 .5 0 0 } 
     { .42 -.42 .42 .42 0 .2 } 
     { .42 .42 -.42 .42 0 .2 }
     { .1 0 0 .1 0 .2 } }
  
  TREE.P
     { .05 .4 .4 .15 (0,1) (0,1) }
  
  TRIANGLE 
     { { .5 0 0 .5 0 0 } 
     { .5 0 0 .5 0 1 } 
     { .5 0 0 .5 1 1 } }
  
  TRIANGLE.P  
     {.3333333333 .333333333 .3333333333 (-1,47,1.21) (2.49,1.77) }
  
  ZIGZIG2 
     { { -.632407 -.614815 -.54537 .659259 3.840822 1.282321 }
     { -.036111 .444444 .210185 .037037 2.071081 8.330552 } }
  
  ZIGZIG2.P 
     { .888128 .111872 (-8,-1) (8,11) }
  
  MANDEL
      PICT PURGE
     (-3,-1.2) (1,1.23) PDIM { # 0h # 0h } PVIEW 1 CF 
     0 .96 FOR y
           y 1.0655 - .5464 / .6 FOR x 
               x y R C DUP ABS 4 * 1 + SQ + 2 / (0,0)
               1 15  FOR n
                    IF DUP ABS 3 PICK >  THEN 1 SF 99 'n' STO
                         ELSE SQ 3 PICK + END
               NEXT 
               DROP2
               IF 1 FC?C THEN DUP PIXON CONJ PIXON ELSE DROP
                    END 
          .03053 STEP 
     .03796 STEP 
     { } PVIEW HPFRACT 
  
  JULIA
      "JULIA PARAMETERS"
     { { "ITERATIONS" "ENTER NUMBER OF ITERATIONS" 0 } { "SEED"
          "ENTER INITIAL POINT" 1 } { "PMIN" "" 1 } { "PMAX" "" 1 } } { } {
          400 (.11,.66) (-3.5,-1.25) (3.5,1.25) } DUP  
     IF INFORM NOT THEN CLEAR HPFRACT KILL END 
     OBJ  DROP
     PICT PURGE { # 0h # 0h } PVIEW PMAX PMIN   n c
            1 c 4 * - SQ 1 + DUP
          IF ABS 1   THEN 2 - NEG END 
          2 / 1 n START 
               c - SQ
               IF RAND .5 < THEN NEG END 
               DUP DUP PIXON NEG PIXON
          NEXT 
          DROP { } PVIEW 
     HPFRACT 
  
  ORBIT
  
      "ORBIT PARAMETERS"
     { "ITERATES:" { } "A:" "B:" "X:" "Y:" "PMIN:" "PMAX:" } { 2 0 } { 900      -.48 .935 4.1 0 (-11,-10) (14,7) } DUP
     IF INFORM THEN 
          OBJ  DROP 
          PICT PURGE { # 0h # 0h } PVIEW PMAX PMIN 
          2 5 PICK 2 * - 3 PICK SQ DUP 3 PICK * 7 PICK 6 PICK * +               SWAP 1 + / 0 
            a b x y c w z
           0 SWAP FOR n 
               x
               IF n 10 > THEN DUP y R C PIXON END 
               'z' STO b y * w + DUP 'x' STO 
               a OVER * SWAP SQ DUP c * SWAP 1 + / + DUP 'w' STO
               z - 'y' STO
          NEXT 
          { } PVIEW
     END 
     HPFRACT 
  
  TREEE
      CLLCD
     { 2 2.2 24 26 12 6 }
     WHILE
          "FRACTAL TREE" 
          { {"LEFT à:" "ENTER LEFT à" 0 } { "RIGHT à:" "ENTER RIGHT
               à" 0 } { "LEFT  :" "ENTER LEFT  " 0 } { "RIGHT  :"               "ENTER RIGHT  " 0 } { "HEIGHT:" "ENTER TRUNK                HEIGHT" 0 } { "LEVELS:" "ENTER RECURSION               LEVELS" 0 } } 
          { 2 2 } 4 ROLL DUP INFORM
     REPEAT 
          DUP OBJ  DROP
           
                 65 ROT + R B 
               32 ROT - R B 
               2  LIST ROT 
               65 + R B 
               32 4 ROLL - R B 
               2  LIST LINE 
                   x1 y1 x2 y2
                      IF 'x2-x1==0' 
                    THEN
                         IF 'y2>y1'
                             THEN 90
                         ELSE 270
                             END
                         ELSE y2 y1 - x2 x1 - / ATAN 57.2957795131 *
                         END
                         IF 'x1>x2'
                    THEN 180 +
                         END 
                
                 0 0   x y height angle level x1 y1 
                      x 'turtx' STO 
                    y 'turty' STO 
                    height 'turtr' STO
                    'turtx' turtt 1.74532925199E-2 * COS turtr *                       STO+
                    'turty' turtt 1.74532925199E-2 * SIN turtr * STO+
                    turtx 'x1' STO
                    turty 'y1' STO
                    'level' 1 STO- 
                    x y x1 y1 Dline EVAL
                        IF 'level > 0' 
                    THEN 
                         x y x1 y1 Point EVAL 
                         'turtt' STO 
                         'turtt' lfang STO+ 
                         turtx turty lhf height * lfang level                         Generate EVAL 
                         x y x1 y1 Point EVAL
                         'turtt' STO
                         'turtt' rtang NEG STO+ 
                         x1 y1 lhf height * rtang level Generate                       EVAL
                         END 
                 
               0 0 0 0 0 0 0 -30 0 0 RCLF 
                 lfalp rtalp lfang rtang height level Dline Point                  Generate turtt turtr turtx turty lhf rhf x y x1                     y1 flags
                 -3 SF RAD
               # 83h # 40h BLANK PICT STO CLLCD { # 0h # 0h }              PVIEW 
               'lhf=2^(-2/(3*lfalp))' DEFINE 
               'rhf=2^(-2/(3*rtalp))' DEFINE 
               x y x1 y height + Dline EVAL 
               x y x1 y height + Point EVAL 
               'turtt' STO
               'turtt' lfang STO+ 
               x1 y height + lhf height * lfang level Generate EVAL
               x y x1 y height + Point EVAL
               'turtt' STO
               'turtt' rtang NEG STO+ 
               x1 y height + rhf height * rtang level Generate EVAL
               { } PVIEW flags STOF 
            EVAL
     END HPFRACT 
  
  END