ascii art mandelbrot drawing program in BASIC

mandel.bas

10 x1=59
11 y1=21
20 i1=-1.0
21 i2=1.0
22 r1=-2.0
23 r2=1.0
30 s1=(r2-r1)/x1
31 s2=(i2-i1)/y1
40 for y=0  to y1
50 i3=i1+s2*y
60 for x=0 to x1
70 r3=r1+s1*x
71 z1=r3
72 z2=i3
80 for n=0 to 29
90 a=z1*z1
91 b=z2*z2
100 if a+b>4.0 goto 130
110 z2=2*z1*z2+i3
111 z1=a-b+r3
120 next n
130 print chr$(62-n);
140 next x
150 print
160 next y
170 end

If you want that cool "decoding the matrix" look, this version cycles through each hex character as it prints. It's way slower, but you can use that time to admire the cool effect.

10 FOR Y=-12 TO 12
20 FOR X=-19 TO 19
30 CA=X*0.0458
40 CB= Y*0.08333
50 A=CA
60 B=CB
70 FOR I=0 TO 15
75 GOSUB 1000
80 T=A*A-B*B+CA
90 B=2*A*B+CB
100 A=T
110 IF (A*A+B*B)>4 THEN GOTO 210
115 PRINT CHR$(8);
120 NEXT I
130 PRINT " ";
140 GOTO 210
210 NEXT X
220 PRINT
230 NEXT Y
900 END
1000 REM print a single hex digit stored in I
1010 IF I>9 THEN J=I+7
1020 IF I<=9 THEN J=I
1030 PRINT CHR$(48+J);
1040 RETURN

A very naive re-implementation of the original version from BASIC into FORTH is:

variable x1
variable y1

variable i1
variable i2
variable i3

variable r1
variable r2
variable r3

variable s1
variable s2

variable z1
variable z2

variable a
variable b

variable n

59 x1 !
21 y1 !
-1e0 i1 f!
1e0 i2 f!
-2e0 r1 f!
1e0 r2 f!
r2 f@ r1 f@ f- x1 @ s>f f/ s1 f! \ L30
i2 f@ i1 f@ f- y1 @ s>f f/ s2 f! \ L31

: mandel
y1 @ 0 do                         \ L40
  i1 f@ s2 f@ i s>f f* f+ i3 f!   \ L50
  x1 @ 0 do                       \ L60
    r1 f@ s1 f@ i s>f f* f+ r3 f! \ L70
    r3 f@ z1 f!                   \ L71
    i3 f@ z2 f!                   \ L72
    0 n !
    30 0 do              \ L80
      z1 f@ fdup f* a f! \ L90
      z2 f@ fdup f* b f! \ L91
      a f@ b f@ f+ 4e0 f> if leave then  \ line 100
      2e0 z1 f@ z2 f@ f* f* i3 f@ f+ z2 f! \ L110
      a f@ b f@ f- r3 f@ f+ z1 f! \ L111
      n @ 1 + n !
    loop \ L120
    62 n @ - emit \ L130
  loop \ L140
  cr \ L150
loop \ L160
;

mandel

bye

Note that I had to use 30 instead of 29 in "line 80" aka 30 0 do to produce the proper output.

>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<==========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======

Here's another gist for the refactor of this into something that's more idiomatic FORTH. I'm interested to find a FORTH for my Z80 retrocomputer to compare speed!