Copyright 2019 jmf
License: WTFPL

This code prints a Mandelbrot set in ASCII art to terminal.

First of all, some variables are declared.
The initial maximum number of iterations is set to 128.

~~~
'x var 
'y var  
'iter var 

#128 'max-iter var-n

#1 'zoom var-n
#0 'posx var-n
#0 'posy var-n
~~~

We are using fixed-point numbers with a scaling factor of 10'000.
That means that the float value 1.0 is represented by the number 10'000.
For that, we need a special multiplication definition.

~~~
:f* * #10000 / ; 
~~~

Now the calculation of the Mandelbrot set value at a specified point is
defined.

~~~
:mb:value (x_y--v) 
  #0  !x 
  #0  !y 
  #-1 !iter 
  [  
    @iter #1 + !iter 
    
    dup-pair  
    #2 @x * @y f* + swap (new_y) 
    @x @x f* @y @y f* - +  (new_x) 
    !x !y 
 
    @x @x f* @y @y f* + #40000 lteq?  
    @iter @max-iter lt? and  
  ] while 
  drop drop @iter 
; 
~~~

In order to display the mandelbrot set nicely, 10 different iteration
levels are filled with their equivalent ASCII signs.

~~~
:ascii-equiv (n--c)
  #9 * @max-iter / 
  #0 [ #32 ] case
  #1 [ $. ] case
  #2 [ $: ] case
  #3 [ $- ] case
  #4 [ $= ] case
  #5 [ $+ ] case
  #6 [ $* ] case
  #7 [ $# ] case
  #8 [ $% ] case
  #9 [ $@ ] case
;
~~~

The user can change some parameters by entering key press sequences.
The following code checks for those key presses...

~~~
:zoom+? dup $+ eq? [ @zoom #2 * !zoom ] if ; 
:zoom-? dup $- eq? [ @zoom #2 / #1 n:max !zoom ] if ; 
:up?    dup $w eq? [ @posy #10000 @zoom / - !posy ] if ; 
:down?  dup $s eq? [ @posy #10000 @zoom / + !posy ]  if ; 
:left?  dup $a eq? [ @posx #10000 @zoom / - !posx ]  if ; 
:right? dup $d eq? [ @posx #10000 @zoom / + !posx ]  if ; 
:resinc? dup $e eq? [ @max-iter #2 * !max-iter ] if ; 
:resdec? dup $q eq? [ @max-iter #2 / #1 n:max !max-iter ]  if ; 
~~~

...and this word bundles all those together.

~~~
:input:handle
  c:get
  zoom+? zoom-?
  up? down?
  left? right?
  resinc? resdec?
  drop
  nl
;
~~~

A quick function draws some information about key bindings and the
current zoom level, as well as the current maximum number of iterations.

~~~
:info:draw
  '+/-_to_zoom;_w/a/s/d_to_move s:put nl 
  'q/e_to_increase_decrease_resolution s:put nl 
  'zoom_level_ s:put @zoom n:put nl 
  'iterations_ s:put @max-iter n:put nl  
;
~~~

Finally the actual drawing code is written. It renders to 25x80
characters. The width of 80 characters is distributed over a set width
of 3.5 (35000) units, the height of 25 characters is distributed over a
set height of 2 units.
This results in a scaling factor of 438 for the width and 800 for the
height.

~~~
:mb:draw 
  #25 [
    #80 [ 
      I #438 * #25000 - @zoom / @posx + 
      J #800 * #10000 - @zoom / @posy + 
      mb:value 
      ascii-equiv c:put 
    ] indexed-times
    nl 
  ] indexed-times  ; 
~~~

Before we start, the terminal is set to character-buffered. This makes
it possible to react to key presses directly, instead of only after
the enter key is pressed.
The last function is a loop that draws the set, some info and gets key-
presses.

~~~
'stty_cbreak unix:system

[ 
  mb:draw 
  info:draw
  input:handle
TRUE ] while 
~~~