( --- Complex arithmetic --- )
( Location of floating point. )
-: precision 10000 ;
+10000 value precision
: sign dup abs / ;
: csq 2dup c* ;
+
+: conj ( x y -- x -y )
+ negate
+;
+
: cmagsq ( x1 y1 -- mag )
- csq abs
+ 2dup conj c* +
;
( --- Mandelbrot set calculations --- )
: iterate ( cr ci zr zi -- cr ci z'r z'i )
- csq c+
+ 2over 2swap csq c+
;
-: inSet? ( cr ci -- res )
- DEBUGON
+100 value maxiter
+: inSet? ( cr ci -- res )
0 0 ( z_0 = 0 )
true ( flag indicating set membership )
- 100 0 do
+ maxiter 0 do
drop
iterate
2dup cmagsq
- 4 >scaled > if
+ 4 0 >scaled > if
false ( not in set )
leave
then
-rot 2drop -rot 2drop
;
-: xsteps 100 ;
-: ysteps 50 ;
+100 value xsteps
+30 value ysteps
( Draw the Mandelbrot Set!)
-: mandel ( x1 y1 x2 y2 -- )
-
- 1 pick 4 pick -
- 2 pick 5 pick do
- i 0 inSet? if
- 42 emit
- else
- '.' emit
- then
+: mandeldraw ( x1 y1 x2 y2 -- )
+
+ cr
+
+ 0 pick 3 pick - ysteps /
+ 1 pick 4 pick do
+
+ 2 pick 5 pick - xsteps /
+ 3 pick 6 pick do
+
+ i j inSet? if
+ 42 emit
+ else
+ space
+ then
+
+ dup +loop
+ drop
+
+ cr
+
dup +loop
+ drop
;
( Clean up - hide non-standard multiplication def. )
hide *
+
+( Default picture )
+: mandel
+ -2 0 >scaled -1 0 >scaled 0 5 >scaled 1 0 >scaled
+ mandeldraw
+;
+
+CR .( Enter 'mandel' to draw the Mandelbrot Set.)