! MANDELBROT PROGRAM: Shows a "rough draft" of the M-set in blue.

! Then allows to click to select a c value and shows the orbit of the z=0 point for 20 iterations.

! It also prints the Xn, Yn values, and it indicates if the point c chosen is in the prisoner or escape (OUT!!!) sets.

!ITERATE in the complex plane : Zn+1 = Zn^2 + C,

!where Zn = Xn + i*Yn and is a complex variable, and

!Xn+1 = (Xn*Xn - Yn*Yn) + Creal,

!Yn+1 = 2*Xn*Yn + Cimag,

SET MODE "graphics"

ASK PIXELS hpix,vpix

LET ratio=hpix/vpix

SET WINDOW -2*ratio,2*ratio,-2,2

SET COLOR "GREEN"

BOX CIRCLE -2,2,-2,2

PLOT -2,0;2,0

PLOT 0,-2;0,2

SET COLOR "BLUE"

FOR j=-100 to 100

FOR k = -100 to 100

LET x = 0

LET y = 0

FOR n=1 to 20

LET x1 = x*x - y*y + j/50

LET y1 = 2*x*y + k/50

LET r2 = x1*x1 + y1*y1

IF r2>4 THEN EXIT FOR

LET x = x1

LET y = y1

NEXT n

IF n=21 THEN PLOT j/50,k/50

NEXT k

NEXT j

BOX KEEP -2,2,-2,2 IN MAND$

DO

CLEAR

SET COLOR "BLACK"

BOX SHOW MAND$ AT -2,-2

PRINT "CLICK TO SELECT A VALUE FOR c"

PRINT

GET POINT cr,ci

LET x=0

LET y=0

PLOT 0,0;cr,ci

PRINT "cr=";cr,"ci=";ci

PRINT

PRINT " x"," y"

PRINT 0,0

PRINT cr,ci

BOX DISK cr-.02,cr+.02,ci-.02,ci+.02

FOR n=1 to 30

LET x1 = x*x - y*y + cr

LET y1 = 2*x*y + ci

LET r2 = x1*x1 + y1*y1

IF r2>16 THEN EXIT FOR

LET x = x1

LET y = y1

PLOT x,y;

PRINT x,y

PAUSE.2

NEXT n

IF n<30 THEN

SET COLOR "RED"

BOX DISK cr-.02,cr+.02,ci-.02,ci+.02

PLOT TEXT, AT cr,ci:" OUT!!!"

END IF

PLOT

DO

GET MOUSE x,y,s

LOOP UNTIL s=2

LOOP

END