Mandelbrot

rem Zoomable Mandelbrot based in Joel Kahn's example
sz=600
font "arial",10,100
graphsize sz,sz
fastgraphics
kt=50:m=4.0
xmin=-2.1:xmax=.6:ymin=-1.5:ymax=1.5
gosub draw
input "press enter to zoom in",a$
xmin=-0.5:xmax=0:ymin=0.5:ymax=1
gosub draw
input "press enter to zoom in",a$
xmin=-0.15:xmax=-.05:ymin=0.9:ymax=1
gosub draw
input "press enter to zoom in ",a$
xmin=-0.14:xmax=-.13:ymin=0.98:ymax=.99
gosub draw
end
 
draw:
clg
refresh
dx=(xmax-xmin)/sz:dy=(ymax-ymin)/sz
for x=xmin to xmax step dx
for y=ymin to ymax step dy
k=0:a=0:b=0
do
# In the iteration z=z^2+c
#z=ai + b
#c=yi + x
tx=a^2-b^2+x
b=2*b*a+y
a=tx
d=a^2+b^2
k=k+1
until not (d <= m and k < kt)
color k*50000000
plot (x-xmin)/dx,(ymax-y)/dy
next y
refresh
next x
# grid
color black
for n= 0 to 9
line n*sz/10,sz,n*sz/10,0
text n*sz/10,5,xmin+(xmax-xmin)*n/10
text 5,n*sz/10,ymax-(ymax-ymin)*n/10
line sz,n*sz/10,0,n*sz/10
next n
refresh
return