! generate simple random fractals recursively
! this one is based on equilateral triangles
! Program to accompany "Problems in Computational Physics" by N. Giordano
! Copyright Prentice Hall 1997
program generate
   option nolet
   randomize
   call init
   input prompt "number of recursive levels -> ": level
   open #1: name "random_fractal."&str$(level), organization text, create new
   x_start = 0         ! initialize some variables then call show()
   y_start = 0
   x_end = 300
   y_end = 0
   print #1: x_start,",",y_start
   call show(x_start,y_start,x_end,y_end,level,#1)
   close #1
end
sub show(xi,yi,xf,yf,level,#1)     ! recursive routine for drawing a random fractal
    if level <= 1 then             ! have hit bottom - just draw a line
       plot lines: xi,yi;xf,yf
       print #1: xf,",",yf         ! and save coordinates to a file
    else
       dx = (xf - xi) / 3          ! divide the interval into three parts
       dy = (yf - yi) / 3
       ctheta = 2 * (rnd - 0.5)    ! pick a random angle - get its cosine and sine
       stheta = sqr(1 - ctheta^2)
                                   ! next choose new points based on underlying
                                   ! "structure" of an equilateral triangle
       call show(xi,yi,xi+dx,yi+dy,level-1,#1)  
       call show(xi+dx,yi+dy,xi+1.5*dx-stheta*dy,yi+1.5*dy+ctheta*dx,level-1,#1)
       call show(xi+1.5*dx-stheta*dy,yi+1.5*dy+ctheta*dx,xi+2*dx,yi+2*dy,level-1,#1)
       call show(xi+2*dx,yi+2*dy,xf,yf,level-1,#1)
    end if
end sub
sub init    ! set up window for plotting
   set window 0,300,-100,200
   clear
end sub