size 8 8

! Based on "C" code by Lode Vandevenne
! http://www.student.kuleuven.ac.be/~m0216922/CG/

set cap round

maxRecursions = 8  ! never make this too big or it'll take forever
angle = 0.2 * pi   ! angle in radians
shrink = 1.8       ! relative size of new branches

! Now follows the recursion function, a function that only draws a single line and calls
! itself a few times, but results in a huge tree!

sub recursion posX posY dirX dirY bsize n

! Here's the part that draws the line. The line is drawn from (posX, posY) to (posX+dirX, 
! posY+dirY). So the position and direction of the line is given as a vector, instead of 
! a begin point, an angle and a size, because direction vectors are much easier to work 
! with. The size parameter itself isn't used to draw the line directly, it's only needed 
! later to calculate the direction vector of the next branches. If the maximum number of 
! recursions is reached, the function returns immediately after drawing the line, without 
! calling itself again.

    local posX2 = posX + bsize * dirX
    local posY2 = posY + bsize * dirY

    if n > 5 then
        set color forestgreen
    else
        set color rgb255(128, 96, 64)
    end if
    set lwidth 0.2/(n+1)+0.005
    amove posX pageheight()-posY
    aline posX2 pageheight()-posY2

    if n < maxRecursions then

! And in the second part of the function, the new position of the new branches is
! calculated as the endpoint of the previous branch, and the new direction vector for
! the new branches is calculated out of the size and current direction of the current
! branch. The new branches are rotated with the angle, the sine and cosine formulas are
! actually the calculation of the rotation matrix. Then the recursion function is called
! again with the new branch as its parameters. This is done twice: once for a branch
! rotated to the right, and then for a branch rotated to the left.

       dirX2 = cos(angle) * dirX + sin(angle) * dirY
       dirY2 = -sin(angle) * dirX + cos(angle) * dirY
       recursion posX2 posY2 dirX2 dirY2 bsize/shrink n+1

       dirX2 = cos(-angle) * dirX + sin(-angle) * dirY
       dirY2 = -sin(-angle) * dirX + cos(-angle) * dirY
       recursion posX2 posY2 dirX2 dirY2 bsize/shrink n+1
   end if
end sub

! The main program doesn't do much more than calling the recursive function.
! The value "h/2.3" in the parameters of the recursion function is the initial 
! length of the first branch (the stem). The coordinates are the begin
! point and direction vector of the first branch.

w = pagewidth()
h = pageheight()

recursion w/2 h-0.1 0 -1 h/2.3 0