! Example of Mandelbrot set.
! Author: Francois Tonneau

size 18 16

! ------------------------------
! Set plot resolution.
! ------------------------------

resolution = 1250           ! Use a value < 1000 if plotting takes too long!

itermax = 30
worth = 4

! ------------------------------
! Cover background with default hue.
! ------------------------------

! We overflow borders by 2 cm to cover possible white margins.
amove -1 -1
box pagewidth()+2 pageheight()+2 fill rgb255(38, 44, 64)

! ------------------------------
! Define plot parameters.
! ------------------------------

xmax = pagewidth()
ymax = pageheight()

dx = xmax/resolution
dy = ymax/resolution

ulow  = -2.20
uhigh =  0.80

vlow  = -1.45
vhigh =  1.45

uspan = uhigh - ulow
vspan = vhigh - vlow

declare sub spot u0 v0
declare sub color iter
declare sub paint hue$

! ------------------------------
! Cover the plot surface.
! ------------------------------

print "This may take a while..."

for x = 0 to xmax step dx
    for y = 0 to ymax step dy
        amove x y
        u0 = (x/xmax * uspan) + ulow
        v0 = (y/ymax * vspan) + vlow
        spot(u0, v0)
    next y
next x

print "Preparing output..."

! ------------------------------
! Implement coloring utilities.
! ------------------------------

sub spot u0 v0
    local u = 0.0
    local v = 0.0
    local iter = 0
    local utemp
    while ((u*u + v*v <= 4) and (iter < itermax))
        utemp = u*u - v*v + u0
        v = 2*u*v + v0
        u = utemp
        iter = iter + 1
    next
    if iter = itermax then
        paint black
    else
        ! To speed up the code, do nothing when iter < worth, leaving the
        ! default background show through.
        if iter >= worth then paint color(iter)
    end if
end sub

sub color iter
    local t = (iter - worth)/(itermax - worth)
    !
    local r0 = 45
    local g0 = 52
    local b0 = 72
    !
    local r1 = 190
    local g1 = 65
    local b1 = 50
    !
    local r2 = 220
    local g2 = 220
    local b2 = 180
    !
    local r, g, b
    if t <= 0.50 then
        r = (1 - t) * r0 + t * r1
        g = (1 - t) * g0 + t * g1
        b = (1 - t) * b0 + t * b1
    else
        r = r2
        g = g2
        b = b2
    end if
    return rgb255(r, g, b)
end sub

sub paint hue$
    set color hue$
    box dx dy fill hue$
end sub