Drawing the Koch fractal using Julia and Compose.

koch.jl

using Compose

function koch_side(n)
    if n == 1
        return compose(context(),
        line([(0,1),(1/3,1),(1/2, 1 - (sin(pi/3)/3)),(2/3,1),(1,1)]))
  else
      ks = koch_side(n - 1)
      return compose(context(),
                       (context(0,2/3,1/3,1/3), ks),
                       (context(1/3,2/3,1/3,1/3, rotation=Rotation(-pi/3,(0,1))), ks),
                       (context(1/3,2/3,1/3,1/3, rotation=Rotation(pi/3, (1,1))), ks),
                       (context(2/3,2/3,1/3,1/3), ks))
    end
end

function koch(n)
    if n == 0
        return compose(context(), polygon([(1/2, 1-sin(pi/3)), (0,1), (1,1)]))
    else
        side = koch_side(n)
        fside = compose(context(rotation=Rotation(pi)),side)

        c = (sin(pi/3)/3) + 1/3

        return compose(context(),
        (context(1/3,0,1/3,1/3), side),
        (context(1/6,c,1/3,1/3, rotation=Rotation(pi/3,(1,0))), fside),
        (context(1/2,c,1/3,1/3, rotation=Rotation(-pi/3,(0,0))), fside))
    end
end

draw(SVG("koch.svg", 5inch, 5inch),
    compose(koch(7), stroke("black"), fill(nothing), linewidth(0.1mm)))