tileable-fractals.sage

# Base 3-w where w is a 6-th root of unity
w = N(exp(I*pi/3))
def dragonpoints(depth):
    if depth <= 0:
        return [(1+w)/3]
    else:
        parta = [z+1 for z in dragonpoints(depth-1)]
        partb = [z/w+w for z in dragonpoints(depth-1)]
        partc = [z+w for z in dragonpoints(depth-1)]
        return [z/(3-w) for z in parta+partb+partc]
def dragoncurve(depth, scale=1, translate=0):
    l0 = dragonpoints(depth)
    l = [z*scale+translate for z in l0] + [z*w*scale+translate for z in l0] + [z*w^2*scale+translate for z in l0] + [z*w^3*scale+translate for z in l0] + [z*w^4*scale+translate for z in l0] + [z*w^5*scale+translate for z in l0]
    return [(z.real(), z.imag()) for z in l]
(sum([polygon(dragoncurve(8,translate=t),color=c) for (t,c) in [(0,Color(0.8,0.8,0.8)), (1,Color(0.8,0.2,0.2)), (w,Color(0.8,0.8,0.2)), (w^2,Color(0.2,0.8,0.2)), (w^3,Color(0.2,0.8,0.8)), (w^4,Color(0.2,0.2,0.8)), (w^5,Color(0.8,0.2,0.8))]]) + sum([polygon(dragoncurve(7,scale=1/(3-w),translate=t),color=c) for (t,c) in [(0,Color(0.9,0.9,0.9)), (1,Color(0.9,0.4,0.4)), (w,Color(0.9,0.9,0.4)), (w^2,Color(0.4,0.9,0.4)), (w^3,Color(0.4,0.9,0.9)), (w^4,Color(0.4,0.4,0.9)), (w^5,Color(0.9,0.4,0.9))]])).show(dpi=192,aspect_ratio=1)

# Base 2-i where i is a 4-th root of unity
i = N(I)
def dragonpoints(depth):
    if depth <= 0:
        return [(1+i)/2]
    else:
        parta = [z+1 for z in dragonpoints(depth-1)]
        partb = [z/i+i for z in dragonpoints(depth-1)]
        partc = [z+i for z in dragonpoints(depth-1)]
        return [z/(2-i) for z in parta+partb+partc]
def dragoncurve(depth, scale=1, translate=0):
    l0 = dragonpoints(depth)
    l = [z*scale+translate for z in l0] + [z*i*scale+translate for z in l0] + [z*i^2*scale+translate for z in l0] + [z*i^3*scale+translate for z in l0]
    return [(z.real(), z.imag()) for z in l]
(sum([polygon(dragoncurve(8,translate=t),color=c) for (t,c) in [(0,Color(0.8,0.8,0.8)), (1,Color(0.8,0.2,0.2)), (i,Color(0.8,0.8,0.2)), (i^2,Color(0.2,0.8,0.2)), (i^3,Color(0.2,0.2,0.8))]]) + sum([polygon(dragoncurve(7,scale=1/(2-i),translate=t),color=c) for (t,c) in [(0,Color(0.9,0.9,0.9)), (1,Color(0.9,0.4,0.4)), (i,Color(0.9,0.9,0.4)), (i^2,Color(0.4,0.9,0.4)), (i^3,Color(0.4,0.4,0.9))]])).show(dpi=192,aspect_ratio=1)