def muk_plot(m0,k):
"""
Return a plot of the binomial fractal measure mu_k
associated to m0, 1-m0, and k.
"""
k = int(k)
m0 = float(m0)
m1 = float(1 - m0)
assert m0 > 0 and m1 > 0, "both must be positive"
v = [(0,0)]
t = 0
two = int(2)
delta = float(1/2^k)
multiplier = float(2^k)
for i in [0..2^k-1]:
t = i * delta
phi1 = i.str(two).count("1")
phi0 = k - phi1
y = m0^(phi0)*m1^(phi1)*multiplier
v.append((t,y))
v.append((t+delta,y))
return v
html("<h1>Mandelbrot's Fractal Binomial Measure</h1>")
@interact
def _(mu0=slider(0.0001,0.999,default=0.3), k=slider([1..14],default=3), thickness=slider([0.1,0.2,..,1.0],default=1.0)):
v = muk_plot(mu0,k)
line(v,thickness=thickness).show(xmin=0, xmax=1, ymin=0, figsize=[8,3])
