1240.sagews

Logistic function and limit cycle gives a nice fractal ...

var('x malthus')
step(x,malthus) = malthus * x * (1-x)
stepfast = fast_callable(step, vars=[x, malthus], domain=RDF)

def logistic(m, step):
    # filter cycles
    v = .5
    for i in range(100):
        v = stepfast(v,m)
    points = []
    for i in range(100):
        v = stepfast(v,m)
        points.append((m+step*random(),v))
    return points

points=[]
step = 0.005
for m in sxrange(2.5,4,step):
    points += logistic(m, step)
point(points,pointsize=1).show(dpi=150)