[Edu-sig] another "must have" generator

[Gregor Lingl]

kirby urner schrieb:
> This is just to get junior experimenting with convergence / divergence
> on the complex plane.  c is our variable.
>
> Per this Wikipedia article (fine to project in class, why not, though
> "teacher reading from encyclopedia" shouldn't come off as mechanical):
>
> See: http://en.wikipedia.org/wiki/Mandelbrot_set
> Also: http://www.4dsolutions.net/ocn/fractals.html
>
> IDLE 3.0a2
>   
>>>> def mandelbrot(c):
>>>>         
> 	z = 0 + c
> 	while True:
> 		yield z
> 		z = z ** 2 + c
>
> 		
>   
May I again add an interesting thing,
this time another indispensable generator,
more exactly: three of them:

def feigenbaum1(c,x):
    while True:
        yield x
        x = c*x*(1-x)


def feigenbaum2(c,x):
    while True:
        yield x
        x = c*x-c*x*x


def feigenbaum3(c,x):
    while True:
        yield x
        x = c*(x-x**2)

       
along with this testing/experimenting function:

def feigenbaumtest(feigenbaum, iterations=80):
    f = feigenbaum(3.93, 0.5)
    for i in range(iterations):
        res = next(f)
    return res

 >>> feigenbaumtest(feigenbaum1, 4)
0.24761176565334103
 >>> feigenbaumtest(feigenbaum2, 4)
0.24761176565334098
 >>> feigenbaumtest(feigenbaum3, 4)
0.24761176565334167
 >>> feigenbaumtest(feigenbaum1, 40)
0.43518828176766455
 >>> feigenbaumtest(feigenbaum2, 40)
0.43518808407096854
 >>> feigenbaumtest(feigenbaum3, 40)
0.43518950764209768
 >>> feigenbaumtest(feigenbaum1)
0.70329204370098442
 >>> feigenbaumtest(feigenbaum2)
0.8147039925205275
 >>> feigenbaumtest(feigenbaum3)
0.66573747868397481
 >>>

Certainly something which demonstrates a (by many)
unexpected relation between maths and computer science.

Regards,
Gregor