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