Talk:Fractals/Iterations in the complex plane/Mandelbrot set interior

Help is welcome --Adam majewski (talk) 07:38, 30 July 2008 (UTC)

dem/m
I ahve put it here to remember about it --Adam majewski (discuss • contribs) 15:47, 25 October 2011 (UTC)

"The Beauty of Fractals gives an almost correct computer program for the distance estimation shown in the right image. A possible reason that that method did not gain ground is that the procedure in this program is seriously flawed: The calculation of zk is performed (and completed) before the calculation of z'k, and not after as it ought to be (z'k + 1 uses zk, not zk + 1). For the successive calculation of z'k, we must know f'(zk) (which in this case is 2zk). In order to avoid the calculation of zk (k = 0, 1, 2, ...) again, this sequence is saved in an array. Using this array, z'k + 1 = 2zkz'k + 1 is calculated up to the last iteration number, and it is stated that overflow can occur. If overflow occurs the point is regarded as belonging to the boundary (the bail-out condition). If overflow does not occur, the calculation of the distance can be performed. Apart from it being untrue that overflow can occur, the method makes use of an unnecessary storing and repetition of the iteration, making it unnecessarily slower and less attractive. The following remark in the book is nor inviting either: "It turns out that the images depend very sensitively on the various choices" (bail-out radius, maximum iteration number, overflow, thickness of the boundary and blow-up factor). Is it this nonsense that has got people to lose all desire for using and generalizing the method?" (Gertbuschmann)