kay@warwick.UUCP (Kay Dekker) (11/04/85)
I've been writing a 'browser' to examine the Mandelbrot set for interesting
areas. It works fine, except for one thing which I haven't been able to
fathom.
The browser decides that a point lies within the set if its magnitude after
a maximum number of iterations is < 2.0.
I've seen browsers posted recently in net.sources, and examined them to see
if they address my difficulty, but no luck.
How should one choose the maximum number of iterations for any particular
region of the complex plane? Sure, one can always pick a value that's
"big enough" for any particular view ("big enough" meaning, intuitively,
that not too many pixels are marked as lying within the set when in fact
they aren't), but having such a large value makes the browser far too slow
when that many iterations aren't needed.
Is there a method for finding adequate values for the maximum? Or must
I continue to rely on trial and error?
Any help or pointers to information gratefully received.
Kay.
--
"Be careful: the system is complex and chaotic, though it
has many attractive features..."
_The Pot-holes of the Yorkshire Moors_
... mcvax!ukc!warwick!flame!kaycsdf@mit-vax.UUCP (Charles Forsythe) (11/10/85)
In article <2346@flame.warwick.UUCP> kay@flame.UUCP (Kay Dekker) writes: >How should one choose the maximum number of iterations for any particular >region of the complex plane? Sure, one can always pick a value that's >"big enough" for any particular view ("big enough" meaning, intuitively, >that not too many pixels are marked as lying within the set when in fact >they aren't), but having such a large value makes the browser far too slow >when that many iterations aren't needed. The "browsers" that I've seen choose a maximum number of 1000, and I think it's arbitrary. The programs also check, on each iteration, whether or not |z|>2. It seems to me, you could increase the maximum iterations to any number. That way, you could intelligently evaluate points that require more than 1000 iterations, while also including those that require less. The only problem is that you increase your wait -- I think that 1000 was picked because they figured that was "long enough." -- -Charles
hutch@sdcsvax.UUCP (Jim Hutchison) (11/11/85)
In article <2346@flame.warwick.UUCP> kay@flame.UUCP (Kay Dekker) writes: > >The browser decides that a point lies within the set if its magnitude after >a maximum number of iterations is < 2.0. > Is this the set relating to the inverse function f(z) = z^2 + c? I guess that is what you are up to (Really, there is much more). You get to iterate the function. It is infact very time consuming. If you wish to just get outlines, then it is cheaper (use error analysis, see also Bresenham, who is never sufficiently blessed). The reason for the choice of 2.0 is that for this given function, if it passes the value of 2.0, then it is going to go to infinity (which is what you are really checking for). The "Mandelbrot Space", (not my term, just as a touchstone), is the area where the function never goes to infinity. The pretty colors ('stones'), are chosen by the speed at which practical infinity is reached. 2.0 = infinity, for proper values of 2.0 :-) >"Be careful: the system is complex and chaotic, though it > has many attractive features..." > _The Pot-holes of the Yorkshire Moors_ Fractals? -- /* Jim Hutchison UUCP: {dcdwest,ucbvax}!sdcsvax!hutch ARPA: hutch@sdcsvax [ Of course, these statements were typed into my terminal while I was away. ] */