Talk:Mandelbrot set: Difference between revisions

Content added Content deleted

Inline

Revision as of 21:02, 14 August 2010

Gnuplot

Like the picture! --Paddy3118 10:42, 23 March 2010 (UTC)

Better description

I think we could use a better description here. I'm no mathemetician, but it looks like most of the Mandlebrot images we see (including most of the code attached to this task page) are stackings of the point sets each iteration. (Makes me wish I had a voxel view) Does that sound correct? --Michael Mol 20:19, 14 August 2010 (UTC)

I don't understand your description, but what usually determines the color is the number of iterations until the point leaves the circle of radius 2 (one can prove that if it ever leaves that circle, it ultimately goes to infinity; of course the reverse holds, too).

The simplest way to draw the set (and the only one which would fulfill a strict definition of "drawing the set") would only use two colors: One color for the points in the set (usually, black is used for those points), and another for points outside the set (the natural choice would be white). Of course, what you can draw is only an approximation of the set (because you only do a finite number of iterations; to actually decide if a point is in the Mandelbrot set you'd need an infinite number of iterations, which isn't possible, of course).

However, the algorithm gives you some more information: It not only tells you whether the point ever left the circle, but it also tells you when it left the circle. And since colored pictures look more interesting than black/white ones, usually that information is used to color the image. --Ce 21:02, 14 August 2010 (UTC)

@@ Line 5: / Line 5: @@
 I think we could use a better description here.  I'm no mathemetician, but it looks like most of the Mandlebrot images we see (including most of the code attached to this task page) are stackings of the point sets each iteration. (Makes me wish I had a voxel view) Does that sound correct? --[[User:Short Circuit|Michael Mol]] 20:19, 14 August 2010 (UTC)
+: I don't understand your description, but what usually determines the color is the number of iterations until the point leaves the circle of radius 2 (one can prove that if it ever leaves that circle, it ultimately goes to infinity; of course the reverse holds, too).
+: The simplest way to draw the set (and the only one which would fulfill a strict definition of "drawing the set") would only use two colors: One color for the points in the set (usually, black is used for those points), and another for points outside the set (the natural choice would be white). Of course, what you can draw is only an approximation of the set (because you only do a finite number of iterations; to actually decide if a point is in the Mandelbrot set you'd need an infinite number of iterations, which isn't possible, of course).
+: However, the algorithm gives you some more information: It not only tells you whether the point ever left the circle, but it also tells you <em>when</em> it left the circle. And since colored pictures look more interesting than black/white ones, usually that information is used to color the image. --[[User:Ce|Ce]] 21:02, 14 August 2010 (UTC)