Title: Are the Mandelbrot Cardoids in fact loose form each other? Post by: kek on February 21, 2011, 03:21:17 PM (http://img835.imageshack.us/img835/2203/cardoid00002.jpg)
I was wondering do the curves in the mandelbrot-set ever reach each other? And if they do at wich iteration-point at wich scale? Title: Re: Are the Mandelbrot Cardoids in fact loose form each other? Post by: lkmitch on February 21, 2011, 05:21:49 PM I believe that they are tangent to each other and only touch at the infinity iteration.
Title: Re: Are the Mandelbrot Cardoids in fact loose form each other? Post by: kek on February 21, 2011, 05:33:30 PM Is there any way to prove it? And would they all touch at same infinity of iterations?
Title: Re: Are the Mandelbrot Cardoids in fact loose form each other? Post by: David Makin on February 21, 2011, 11:01:28 PM Is there any way to prove it? And would they all touch at same infinity of iterations? I don't think you could "globally" prove it, but anything's possible ;) and Yes in the sense that for all such points it would take infinite iterations to confirm that they are such a point - of course it would also require infinite mathematical accuracy/resolution. It should also be noted that *all* inside points on the boundary of the full inside i.e. effectively all the true Mandelbrot (boundary) Set are in fact such points, the problem is that some of the bulbs/cardioids they are part (the edge) of are also infinitely small. |