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Welcome to Fractal Forums > Real World Examples & Fractical Applications > Fractals Applied or in Nature > Philosophy > Are the Mandelbrot Cardoids in fact loose form each other?
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Author Topic: Are the Mandelbrot Cardoids in fact loose form each other?  (Read 1495 times)
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kek
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« on: February 21, 2011, 03:21:17 PM »

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?
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lkmitch
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« Reply #1 on: February 21, 2011, 05:21:49 PM »
I believe that they are tangent to each other and only touch at the infinity iteration.
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kek
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« Reply #2 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?
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David Makin
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« Reply #3 on: February 21, 2011, 11:01:28 PM »
Quote from: 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?

I don't think you could "globally" prove it, but anything's possible wink
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.
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