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Author Topic: Quick test question  (Read 2238 times)
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David Makin
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« on: January 15, 2011, 12:32:44 PM »

Here is a test question:

If you draw a straight line across the Mandelbrot Set such that the line intersects the true "inside" of the Set and not just the boundary, then how many Mandelbrot Set boundary points lie on the line ?

I will unlock the topic when I think enough folks have considered the possible answer wink
(Please do not give the answer in other threads)
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David Makin
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« Reply #1 on: January 16, 2011, 02:22:12 PM »

Was hoping for a lot more than 32 readers before I unlock this, especially those less familiar with fractals and the Mandelbrot Set - please see first post in thread.....
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David Makin
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« Reply #2 on: February 01, 2011, 12:42:42 AM »

Anyone think they know the answer ?
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Sockratease
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« Reply #3 on: February 01, 2011, 12:49:44 AM »

I have a totally Uneducated Guess!

Either 2, or an Infinite Number.

2 if you count the entry and exit points along the border, but Infinite if you want my original first thought which I could not back up logically in any way...
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kek
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« Reply #4 on: February 01, 2011, 01:31:07 AM »

I don't really understand your question. Is the only possibillity for this like line B or every line like line A as well



But actually I think there will be infinite cause of all the tiny cardioids on the outside regions of the Mandelbrot-set.


next question is of course how infinite is this?
« Last Edit: February 01, 2011, 01:35:29 AM by kek » Logged
marius
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« Reply #5 on: February 01, 2011, 02:44:59 AM »

Here is a test question:

If you draw a straight line across the Mandelbrot Set such that the line intersects the true "inside" of the Set and not just the boundary, then how many Mandelbrot Set boundary points lie on the line ?

I will unlock the topic when I think enough folks have considered the possible answer wink
(Please do not give the answer in other threads)

0 since there are no 'boundary' points
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David Makin
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« Reply #6 on: February 01, 2011, 04:34:11 AM »

The answer is infinity simply because (in the infinite limit) the dimension of the boundary is 2 (everywhere).

Please note that by "boundary" points I mean those points that are "inside" but adjacent to the "outside" to infinite resolution - the classic exampe being (-2,0).

As to the lines A and B, both would qualify - in fact any straight line drawn through the whole Set at any angle (from "outside" through "inside" back to "outside") would produce the same result.
The x (real) axis of course has an infinite number of boundary points in the spike.

Note that if a curved line were allowed then even restricting it such that it must start "outside" pass through to "inside" and back to "outside" the answer would be any number of points from 2 to infinity (assuming it isn't allowed to cross or touch itself).
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