The MLC (for Mandelbrot locally connected) conjecture in the article states that all points in the Mandelbrot Set are continuously connected to one another. I have another conjecture of my own: There are no closed loops in**(the "filaments" of)**the Mandelbrot Set, i.e, there are no "/white/ islands", but I am unable to formulate this exactly in formal mathematical terms. A white island would be an area of space not in the Mandelbrot Set, but completely surrounded by a portion of the Mandelbrot Set. My conjecture says that such white islands do not exist. How do you even define a "visible filament", when it becomes something else entirely (and much more complicated) upon zooming into it? (Mostly, it is simply an infinitely long segment of the Mandelbrot Set between any two points of the set, however, picking the two end points of a visible segment is also difficult, as zooming into such a point also becomes a frilly design, unless, e.g., it is on the finite straight line west of the Mandelbrot Set.) Lee Skinner On 1/26/2024 11:25 AM, David W. Jones wrote:
The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal
https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-...
--- David W. Jones gnome@hawaii.rr.com exploring the landscape of god http://dancingtreefrog.com
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