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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