3 ms·

It means you can choose two points inside the Mandelbrot set and always find a curve that connects the two without you ever needing to lift the pencil.

• hermitcrab 3y ago
  Isn't that "connected" rather than "locally connected"?
  • crazygringo 3y ago
    I'm aware that "locally connected" has a very specific meaning in math: https://en.wikipedia.org/wiki/Locally_connected_space https://en.wikipedia.org/wiki/Locally_connected_space Unfortunately I don't have the slightest idea what it actually means... that article does not have any ELI5 sentence within it.
    • hermitcrab 3y ago
      >Unfortunately I don't have the slightest idea what it actually means Not just me then? ;0)
      • G3rn0ti 3y ago
        There are some in hints in TFA: "MLC posits that the Mandelbrot set isn’t just connected; it’s locally connected — no matter how much you zoom in on the Mandelbrot set, it will always look like one connected piece. For instance, a circle is locally connected. An extremely fine-toothed comb, on the other hand, is not. Though the entire shape is connected, if you skip over the shaft and instead zoom in on the tips of some of its teeth, you’ll just see a bunch of separate line segments."