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In How the Grinch Stole Christmas, the town of Whoville is situated between a few drooping mountains. Here's an example taken from the movie:

Drooping Mountain: Mt. Crumpit

The tip droops, and the mountains can rise either straight up, or as in this case, at an angle. I find this geographical feature fascinating, and I'd love to have mountains that droop as part of my world.

What geological history would it take to have mountains predominantly be of this type?

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    $\begingroup$ None? Or a highly advanced civilization that engineers it? Or just have them because you want it, but never explain it? Lots of stories have elements that just are. I wouldn't feel obliged to explain everything in a story. Some things are hidden under the surface, some are just unsolved mysteries. $\endgroup$
    – Trioxidane
    Commented Jul 26, 2020 at 17:23
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    $\begingroup$ Not a natural feature, that's for sure. (And even if engineered by a mad geoengineer, they wouldn't last long. Stone is not all that strong in tension.) $\endgroup$
    – AlexP
    Commented Jul 26, 2020 at 18:36
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    $\begingroup$ The only geological thing I can think of is the surroundings became extremely hot sometime after they formed. But that kind of heat would also sterilize the environment so life would have had to form soon after before they could erode away. Maybe you could attribute it to the byproducts of biological activity similar to coral reefs or diatomaceous earth. Perhaps some plants could have roots running along the top side to provide tensile strength as AlexP pointed out. $\endgroup$
    – DKNguyen
    Commented Jul 26, 2020 at 18:43
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    $\begingroup$ scp-wiki.net/the-sideways-mountain $\endgroup$
    – Andrew Brēza
    Commented Jul 26, 2020 at 18:52
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    $\begingroup$ Assuming these are the same or similar Whos as those we see in Horton Hears a Who, it's probably worth noting that their entire world is located within a single speck of dust, and so their "geology" is not quite on the same scale as ours ;) $\endgroup$
    – Steve-O
    Commented Jul 27, 2020 at 15:45

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You cannot make that with stone, for it would crumble away.

You can maybe start with a sloped mountain, ending in a vertical cliff. Then, the slope is colonized by vegetation: a light, but ligneous and largely epiphytic vegetation that creates enormous mats. With the prevailing winds going upslope, over the centuries the whole mountain gets covered with a thick mat tens of meters deep. Strong roots keep the whole mat together.

Then, the mat starts growing over the top. Being much lighter than stone, and much more resistant to traction (you'll need to handwave this a bit, I fear), it does crumble slightly every year, but the growth is enough to compensate.

While ill-advised to stay immediately below the droop, because there's a more or less continuous rain of debris, the area below is inhabitable.

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Hoodoos and hand waving

A Hoodoo is an unusual geological formation formed when a softer rock is protected underneath a layer of harder rock. Here's an example from Wikipedia:

An example of a hoodoo

You could conceivably imagine a gigantic mountain that is gradually eroded over time, leaving just the drooping part that's protected by the layer of tougher rock. It's not likely that a mountain exactly like the movie would exist in nature, but you can wave your hands a little to make it sound plausible.

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    $\begingroup$ Then you have idiots who come by and knock over the caps like they do where I live so no one is allowed to go near them anymore. $\endgroup$
    – DKNguyen
    Commented Jul 26, 2020 at 19:55
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    $\begingroup$ @DKNguyen yeah if it can be done, it will be. Aided in an exhibit where there was a real whale heart on display. First day we found out that a group of teenagers were learning more than we thought. Namely the strength of a whale heart vs various objects like a ballpoint held like a knife in American Psycho. $\endgroup$
    – Trioxidane
    Commented Jul 26, 2020 at 20:11
  • $\begingroup$ provided the "mountain " is a mountain but just a single small rock outcrop. $\endgroup$
    – John
    Commented Jul 26, 2020 at 20:29
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Glaciers will do it, e.g. Preikestolen in Norway: https://en.wikipedia.org/wiki/Preikestolen and Mt. Thor in northern Canada: https://en.wikipedia.org/wiki/Mount_Thor A search for "overhanging mountains" will give many other examples. Also consider snow cornices.

Note that the droop in the OP's picture seems more like an effect of perspective...

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  • $\begingroup$ +1 for suggesting snow cornices — I was about to suggest that as a separate answer before I noticed you already mentioned it! $\endgroup$
    – bradrn
    Commented Jul 27, 2020 at 13:30

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