Landform configurations in higher dimensions

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Landform configurations in higher dimensions

Postby Teragon » Sat May 07, 2016 6:56 pm

Considering possible landform configurations in 2D (= 1D to go) there are just four possibilities: (1-)Plain (P), (1-)hollow (H), (1-)top (T) and slope (S). More complex types of landform configuration in three and higher dimensions may be build just by combining them, one for each direction you can go. Slope is a bit different as it can always just occur in one direction. I'm leaving this one apart for simplicity and because it's just an attribute a plain can have.

I'm suggesting a systematic name for landform configurations in arbitrarily high dimensions (I like to go up to 6, because according to my experience it's typically up to here, where new, educative concepts emerge and where you often need to go to, if you want to generalize something to n dimensions). Depending on which 2D elements are present in one configuration, we can distinguish 7 types: Plains (P), valleys (P+H), hollows (H), saddles (H+T), tops (T), ridges (P+T) and the one thing three dimensions are just not enough for, valleyridges (P+H+T). The configurations may also be uniquely defined by the abbreviations in the brackets. The number of directions with the respective basic element are indicated by the number in front of the corresponding letter (the 1 is left apart). The number in front of P is the number of dimensions that configuration is extended in, the number in front of P gives you the dimensionality of the view downwards. All numbers together give the dimensionality of the space they live in minus one.

2D
1-Plain (P)
1-Hollow (H)
1-Top (T)

3D
Plain (2P)
Valley (P+H)
Ridge (P+T)
Hollow (2H)
Saddle (H+T)
Top (2T)

4D
3-Plain (3P)
Plainvalley (2P+H)
Plainridge (2P+T)
Hollowvalley (P+2H)
Valleyridge (P+H+T)
Topridge (P+2T)
3-Hollow (3H)
Hollowsaddle (2H+T)
Topsaddle (H+2T)
3-Top (3T)

5D
4-Plain (4P)
3-Plainvalley (3P+H)
3-Plainridge (3P+T)
Plainhollowvalley (2P+2H)
Plainvalleyridge (2P+H+T)
Plaintopridge (2P+2T)
3-Hollowvalley (P+3H)
Hollowvalleyridge (P+2H+T)
Valleyridgetop (P+H+2T)
3-Topridge (P+3T)
4-Hollow (4H)
3-Hollowsaddle (3H+T)
Hollowtopsaddle (2H+2T)
3-Topsaddle (H+3T)
4-Top (4T)


6D
5-Plain (5P)
4-Plainvalley (4P+H)
4-Plainridge (4P+T)
3-Plainhollowvalley (3P+2H)
3-Plainvalleyridge (3P+H+T)
3-Plaintopridge (3P+2T)
Plain-3-Hollowvalley (2P+3H)
Plainhollowvalleyridge (2P+2H+T)
Plainvalleyridgetop (2P+H+2T)
Plain-3-Topridge (2P+3T)
4-Hollowvalley (P+4H)
3-Hollowvalleyridge (P+3H+T)
2-Hollowvalleyridgetop (P+2H+2T)
Valleyridge-3-Top (P+H+3T)
Rigde-4-Top (P+4T)
5-Hollow (5H)
4-Hollowsaddle (4H+T)
3-Hollowtopsaddle (3H+2T)
Hollow-3-Topsaddle (2H+3T)
4-Topsaddle (H+4T)
5-Top (5T)
What is deep in our world is superficial in higher dimensions.
Teragon
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Re: Landform configurations in higher dimensions

Postby gonegahgah » Mon May 09, 2016 1:35 pm

Nice lists Teragon. Quite interesting to see the different possibilities afforded by the higher dimenions :)
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Re: Landform configurations in higher dimensions

Postby Mecejide » Wed Apr 03, 2019 5:03 am

I think “top” should be renamed to hill, because hill is already in use with the same meaning.
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