#Godot 4D

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craggy bluff
runic sapphire
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This got me wondering
I know non integer bases such as base pi exist
Do non integer dimensions exist

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πD

craggy bluff
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But there are curved spaces, compactified dimensions, and non-space dimensions like time.

sharp spire
queen coyote
# runic sapphire This got me wondering I know non integer bases such as base pi exist Do non inte...

Ofc mathematicians have done this but not really in the way normal hyper-dimensional spaces work. I don't really understand it but I know it exists. To my understanding it's used to do some specific calculations with fractals or something
Anyway if you are good with maths then you can read up more on wiki: https://en.wikipedia.org/wiki/Hausdorff_dimension

Hausdorff dimension

In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape...

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To give a really basic view on how it works (again I don't really properly understand it so I may be wrong)
Essentially it works by mapping information across dimensions
Eg if you have 3 dimensions but only have 2 to store the information you could encode the 3rd dimension into another dimension, so dimesnion 1 could become x + z and dimension 2 could become x + y
In theory this has all the information of 3 dimensions in 2 dimensions as from the mathematical perspective numbers are infinite so there's always room to add more. In computers this reduces the maximum of a given dimension but often not an issue

Using the same principle you can encode the information in more complex ways to produce non integer dimensions
I still don't really understand why they do it, but they do 😛