มิติ เศษส่วน

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Non integer dimension Wiki

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In mathematics, more specifically in fractal geometry,

a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern
(strictly speaking, a fractal pattern) changes with the scale at which it is measured.

It has also been characterized as a measure of the space-filling capacity of a pattern that
tells how a fractal scales differently from the space it is embedded in;
a fractal dimension does not have to be an integer.[1][2][3]

Wiki

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To explain the concept of fractal dimension, it is necessary to understand
what we mean by dimension in the first place.
Obviously, a line has dimension 1, a plane dimension 2, and a cube dimension 3.
But why is this? It is interesting to see students struggle to enunciate why
these facts are true.

They often say that a line has dimension 1 because there is
only 1 way to move on a line.
Similarly, the plane has dimension 2 because there are 2 directions in which to move.
Of course, there really are 2 directions in a line -- backward and forward --
and infinitely many in the plane.

What the students really are trying to say is there are
2 linearly independent directions in the plane.
Of course, they are right. But the notion of linear independence is quite sophisticated
and difficult to articulate.
Students often say that the plane is two-dimensional because it has two dimensions,
meaning length and width.

Another pitfall occurs when trying to determine the dimension of a curve in the plane
or in three-dimensional space.
An interesting debate occurs when a teacher suggests that these curves
are actually one-dimensional. But they have 2 or 3 dimensions, the students object.

https://math.bu.edu/DYSYS/chaos-game/node6.html