Semi-dimensional shapes and other curves

I just discovered that shapes with half-integer dimensions have a simple square construction by subdividing by 4. An example is labelled the quadratic type 2 curve (or sometimes Minkowski sausage) with dimension 1.5. However this curve comes in a left and right handed form. Another example I made here:

It is also possible to build 2.5D surfaces, an example is here, however this surface intersects. It is possible to make a non-intersecting surface, which is approximately a 3D version of the above:

And here's a 1.5D curve in 3D space:

A 2.5D curve in 3D space is a bit more of a challenge

These ideas are explored in some more detail in my book Exploring Scale Symmetry, published by World Scientific.