2 and a bit dimensions

Dimensions in the context of fractals is defined as "pattern replication". That is not the same as what you're saying (extending dimensions in directions orthogonal to the previous dimensions).

>>8500884
you are naive. wait until you get to mouse picking and collision before you say 3d is just as easy as 2d.
and you are lucky the opengl guys already figured out projection matrices for us because that shit is fucking magic

>>8500988
I think fractal dimensions deserve a more in-depth analysis.
The fractal dimension does seem to justify the shape: a flat fractal will typically have between one and two dimensions, and 3D ones will typicall have between two and three.
There are 3D ones with less than two dimensions, but they seem to be very skinny; and if one thinks of dimensions as "how many directions you can move in" it makes sense that a skinny 3D fractal could have a dimensionality below 3.

And if fractal dimensions seem justified in their values, perhaps we don't have a proper way of understanding non-integer dimensions.

With calculating non-integer dimensions, it's based on the number of copies of an object needed for one a certain number of times the size, but I'd be interested in an answer to a question like "With a square-cube thing of 2.5 dimensions, how many copies would be needed to double the size and how would they be arranged"?

>>8501357
Keep in mind I was just saying this for OP to understand the implicit assumption he was making in his choice of word. Of course fractal dimensionality is not as simple as self-replication, but I have a hard time imagining implementing a new "direction" with fractals on computer graphics. What you're saying is still interesting, of course, but not necessarily what OP was looking for, I think.

>>8502017
It's still potentially applicable to computer graphics, there just needs to be more rigid maths surrounding non-integer dimensions.
It's possible to calculate the non-integer dimension of something, but it's not possible to do anything from a starting point of a specific non-integer dimension.
For example, there's squares and cubes and stuff for every integer dimension, but what is the 2.5 dimensional equivalent of a cube?
Until we can answer questions about specific non-integer dimensions rather than just say what the non-integer dimension of something is, it seems nonsensical to say anything about their applicability to an area.

>>8501145
Projection matrices are ezpz. Now hidden line detection and culling ARE actual magic.