In the standard model of cosmology, space and time are combined into a 4D space-time manifold consisting of three dimensions of space and one dimension of time. In this model, dimensions are restricted to being whole numbers such as 1D, 2D, 3D and 4D and all dimensions are said to be orthogonal to each other. The idea of a fractional dimension has no meaning in the 4D space-time manifold.
In a fractal Universe, which I affectionately refer to as an OMniverse, fractional dimensions are allowed. This new degree of freedom allows the OMniverse to continuously evolve, from the zeroth dimension of time to the first dimension of light to the second dimension of space through to the third dimension of matter, and so on. This is the reason that evolution always toward an increase in complexity. In the fractal paradigm, an increase in fractal dimension always corresponds to increase in the complexity of the fractal “curve”. This is especially noticable in the Mandelbrot Set where the event horizon “curve” continuously increases in complexity with each iteration.
“Time is the Zeroth dimension.” FractalWoman
This “dimensional evolution” is expressed in many ways in nature. The way a plant grows is a great example of this. The plant starts in the zeroth dimension (the seed). It then transitions into the first dimension (the branch) and then the second dimension (the leaf). Finally, it transitions into the third dimension (the flower). These are all fractal dimensions of course. The flower then feeds back to the zeroth dimension in the creation of the seed, thus closing the loop of creation.
Fractal dimensions are the rule and not the exception in a fractal OMniverse. In order to understand nature, we must first embrace the fractal paradigm.