Fractal geometry is one of the most fascinating theories about the real world. The concept that a simple pattern, applied to itself over and over, can produce shapes found in nature is simply amazing. This capacity to describe real things inspired me to include fractals in A Lifetime Waiting For Eternity.
How it is at small scale, it is at large scale
There are many examples where similar (or self- similar) behaviours are found at different scales. Take the example of the Romanesco Broccoli (picture above) with each bud composed of a series of smaller buds. Or look at the Nautilus shell, with a shape that resemble the microscopic marine snail and the cosmological Milky Way galaxy. This self-similarity found at different scales is one of the most attractive properties of fractals. Fractals look "roughly" the same on any scale. So I took this concept and, after playing around for a while, I applied it to Ely's multi-dimensional world.
A self-similar space
What if, what we call scales can be visualized as storeys of a building. The space where we live in would be made of layers or "storeys". A galactic scale is a "storey" many levels above our "storey" and the microscopic scale is a "storey" many levels below. In the same way we can get to a window of a building and look up or down to see different storeys, we can get a microscope and look down into small scales or get a telescope and look up at large scales (e.g. the universe).
The interesting thing about this conceptualisation of a self-similar world is that each scale represents a storey where living beings can move, interact, exist. However, in Ely's world, I needed also to make the characters actually "walk" down to smaller scales like we do when we walk down from a storey to a lower one using the stairs in a building. So, I used the analogy of a stair to create a dimension that is perpendicular to all other 10 dimensions of the M-theory, allowing Ely to move up and down across scales.
The additional dimension expands the stage where characters perform their actions. So far Ely's world is made of:
our well-known 3D space,
time as a volumetric dimension
scales as space "storeys"
And there are many other dimensions ready to be discovered ...