Beyond space and time: Fractals, hyperspace and more

We don't have any trouble coping with three dimensions – or four at a pinch. The 3D world of solid objects and limitless space is something we accept with scarcely a second thought. Time, the fourth dimension, gets a little trickier. But it's when we start to explore worlds that embody more – or indeed fewer – dimensions that things get really tough.
These exotic worlds might be daunting, but they matter. String theory, our best guess yet at a theory of everything, doesn't seem to work with fewer than 10 dimensions. Some strange and useful properties of solids, such as superconductivity, are best explained using theories in two, one or even no dimensions at all.
Prepare your mind for boggling as we explore the how, why and where of dimensions. [Click on the images...]

0D - On the dot
Surely, with no dimensions there's no room for anything,
so a 0D space must amount to nothing at all –mustn't it?

1D - Walk the line

Add one dimension, and physics starts to look a little familiar.

1.5D - Fractal landscapes

Welcome to the irregular landscapes between the familiar
worlds of one, two and three dimensions.

2D - Vistas of flatland

Physics in one dimension is too simple to be satisfying,
and three dimensions are complicated and messy.
Two-dimensional "flatland" is just right.

3D - We're here because we're here?

Flatland and multi-dimensional hyperspace make fine playgrounds for
the mind, but our bodies seem stuck in a space of three dimensions.

4D - Time, the great deceiver

Space consists of three dimensions.
Time, we are told, is also a dimension.
So how come it is so different to the others?

5D - Into the unseen

By adding a fifth dimension to space-time,
it is possible to show that gravity and electromagnetism
are two aspects of one and the same force.

6D - Two-timing

Whenever physicists invoke extra dimensions,
they always seem to mean the space kind.
Why can't we have more time?

8D - Surfer's paradise

Eight dimensions is a rarefied space that is home to the octonions,
"the crazy old uncle nobody lets out of the attic".

10D - String country

Ten dimensions, and we finally reach the fabled land of string theory.
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