How does string theory relate to dimensions?

String theories require extra dimensions of spacetime for their mathematical consistency. In bosonic string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional.

What is a fractal relationship?

Fractal features means that the body has distinct dimensions for the geometry and the spectrum and at least one of them is a fractional number. This is quite a different behavior than that of a usual body. Traditionally, a uniform physical body has a single dimension for both, and it is an integer number.

What dimensions are fractals?

In fact, all fractals have dimensions that are fractions, not whole numbers. We can make some sense out of the dimension, by comparing it to the simple, whole number dimensions. If a line is 1-Dimensional, and a plane is 2-Dimensional, then a fractional dimension of 1.26 falls somewhere in between a line and a plane.

How are fractals related to chaos theory?

Fractals are infinitely complex patterns that are self-similar across different scales. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals.

Why does string theory require so many dimensions?

Any more dimensions would result in too much supersymmetry and a theoretical structure too simple to explain the complexity of the natural world. This is reminiscent of Joe Polchinski’s argument (somewhat tongue-in-cheek, somewhat serious) that all attempts to quantize gravity should eventually lead to string theory.

Are there fractional dimensions?

A point has dimension 0, a line has dimension 1, and a plane has dimension 2. For instance, a block of wood is 3-dimensional because you need three coordinates to specify any point inside. The standard Cantor set has fractional dimension!

How much is the highest dimension a fractal can have?

Their fractal dimensions can be anything from 1 to 3, including exactly 2. As soon as the dimension is greater than 1, by the above definition it’s a fractal. Smooth curves have Hausdorff dimension 1.