Mandelbrot wrote:
A fractal is a shape whose “Hausdorff dimension” is greater than its “topological dimension.”
In simple (and less precise) terms:
Fractals are shapes with a non-integer dimension.
Shapes that are rough, and that stay rough as you zoom in.
For a purely geometric shape to be a genuine fractal,
it has to keep looking rough, even as you zoom in infinitely far.
Please correct me if I'm wrong.
Do Fibonacci spirals qualify as fractals? If not, why?
How do you measure the Hausdorff dimension or 'roughness' of a spiral?
Best Answer
No, a Fibonacci spiral is not a fractal - it's a smooth curve and has dimension one
Here is a fractal spiral:
The distinction is that this set is self-similar - it consists of two copies of itself one blue copy, scaled by the factor 0.98, and one orange copy, scaled by the factor 0.08. The dimension can be computed using the theory of self-similar sets; it's approximately 1.4135.