Think about it. Zooming in on the center of a perfect spiral you will continue to see the same overall shape, which makes it a self-similar shape. But, as Wikipedia points out, not all self-similar shapes are fractals.

A fascinating example of self-similarity is a straight line. Divide a straight line into little pieces... you get mini straight lines. But apparently one of the requirements for a shape to be considered fractal is that it be difficult to mathematically describe using Euclidean Geometry - and obviously since the line is the building block of Euclidean Geometry that is the farthest thing from being true.

But what about a spiral. Googling "Is a spiral a fractal" largely got me nowhere, except for one person who answered 'no' because it is not "rough" enough. But I think a spiral is still quite difficult to mathematically describe - as in graph - using Euclidean Geometry...right? And isn't the Fibonacci Spiral tied in with Fractal Geometry? I think this person was thinking of the fractal dimension of something, which basically describes roughness or complexity.

Seriously though. Spirals are self similar and difficult to describe using Euclidean Geometry. Is that good enough? Can anyone speak with any authority on this? I would greatly appreciate it.

EDIT: /r/askmath has failed me.