Wurman, [@nova04].[]{data-label="fig:tornado_fractal"}](tornadofractal.png){width="\textwidth"}

Fractals are mathematical objects useful as idealizations of structures and phenomena in which features and patterns repeat on progressively smaller and smaller scales [@mandelbrot83]. Such structures exhibit geometrical complexity that can be, in a simplified way, captured by a fractal dimension of the object, a number that describes how the fractal pattern changes with scale. For example, the fractal dimension of the well-known Koch snowflake shown in Figure \[fig:snowflake\] is $\log{4}/\log{3}\approx1.26186$, which indicates that the object has enough “turns” to not be a $1$-dimensional curve, but is far from filling up a planar region of dimension $2$. An early discussion of fractals in fluid mechanics can be found in [@turcotte88].

![Construction of the Koch snowflake starting from an equilateral triangle and showing the first four steps. The limiting fractal object is known as the Koch snowflake and it has a fractal dimension of $\log{4}/\log{3}\approx1.26186$.[]{data-label="fig:snowflake"}](KochFlake_2){width="\textwidth"}

Chorin discusses quantities with fractal dimensions in his study of turbulent flows [@chorin]. Through numerical experiments he finds fractal dimensions of the axes of vortices he studies to be related to the “temperature” of the vortex. “Hot” negative-temperature vortices have a smooth axis, while at temperatures of positive or negative infinity the vortex has 