The brine microstructure of sea ice and its strong dependence on temperature govern key processes critical to the role of sea ice in climate and the polar marine ecosystems. The brine phase also largely determines electromagnetic behavior in sea ice remote sensing. It has long been suspected that the brine microstructure displays fractal characteristics, a self-similar geometry over varying scales. Here I present the first comprehensive, quantitative study of the fractal dimension of brine in sea ice and how it depends on temperature and porosity. Using X-ray tomography data from Arctic sea ice, for both columnar and granular ice, we employ three different methods of computing the fractal dimension. We find all data agreed closely with a simple theoretical curve relating fractal dimension to porosity, which holds for exactly self-similar porous media, such as the famous Sierpinski triangle, as well as statistically self-similar porous media, like sandstones. Furthermore, we discovered there exists an ordinary differential equation model which accurately represents the evolution of the fractal dimension and porosity of the sea ice data through changes in temperature. This ODE has also been shown to hold for the porosity and fractal evolution of exactly self-similar geometries, namely the Sierpinski triangle and the Apollonian gasket. These findings open the door to sea ice applications of widely used theoretical models and tools for predicting the fluid and electromagnetic transport properties of composites with fractal microstructure. We also explore the influence of the fractal geometry of the brine phase on how microbial life is organized in this multiscale porous habitat.