With global warming becoming an ever-present danger, it is important that we work to reduce our carbon emissions. As such, hydrogen has been proposed as a green alternative to natural gas for energy conversion in gas turbines. Unlike natural gas, cleanly produced hydrogen is carbon neutral when burned, making it an eco-friendly option. However, due to its low molecular weight and high reactivity, hydrogen expresses some unique properties during combustion, such as unstable flame fronts that propagate in a fractal nature. These instabilities strongly modify the global properties of hydrogen flames, such as flame speed, that are relevant to engineering systems like gas turbines. Good models to predict the effects of these instabilities do not currently exist. Accurate simulations of hydrogen flames at small scales are possible with Direct Numerical Simulation (DNS) which solve the Navier-Stokes (NS) equations. However for full combustor scales this is computationally intractable. In this work, three-dimensional laminar and turbulent hydrogen flames at a small scale were simulated using DNS using the Pele Suite of Computational Fluid Dynamics (CFD) software. Python and C++ codes were created to analyze the data both by extracting joint probability density functions of thermochemical quantities and by generating one-dimensional paths along gradients of a progress variable representative of one-dimensional flames. These probability density functions and flame paths were compared to results of computationally affordable one-dimensional flame solutions with a particular emphasis on exploring the effects of curvature on flame properties. Through this research, a large amount of simulation data was generated which will be used with convolutional neural networks to try and develop an accurate and efficient model for hydrogen flames in future research.