Extensive Scaling from Computational Homology and Karhunen-Lo\`{e}ve decomposition: Analysis of Rayleigh-B\'{e}nard Convection Experiments

Spatiotemporally-chaotic dynamics in laboratory experiments on convection are characterized using a new dimension, $D_{\rm {CH}}$, determined from computational homology. Over a large range of system sizes, $D_{\rm{CH}}$ scales in the same manner as $D_{\rm{KLD}}$, a dimension determined from experimental data using Karhuenen-Loeve decomposition. Moreover, finite-size effects (the presence of boundaries in the experiment) lead to deviations from scaling that are similar for both $D_{\rm{CH}}$ and $D_{\rm{KLD}}$. In the absence of symmetry, $D_{\rm{CH}}$ can be determined more rapidly than $D_{\rm{KLD}}$.