The variety of DNA loops formed by a protein such as Lac Repressor (LacI), predicted to populate multiple loop topologies and geometries, increases the uncertainty of models that have not been experimentally verified. We created a method for evaluating the multitude of LacI-DNA looped states using FRET with fluorophore position variants (FPVs) on a landscape DNA constructs with dual operator phasing variants bracketing an intrinsically curved DNA sequence. The FRET signature for each FPV corresponds to a specific LacI-DNA loop topology, and when applied to the landscape of constructs we could systematically explore DNA sequence dependent LacI mediated DNA looping. The FRET efficiencies calculated for each FPV landscape revealed the first unambiguous detection of antiparallel (A1 and A2) and distributions among parallel loop (P1) and antiparallel loops. The FRET efficiency maximum of each FPV landscape was used to calculate the loop population distribution for each topology assuming a uniform population at the peaks. The differences in the observed peak FRET among FPV landscapes led to an unavoidable estimate of loop populations with an extended LacI-DNA loop geometry, and also slightly extended LacI-DNA loop in the cases of antiparallel loops. The addition of saturating inducer to the FPV landscape demonstrated that IPTG-LacI-DNA loops have different properties than uninduced loops: they have increased instability, increased competition among previously energetically unfavorable states, and presumably have increased switching between specific and nonspecific LacI-DNA interactions. This multivariate data set confirms that rod mechanics models of DNA looping should also consider protein flexibility, and also demonstrates the importance of protein flexibility in modeling genetic regulatory circuits that are similar to the "hydrogen atom of gene regulation", the lac operon.