Which visual displays do we aesthetically appreciate, and why? Order and complexity have often been suggested as important factors related to appreciation (Van Geert & Wagemans, 2020), but the multidimensional nature of both order and complexity has often been ignored. In a series of studies using diverse methods, we used the recently developed OCTA toolbox (Van Geert, Bossens, & Wagemans, 2023) to characterize the interrelations between multiple stimulus dimensions, perceived order and complexity, and aesthetic appreciation in multidimensional but parametrically controlled stimulus spaces. Using a 2AFC task, we investigated whether individuals’ preferred complexity levels for color, shape, and size depended on the level of order present in the display. Results indicated that not all types of complexity were appreciated similarly, and that complexity was more often preferred in highly ordered stimuli than in stimuli with a lower order level. In a rating task, we examined perceived order, complexity, pleasantness, and interest for a parametrically controlled set of 1611 stimuli varying systematically in various order and complexity dimensions. Results confirmed the differential relation of different types of appreciation to order and complexity, and clarified the extent to which different objective order and complexity manipulations influence perceived order and complexity. Using a recently developed efficient sampling method called Gibbs Sampling with People (GSP), we are now examining perceptual and aesthetic evaluations for multiple fine-grained, continuous parametric stimulus dimensions. The results of these GSP studies will allow us to characterize the interrelations between order, complexity, and appreciation as well as the consistency of these interrelations (a) across stimulus dimensions, (b) across parametrizations, and (c) across methodological techniques.