Describing the hierarchical nature of filaments has been identified as one of the present challenges challenges in ISM studies. We present the first results of the Early ALMA Survey of the "Emergence of high-mass stars in complex fiber networks" (EMERGE) project. We combined large-scale, molecular line ALMA + IRAM30m observations of 7 target regions in Orion, including low- and high-mass star-forming clouds in different evolutionary stages, all homogeneously sampled at ~2000 AU resolution. Our analysis of their internal gas structure and kinematics identifies the presence of dense fibers in all these regions, only resolved at ALMA resolutions. Our results demonstrates how the presence of "filaments within filaments" is an intrinsic property of the gas fragmentation process in the ISM during the formation of filaments and cores.